diff --git a/-NE4T4oBgHgl3EQf3w1M/content/2301.05308v1.pdf b/-NE4T4oBgHgl3EQf3w1M/content/2301.05308v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c42f67c890155687eb55ccc34ac5c5738f9b73fc --- /dev/null +++ b/-NE4T4oBgHgl3EQf3w1M/content/2301.05308v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cb15380bf1e3a1f8b4416919b9927e7bcb47ccc4dcb9bffe0be81d0de553810b +size 779413 diff --git a/-NE4T4oBgHgl3EQf3w1M/vector_store/index.faiss b/-NE4T4oBgHgl3EQf3w1M/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..128c35379d500220fc8f2650a2a3697960813f1b --- /dev/null +++ b/-NE4T4oBgHgl3EQf3w1M/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f4cf06bc7a7b29a8407541611429447a83bf44cc1a24c9b6a02750faf8545093 +size 5046317 diff --git a/-NE4T4oBgHgl3EQf3w1M/vector_store/index.pkl b/-NE4T4oBgHgl3EQf3w1M/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..e800f8cc567cd09e2b28a9c5a993e160cd6c584a --- /dev/null +++ b/-NE4T4oBgHgl3EQf3w1M/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c1b0b8b531133787518bb2e2a7ab8a9d041ae4994a35c9e1de01834d921c76ce +size 198552 diff --git a/-dE1T4oBgHgl3EQfUgPr/content/2301.03092v1.pdf b/-dE1T4oBgHgl3EQfUgPr/content/2301.03092v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6ebb3600083d1d3d147185f9026a8d55c3fedefb --- /dev/null +++ b/-dE1T4oBgHgl3EQfUgPr/content/2301.03092v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:963ff41fd0c03920ac247feda7e3de266016de0759e6387e397ed24092f0a1c1 +size 2498776 diff --git a/-dE1T4oBgHgl3EQfUgPr/vector_store/index.faiss b/-dE1T4oBgHgl3EQfUgPr/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..1ac40958a73dcfc485f3a48c5d4d2b541891d48a --- /dev/null +++ b/-dE1T4oBgHgl3EQfUgPr/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7025cfd42d584d682d8af5cc1bc49556918e3d3157010e9a7c7a21eaa300214e +size 3473453 diff --git a/.gitattributes b/.gitattributes index 69614094998de2e97e57c48ba5e94dbf998035f2..ab70b5fde5f7f14a61cbeef57ce90c411d2d3edd 100644 --- a/.gitattributes +++ b/.gitattributes @@ -8591,3 +8591,71 @@ HdE1T4oBgHgl3EQfXgSr/content/2301.03128v1.pdf filter=lfs diff=lfs merge=lfs -tex adFPT4oBgHgl3EQfvjWp/content/2301.13160v1.pdf filter=lfs diff=lfs merge=lfs -text UdE0T4oBgHgl3EQf2gJy/content/2301.02713v1.pdf filter=lfs diff=lfs merge=lfs -text T9AyT4oBgHgl3EQf8fpt/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +CtFJT4oBgHgl3EQfAiym/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +HdE1T4oBgHgl3EQfXgSr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +2dFAT4oBgHgl3EQfDhxB/content/2301.08416v1.pdf filter=lfs diff=lfs merge=lfs -text +ZtAzT4oBgHgl3EQfK_te/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +adFPT4oBgHgl3EQfvjWp/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +CtFJT4oBgHgl3EQfAiym/content/2301.11421v1.pdf filter=lfs diff=lfs merge=lfs -text +CNE3T4oBgHgl3EQfUQpw/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +PtAzT4oBgHgl3EQfWvyr/content/2301.01307v1.pdf filter=lfs diff=lfs merge=lfs -text +2dFAT4oBgHgl3EQfDhxB/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +m9AzT4oBgHgl3EQfqP2M/content/2301.01626v1.pdf filter=lfs diff=lfs merge=lfs -text +PNE0T4oBgHgl3EQf1AIP/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +hdAyT4oBgHgl3EQfkPgm/content/2301.00428v1.pdf filter=lfs diff=lfs merge=lfs -text +39AyT4oBgHgl3EQfo_il/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +wtFPT4oBgHgl3EQfPjQO/content/2301.13038v1.pdf filter=lfs diff=lfs merge=lfs -text +9dE4T4oBgHgl3EQfDQsU/content/2301.04867v1.pdf filter=lfs diff=lfs merge=lfs -text +-NE4T4oBgHgl3EQf3w1M/content/2301.05308v1.pdf filter=lfs diff=lfs merge=lfs -text +f9A0T4oBgHgl3EQfHv-A/content/2301.02065v1.pdf filter=lfs diff=lfs merge=lfs -text +lNE2T4oBgHgl3EQfIwaA/content/2301.03684v1.pdf filter=lfs diff=lfs merge=lfs -text +y9FLT4oBgHgl3EQfnS-e/content/2301.12127v1.pdf filter=lfs diff=lfs merge=lfs -text +v9E4T4oBgHgl3EQfXQwv/content/2301.05039v1.pdf filter=lfs diff=lfs merge=lfs -text +4dFIT4oBgHgl3EQf6yuB/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +-dE1T4oBgHgl3EQfUgPr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +WNFRT4oBgHgl3EQf9DhY/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +0dAyT4oBgHgl3EQfbfdc/content/2301.00263v1.pdf filter=lfs diff=lfs merge=lfs -text +6tAzT4oBgHgl3EQfgPwz/content/2301.01464v1.pdf filter=lfs diff=lfs merge=lfs -text +wtFPT4oBgHgl3EQfPjQO/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +R9E0T4oBgHgl3EQfUgAs/content/2301.02250v1.pdf filter=lfs diff=lfs merge=lfs -text +p9AzT4oBgHgl3EQfOvtl/content/2301.01171v1.pdf filter=lfs diff=lfs merge=lfs -text +rNFQT4oBgHgl3EQftzab/content/2301.13393v1.pdf filter=lfs diff=lfs merge=lfs -text +b9AzT4oBgHgl3EQf2_6M/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +PtAzT4oBgHgl3EQfWvyr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +hdE5T4oBgHgl3EQfFQ6l/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +0dAyT4oBgHgl3EQfbfdc/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +K9FAT4oBgHgl3EQfwR5T/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +ZtAzT4oBgHgl3EQfK_te/content/2301.01106v1.pdf filter=lfs diff=lfs merge=lfs -text +K9AzT4oBgHgl3EQfkP22/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +NdFOT4oBgHgl3EQf2jRR/content/2301.12942v1.pdf filter=lfs diff=lfs merge=lfs -text +fdA0T4oBgHgl3EQfHf_u/content/2301.02063v1.pdf filter=lfs diff=lfs merge=lfs -text +2tAzT4oBgHgl3EQffPw3/content/2301.01448v1.pdf filter=lfs diff=lfs merge=lfs -text +K9FAT4oBgHgl3EQfwR5T/content/2301.08680v1.pdf filter=lfs diff=lfs merge=lfs -text +1dAzT4oBgHgl3EQfRfuL/content/2301.01217v1.pdf filter=lfs diff=lfs merge=lfs -text +ndAyT4oBgHgl3EQf__rr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +fdA0T4oBgHgl3EQfHf_u/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +V9AzT4oBgHgl3EQfmP0G/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +1dAzT4oBgHgl3EQfRfuL/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +rNFQT4oBgHgl3EQftzab/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +AtE2T4oBgHgl3EQfRQeF/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +-dE1T4oBgHgl3EQfUgPr/content/2301.03092v1.pdf filter=lfs diff=lfs merge=lfs -text +b9AzT4oBgHgl3EQf2_6M/content/2301.01823v1.pdf filter=lfs diff=lfs merge=lfs -text +AtE2T4oBgHgl3EQfRQeF/content/2301.03779v1.pdf filter=lfs diff=lfs merge=lfs -text +MdE1T4oBgHgl3EQfZQR8/content/2301.03148v1.pdf filter=lfs diff=lfs merge=lfs -text +V9AzT4oBgHgl3EQfmP0G/content/2301.01558v1.pdf filter=lfs diff=lfs merge=lfs -text +BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf filter=lfs diff=lfs merge=lfs -text +nNAzT4oBgHgl3EQfN_vv/content/2301.01160v1.pdf filter=lfs diff=lfs merge=lfs -text +a9E4T4oBgHgl3EQfPAy5/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +-NE4T4oBgHgl3EQf3w1M/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +WdFIT4oBgHgl3EQfhytq/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +tNE1T4oBgHgl3EQfjgS9/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +p9AzT4oBgHgl3EQfOvtl/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +StE0T4oBgHgl3EQfUwAJ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +mtFLT4oBgHgl3EQffC-V/content/2301.12093v1.pdf filter=lfs diff=lfs merge=lfs -text +29E1T4oBgHgl3EQf5wUG/content/2301.03514v1.pdf filter=lfs diff=lfs merge=lfs -text +BNE1T4oBgHgl3EQfpQVQ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf filter=lfs diff=lfs merge=lfs -text +m9AzT4oBgHgl3EQfqP2M/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +CNE3T4oBgHgl3EQfUQpw/content/2301.04449v1.pdf filter=lfs diff=lfs merge=lfs -text +QNFJT4oBgHgl3EQfJSzf/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +a9AyT4oBgHgl3EQfiviR/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text diff --git a/0dAyT4oBgHgl3EQfbfdc/content/2301.00263v1.pdf b/0dAyT4oBgHgl3EQfbfdc/content/2301.00263v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2f284bdd8f8579af6515fb0b74f78c17b1d88799 --- /dev/null +++ b/0dAyT4oBgHgl3EQfbfdc/content/2301.00263v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:383d104b63d3c704f0d7a1730b5560ad914a6d87b986501fedfa9d25fa348190 +size 212710 diff --git a/0dAyT4oBgHgl3EQfbfdc/vector_store/index.faiss b/0dAyT4oBgHgl3EQfbfdc/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..78fdec2caafb329db5ba0729e25244852dd0f16f --- /dev/null +++ b/0dAyT4oBgHgl3EQfbfdc/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:886c731c1cd7d302dcf5a5f6f276cbb90134c04516ea93377d8cf5bd5af30fb5 +size 2818093 diff --git a/0dAyT4oBgHgl3EQfbfdc/vector_store/index.pkl b/0dAyT4oBgHgl3EQfbfdc/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..8bc1bc5bedc0ff0af2410dabcaa3f0dfa9fe93cb --- /dev/null +++ b/0dAyT4oBgHgl3EQfbfdc/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e3c8a04fe5dd497b18de5fba25ecb2361cfcb4708379b4f3c58ed77913246e4c +size 106120 diff --git a/19FAT4oBgHgl3EQfkR2N/content/tmp_files/2301.08610v1.pdf.txt b/19FAT4oBgHgl3EQfkR2N/content/tmp_files/2301.08610v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..7219d9542d2843afc7c419419aed07a32af26615 --- /dev/null +++ b/19FAT4oBgHgl3EQfkR2N/content/tmp_files/2301.08610v1.pdf.txt @@ -0,0 +1,1284 @@ +Platform for Probing Radiation Transport Properties of Hydrogen at Conditions +Found in the Deep Interiors of Red Dwarfs +J. Lütgert,1, 2, 3, ∗ M. Bethkenhagen,4 B. Bachmann,5 L. Divol,5 D. O. Gericke,6 S. H. Glenzer,7 +G. N. Hall,5 N. Izumi,5 S. F. Khan,5 O. L. Landen,5 S. A. MacLaren,5 L. Masse,5, 8 +R. Redmer,1 M. Schörner,1 M. O. Schölmerich,5 S. Schumacher,1 N. R. Shaffer,9 +C. E. Starrett,10 P. A. Sterne,5 C. Trosseille,5 T. Döppner,5 and D. Kraus1, 2, † +1Institut für Physik, Universität Rostock, Albert-Einstein-Str. 23, 18059 Rostock, Germany +2Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany +3Institute of Nuclear and Particle Physics, Technische Universität Dresden, 01069 Dresden, Germany +4École Normale Supérieure de Lyon, Université Lyon 1, +Laboratoire de Géologie de Lyon, CNRS UMR 5276, 69364 Lyon Cedex 07, France +5Lawrence Livermore National Laboratory, Livermore, CA 94550, USA +6Centre for Fusion, Space and Astrophysics, Department of Physics, +University of Warwick, Coventry CV4 7AL, United Kingdom +7SLAC National Accelerator Laboratory, Menlo Park, CA 94309, USA +8CEA-DAM, DIF, F-91297 Arpajon, France +9Laboratory for Laser Energetics, University of Rochester, +250 East River Road, Rochester, NY 14623, USA +10Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, USA +(Dated: January 23, 2023) +We describe an experimental concept at the National Ignition Facility for specifically tailored +spherical implosions to compress hydrogen to extreme densities (up to ∼ 800× solid density, +electron number density ne ∼ 4 × 1025 cm−3) at moderate temperatures (T ∼ 200 eV), i.e., to +conditions, which are relevant to the interiors of red dwarf stars. The dense plasma will be probed +by laser-generated x-ray radiation of different photon energy to determine the plasma opacity due +to collisional (free-free) absorption and Thomson scattering. The obtained results will benchmark +radiation transport models, which in the case for free-free absorption show strong deviations at +conditions relevant to red dwarfs. This very first experimental test of free-free opacity models at +these extreme states will help to constrain where inside those celestial objects energy transport is +dominated by radiation or convection. Moreover, our study will inform models for other important +processes in dense plasmas, which are based on electron-ion collisions, e.g., stopping of swift ions or +electron-ion temperature relaxation. +I. +INTRODUCTION +Red dwarfs (M dwarfs) are the lightest and coolest +main sequence stars and make up ∼ 70 % of all stars +in the Sun’s neighborhood. [1, 2] Prominent examples +are our nearest neighbor Proxima Centauri (0.12 M⊙) +or TRAPPIST-1 (0.089 M⊙), +which is only slightly +larger than Jupiter, but much more massive. +The +interiors of red dwarfs mainly consist of hydrogen- +helium mixtures, which are progressively shaped by +screening effects, ion-ion correlations, and degeneracy +as temperature decreases and density increases. [3] +These many-particle effects are challenging to model, in +particular, for calculations of radiation transport, which +plays a major role in modeling of sub-stellar objects and +stars. From the solar abundance problem, we know that +∼ 20 % changes in opacity have paramount impact on +our understanding of stellar interiors. [4, 5] Whether +energy can effectively be transported via radiation or, +if radiation is not sufficient, convection sets in, is a +∗ julian.luetgert@uni-rostock.de +† dominik.kraus@uni-rostock.de +property that is particularly influenced by stellar opacity. +In general, the physics of red dwarfs is poorly understood +in comparison with the hotter interior of the Sun, which +is much closer to the ideal plasma state. +Figure 1 shows simulated pressure-temperature profiles +of stars on the main sequence, demonstrating the extreme +plasma conditions present inside those celestial objects. +The curves were obtained using the MESA code for +stellar evolution [6–10] (see the appendix for details on +these simulations). +The inset illustrates the schematic +interiors of stars from the core (m/M = 0) to the +photosphere (m/M = 1) divided into radiative and +convective zones for stars with a solar composition of +elements. +Red dwarfs are characterized by masses +between 0.075 and 0.5 solar masses so that their typical +mass-temperature ratios overall place red dwarfs in a +regime, where convection dominates the outer regions. +Depending on the size of the individual object, a more or +less developed radiative core is present. +The smallest +red dwarfs (M +≲ +0.2 M⊙) are thought to be fully +convective. +In this case, the fusion reactions in the +core are permanently re-fueled by hydrogen from the +outer layers. Combined with the low fusion rates due to +the relatively low core temperatures, convection possibly +arXiv:2301.08610v1 [physics.plasm-ph] 20 Jan 2023 + +2 +FIG. 1. +Pressure-temperature profiles for various celestial +objects calculated using the MESA package. [6–10] Solid +lines denote convective regions while dots indicate a layer of +radiative energy transport. The gray shaded area shows the +conditions, which we intent to generate in our experiment. +Inset: Mass coordinate m/M along stellar interior profiles for +objects with solar composition divided into radiative (white, +dotted lines) and convective (gray, solid curves) regions over +total object mass M relative to the Sun’s mass M⊙. The gray- +scale dataset was published by Kippenhahn et al. [11] while +the colored lines show the MESA calculations of the main +figure. +allows some red dwarfs to last trillions of years until +all hydrogen fuel is exhausted. However, even a small +radiative core can strongly change this behavior and +its existence crucially depends on the effectiveness of +radiation transport in highly compressed matter. +Moreover, the internal structure of a star has a +major impact on the activity of its surface. [12] The +boundary between a radiative core and a convective +layer can lead to strong magnetic fields and a turbulent +atmosphere, [1, 13, 14] including radiative and plasma +outbursts that may threaten life on nearby planets. +Therefore, understanding the radiative properties of the +complex plasmas within a host star is crucial when +judging the possibility of an exoplanet to host life – +especially for red dwarfs where the habitable zone is +thought to be found relatively close to the star itself due +to the low surface temperature. [15] +For red dwarf stars, the thermodynamic conditions +at the boundary between radiative core and convective +envelope are estimated to be in a pressure regime of few +Gbars and temperatures of few million Kelvin. [1, 11] +Corresponding free electron densities are in the range of +few 1025 cm−3, which results in Fermi energies of similar +order as the thermal energy of the free electrons. The +energy transport in this so-called warm dense matter +regime [16] is extremely difficult to calculate, which gives +rise to significant uncertainties in modeling the energy +transport inside red dwarfs. +II. +THEORY +For stellar interiors, the radiative opacity κrad is +usually divided into three contributions: [17] +κrad = κbf + κff + κT , +(1) +where κbf is the opacity contribution by bound-free +absorption, κff denotes the free-free contribution and +κT = ZσT /mi the absorption due to Thomson scattering +from free electrons, which is solely dependent on the +Thomson scattering transport cross section σT , [18, 19] +the average ion charge state Z and the average ion mass +mi of the plasma. While Rayleigh scattering might be of +interest for the atmosphere of K and M class stars, [20] +the high ionization in hotter photospheres and deep +within even the smallest stars often justifies to neglect its +contribution to κrad. For the solar abundance problem, +the bound-free opacity of metals is probably most +relevant, but deep in the solar radiation zone as well as for +many red dwarfs, particularly those with low metallicity, +hydrogen free-free opacity, i.e., absorption due to inverse +bremsstrahlung, is the dominant absorption mechanism +of radiation. [17] For these red dwarfs, the absolute values +for free-free absorption determine where convection +or radiation will be the dominant energy transport +mechanism. +Figure 2 shows a density-temperature diagram of +dominating +absorption +mechanisms +thought +to +be +present for the composition of population I stars in +comparison with red dwarf interiors and the Sun. While +bound-free transitions dominate at low densities and +temperatures, free-free absorption starts to outrun the +bound-free opacity with the increase in density due to +increasing electron-ion collision rates as well as pressure +ionization of heavier elements. [21] At the highest +densities, conduction by degenerate electrons becomes +more efficient than radiation transport, whereas for low +densities and highest temperatures, photon scattering +from electrons (Thomson or Compton, depending on +photon energy) is most significant. +A. +Analytical models +A classical +treatment of +the spectral absorption +coefficient due to inverse bremsstrahlung, derived from +the description of electron-ion collisions in a weakly +coupled plasma environment, yields for the absorption +coefficient αff, [22] +αff(ν) = ρκff(ν) ∝ Z2neni +ν3√ +T +� +1 − exp +� +− hν +kBT +�� +gff(ν, T), +(2) + +.3 +FIG. 2. +Dominating opacities in different regimes of the +density-temperature diagram for a composition of elements as +in population I stars. [17] The colored lines show densities and +temperatures realized within main-sequence stars according +to the “MESA” stellar evolution code [6–10] with solid lines +representing convective layers. The proposed experiments will +probe conditions similar to the interiors of red dwarf stars +where free-free absorption is expected to dominate (indicated +by the shaded region). +where ν denotes the x-ray frequency, ρ is the mass +density, Z is the average degree of ionization, ne is +the free electron number density, ni is the ion number +density, T is the plasma temperature, h is Planck’s +constant, and kB is Boltzmann’s constant. +Additional +corrections due to quantum and correlation effects are +accounted for in a frequency-dependent correction factor +gff(ν, T), the so-called Gaunt factor. [23] For a weakly +coupled ideal plasma, the Gaunt factor can be interpreted +as the logarithm of the ratio of maximum impact +parameter bmax and minimum impact parameter bmin +in the corresponding electron-ion collision (the so-called +Coulomb logarithm [24]): +gff(ν, T) = +√ +3 +π ln +�bmax +bmin +� +. +(3) +This formalism is equivalent to the classical treatment +of several other important plasma effects that involve +Coulomb collisions of electrons and ions, e.g., stopping +power of ions or electron-ion temperature equilibration +in dense plasmas. [25] The maximum impact parameter +bmax is usually given by min(ve/2πν, λs) where ve is the +average velocity of the electrons, ν is the x-ray frequency, +and λs is the screening length due to the surrounding +plasma. On the other hand, bmin can be expressed as +max(b⊥, λth), where b⊥ = Ze2/(4πϵ0mev2 +e) is the impact +parameter for an electron being deflected perpendicular +to its direction of incidence and λth denotes the thermal +de Broglie wavelength of the electrons. +However, for conditions relevant to the interiors of +red dwarfs [e.g., ne ∼ few 1025 cm−3, Te ∼ few 100 eV +(Ref. [3])], we find ve/2πν +< +λth, i.e., a negative +Coulomb logarithm for x-ray frequencies larger than the +plasma frequency. Thus, this simple classical treatment +assuming a weakly coupled plasma is not appropriate +for +such +conditions. +Indeed, +more +sophisticated +approaches have been developed to accommodate these +conditions. [26, 27] +B. +Average Atom and Density Functional Theory +calculations +Figure 3 shows Average Atom calculations with a +Mean Force potential (AA-MF) [28] and state-of-the- +art Density Functional Theory Molecular Dynamics +(DFT-MD) simulations [29] compared to the analytical +model for the free-free opacity with constant Gaunt +factor and calculations by van Hoof et al. [30, 31] +The +first +two +simulation +methods +have +previously +been applied successfully for calculating the equation- +of-state +(EOS) +and +transport +properties +of +dense +plasmas. [28, 32–34] The DFT-MD simulations were +performed +with +up +to +256 +hydrogen +atoms +using +the program package VASP. [35–38] Our considered +density range spans 20 −150 g cm−3 at 100, 150, and +200 eV. The simulations use the Baldereschi mean value +point [39] and the Coulomb potential with an energy +cutoff of 10 000 eV. +Each DFT-MD point was run for +20 000 time steps with a time step size between 3 as +(attoseconds) and 8 as depending on the thermodynamic +conditions. +The temperature was controlled with +a Nosé-Hoover thermostat. [40] Subsequently, +10 – +20 snapshots were selected from each trajectory to +calculate the electrical conductivity and opacity applying +the +Kubo-Greenwood +formalism +[41, +42] +and +the +Kramers-Kronig relation. +For details on the AA- +MF calculations (which were performed for identical +temperatures +and +pressures), +we +refer +to +previous +publications. [28, 43–46] +While the DFT-MD simulation naturally includes +many-body effects in the description of wavefunctions +and the density of states due to the multiple ions included +in the simulation, the AA-MF approach, which is strictly +speaking also DFT-based, simplifies the calculation by +exclusively relying on the atom-in-jellium model. Either +of the two formulations calculates opacity from the real +part of the electrical conductivity. +Both approaches +agree on the quantity of extinction remarkably well, +supporting each other. +This result is particularly +noteworthy as the similarity of the AA-MF calculation +with DFT-MD – for the specific case of hydrogen – +is highly desired: +While DFT-MD is generally more +accurate, AA-MF is computationally significantly less +expensive and should be favored if benchmarks can +show good agreement between the two methods. +At +the same time, the consistency of the computed opacity +illustrates impressively that extreme states of matter +can be treated by DFT-MD nowadays with the increase + +:4 +FIG. 3. Opacity for a (25 %/75 %) HT mixture at an electron +density ne = 5 × 1025 cm−3 and a temperature of T += +100 eV (solid and dotted lines) or T += 150 eV (dashed), +respectively, according to different models. +The blue and +purple lines depict DFT-MD and AA-MF calculations. The +other solid curves show the analytical model for free-free +extinction [Eq. (2)] with a Gaunt factor equal to unity +(black line) or values calculated by van Hoof et al. [30, 31] +(red). For comparison, the opacity due to Thomson scattering +for a temperature of T = 100 eV is shown as the dotted +black line. +The AA-MF calculation at 150 eV and the +inset depicting the relative difference between the two results +[∆κAA = 2(κ150 eV +AA +− κ100 eV +AA +)/(κ150 eV +AA ++ κ100 eV +AA +)] show that +the temperature influence is very small for photon energies +above 3 keV due to the degenerate conditions. +in computational power and, hence, number of energy +bands included in the calculation. +Both methods show a discrepancy to the calculation +of the free-free opacity from the semi-classical formula +[Eq. (2)], as it can be seen in Fig. 3. +The simplest +approach of setting the Gaunt factor to unity reproduces +the classical result of Kramers. [22] Introducing quantum- +mechanical corrections, van Hoof et al. [30, 31] provide +easily applicable, tabulated values for gff by following +the seminal work of Karzas and Latter. [47] However, this +calculation is requiring more assumptions than the AA- +MF or the DFT-MD model, e.g., the velocity distribution +of the electrons (with is assumed to be Maxwellian) in +order to calculate thermally averaged free-free Gaunt +factors and from these opacities. [30, 31] Other authors +perform similar calculations but integrate over the Fermi +distribution of a degenerate electron gas. [24] +In fact, for dense plasma conditions comparable to +the interiors of main sequence stars, even advanced +calculations of the Gaunt factor vary by more than 50 % +for frequencies larger than the plasma frequency. [27] In +particular, the specific treatment of dynamic screening, +strong collisions, and re-normalization due to higher +moments can make a significant difference in comparison +to widely-used Born approximation treatments of the +Gaunt factor. [27] Deviations are particularly significant +in the photon energy regime from ∼ 500 eV to few keV, +which is the dominant contribution when calculating the +Rosseland mean opacity for the Sun and smaller stars. +Indeed, varying the opacity by 50 % can change the radii +of the boundaries between convection and radiation zone +by up to 10 %, which, given the underlying density and +temperature gradients, would significantly impact our +general understanding of stars. [5, 48] +III. +EXPERIMENTAL CONCEPT +Using the largest laser system in the world, namely, the +National Ignition Facility (NIF) at Lawrence Livermore +National Laboratory, [49] it is now possible to create +and probe matter states relevant to stellar interiors in +the laboratory. [50, 51] To address the questions raised +above, we have developed a concept to leverage NIF’s +unique capabilities to create relevant conditions and +obtain a very first test of free-free opacity models in +this very important plasma regime via x-ray absorption +measurements of highly compressed hydrogen during +the stagnation phase of layered capsule implosions. In +this way, not only the various existing models and +resulting tables for the Gaunt factor will be tested, but +also modern DFT-MD and AA-MF simulations, which +provide the absorption coefficient, can be benchmarked. +Finally, due to the equivalent physics involved (electron- +ion collisions in dense plasma environments [26]), our +results on free-free absorption will inform models for +swift ion stopping in warm dense matter as well as +corresponding electron-ion equilibration times. +A. +Experimental setup +A sketch of the experimental setup is shown in Fig. 4. +We will use 184 out of the 192 NIF laser beams to heat +a gold Hohlraum creating a quasi-thermal radiation field +that implodes a layered fuel capsule at the center of the +Hohlraum. +The capsule is comprised of a 57 µm thick +beryllium ablator shell, containing a 83 µm thick layer of +cryogenic solid hydrogen. +The temporally shaped radiation field created by the +laser drive will ablate the Be shell and, hence, accelerate +the payload inward. +Upon stagnation, a high density +hydrogen layer with ρ > 100 g cm−3 is formed while most +of the Be ablator has been ablated. +The +implosion +design +is +derived +from +inertial +confinement fusion (ICF) implosions at the NIF [54] +and applies a well-tested model that matched a variety +of spherical DT implosion experiments in NIF’s ICF + +5 +FIG. 4. Schematic of the experimental setup. Using NIF’s +laser beams, a nearly Planckian x-ray bath (see bottom right) +is created by heating a gold Hohlraum with a fuel capsule +at its center. Upon stagnation, the solid hydrogen layer is +compressed to mass densities larger than 100 g cm−3. +Two +Hohlraum windows allow for measuring the transmission of +high density hydrogen using x rays created in a stagnating +plasma inside the backlighter tube. Fielding NIF’s Crystal +Backlighter Imager [52] and the single line-of-sight (SLOS) +detector [53] enables us to acquire narrow bandwidth high- +resolution radiography images of the implosion. +program. [54, 55] In contrast to ICF implosions aiming for +high neutron yield,[56] the peak radiation temperature +of our Hohlraum drive (Trad = 170 eV) is significantly +reduced, deliberately slowing down the implosion to ∼ +200 km s−1 with the goal of creating extreme densities +(∼ 150 g cm−3) at moderate temperatures (∼ 200 eV) +while reducing x-ray and neutron-related background +signals near stagnation that would affect the radiography +measurement. These conditions are directly relevant to +the interiors of red dwarfs. +The dense plasma states will be probed by x-ray line +emission, which is created by the eight remaining NIF +beams that heat a backlighter tube. +We will perform +2D-imaging radiography of the implosion and stagnation +phase using two different photon energies by varying +the backlighter tube material. Vanadium will result in +5.2 keV line emission from 1s2p→1s2 (He-α) transitions +of helium-like ions. In the same way, helium-like cobalt +ions will produce 7.2 keV photons. +NIF’s Crystal Backlighter Imager (CBI) system [52] +will allow for high-resolution, nearly monochromatic +radiography images of the imploding and stagnating +sphere. A gated single-line-of-sight (SLOS) detector [53] +will provide four images per implosion with a time delay +of ∼ 100 ps between consecutive images. +From the +radiography images, we will infer radial profiles of the +opacity through Abel inversion [57, 58] and forward +fitting methods. +FIG. +5. +(a) +1D +radiation-hydrodynamics +simulations +performed using the HYDRA code, [59] showing the mass +density ρ at a given radius r and time t. +Our experiment +intends +to +probe +around +stagnation +when +the +highest +fuel compression is predicted. +Density, temperature, and +ionization profiles around this time (∼ 11.5 ns after the start +of the drive laser) are plotted in (b) and predict hydrogen +mass densities in excess of 150 g cm−3 in the HT mixture with +a molar mass of 2.5 g mol−1. +B. +Radiation hydrodynamic simulations +The reduced implosion velocity minimizes the hot +spot x-ray emission at stagnation to improve the signal- +to-noise ratio of the physics measurements. +For the +same reason, we use a (25 %/75 %) HT mixture (which +is hydrodynamically equivalent to 50 %/50 % DT) for +the ice layer to minimize the neutron yield and the +related background signals. +Tritium is required to +enable the hydrogen ice layer formation through beta +layering, where self-heating from beta decay leads to +a redistribution of HT ice with time. [60–62] Figure 5 +shows an overview of the ∼ 11 ns implosion trajectory +simulated with HYDRA-1D. [59] Compared to previous +ICF experiments with Be shells, [54] the ablator thickness +is reduced to 57 µm to decrease the remaining ablator +mass to near zero, which will maximize the radiography +contrast of the hydrogen layer. +Figure 5(b) illustrates +examples of radial density, ionization, and temperature +profiles predicted by hydrodynamic simulations. +The +high-density portion of the profiles consists of hydrogen +(HT) only. +Our simulations predict that the material +is compressed to mass densities exceeding 150 g cm−3, +which corresponds to electron densities of 3.6×1025 cm−3, + +6 +FIG. 6. Beryllium content of the capsule close to stagnation +as a function of time t and radius r. The dash-dotted dark +line shows the interface of ablator and fuel for a simulation +without mixing. The dashed lines depict contours of constant +density in the highly compressed HT. For the times we intend +to probe (around −0.4 ns to −0.2 ns), the Be is not predicted +to contaminate this dense part of the fuel. The values on the +abscissa are given relative to the time where the rebounding +shock wave coincides with the fuel-ablator interface. +at a temperature of ∼ 200 eV. These parameters result in +Fermi energies of ∼ 400 eV and, thus, ∼ 2× larger than +the thermal energies. Hence, we will probe degenerate +plasma conditions as expected in the interiors of red +dwarf stars. In addition, these conditions are expected +to limit the influence of temperature on the free-free +absorption, since the 1/ +√ +T term in the expression for +the inverse bremsstrahlung [Eq. (2)] can be replaced +approximately by 1/√TF , where TF denotes the Fermi +temperature. This behavior is supported by the results +from DFT-MD and the Average Atom Compared to +previous ICF experiments with Be shells, [54] the ablator +thickness is reduced to 57 µm to decrease the remaining +ablator mass to near zero, model, which indicates that +the opacity is more sensitive to the Fermi temperature +than the electronic temperature under dense degenerate +plasma conditions (see Fig. 3 and inset). +The weak +dependence on T is highly beneficial for the analysis and +interpretation of our data, as we can determine opacity +and from there infer density, while a direct measurement +of temperature would require additional diagnostics – for +example x-ray Thomson scattering. [63] +Reducing the ablator shell thickness and decreasing +the remaining mass at stagnation might come with +increased +risk +of +hydrodynamic +instability +at +the +ablator-ice interface and ablator material mixing into +the compressed ice layer. +For a more quantitative +estimate of mixing, we have performed 1D capsule-only +simulations using a buoyancy-drag mix model, [64] which +was successful in explaining experimental performance +observations of previous layered Be implosions. [54] In +addition, more recently the buoyancy-drag mix model has +been calibrated in a focused series of experiments using a +thin ice layer of varying thickness and detecting neutronic +signatures of deuterated plastic, originally located near +the inside of a plastic shell, mixing through the ice +layer into the hot spot. [65] Figure 6 shows the results +for our significantly slower implosion design in terms of +atomic Be fraction as function of radius and time. The +demarcation line between the Be ablator and the HT ice +is indicated as a dot-dashed line. We have labeled the +time of minimum radius of this interface by tmin, which +coincides with the time when the rebounding shock wave, +which leads to the formation of the high-compression +HT ice, passes this interface. +Our simulations clearly +show that Be does not mix into the high-compression +HT ice layer. The radiography measurements are aimed +to record transmission images between 400 and 200 ps +before tmin, which, hence, is not affected by Be mixing +into the high compression HT ice layer. +IV. +SIMULATED RADIOGRAPHY SIGNAL +Synthetic radiography images (see Fig. 7 and the +appendix for more details) show a clear limb feature at +the boundary of the central hydrogen and the beryllium +layer. Applying mass conservation, this feature will be +used as constraint for the density of the encapsulated +hydrogen at smaller radii as the total initial fuel mass can +be accurately characterized. Toward the outer edges of +the radiography field-of-view of 600×600 µm2, we expect +the plasma to become fully transmissive to the probe +radiation, which will be used to normalize the opacities +measured at smaller radii and obtain absolute values of +the radial absorption coefficient. +In the investigated density and temperature regime, +opacity due to Thomson scattering is expected to reach +similar values as free-free absorption. As absorption due +to Thomson scattering scales linearly with ne and free- +free opacity with n2 +e, this effect can become particularly +significant in the lower density regions of the imploded +capsule. +To disentangle both mechanisms, we will +perform the absorption measurements at two photon +energies (5.2 keV and 7.2 keV as described above). While +disagreeing in the actual magnitude, all but the classical +approach (gff = 1) presented in Fig. 3 find the same +proportionality of the free-free opacity with ∼ 1/(hν)(7/2) +for high photon energies hν. Classically, the Thomson +cross-section is in fist order independent of probing +frequency and temperature, which would allow us to +separate the two contributions to the signal. While this +assumption might give a reasonable first estimate, our +AA-MF simulations (see Fig. 3) indicate in accordance +with previous calculations by Boercker [18] that this +description as a constant is not applicable at the extreme +conditions we intend to probe. +However, models of +the Thomson scattering have to provide only the ratio +between the cross-section at the two backlighter energies + +7 +FIG. 7. +(a) Simulated detector image including free-free +(AA-MF calculations) and bound-free [66] absorption as well +as Thomson scattering [18] for 5.2 keV (top) and 7.2 keV +(bottom) backlighter energy. +The colorbar indicates the +expected number of photons per pixel. +Albeit the limited +temporal and spatial resolution of the detector, the interface +between the HT mixture and the beryllium ablator is +predicted to be visible at least for the lower energy. +(c) +Absorption coefficient profiles and (b) integrated total capsule +transmission T for a 5.2 keV backlighter close to the time +where the highest density in the hydrogen is reached. As the +lower figure shows, different models for the free-free opacity +result in notable changes of the total transmission. +All +presented plots assume a perfectly symmetrical implosion, no +mixing between fuel and ablator and a beryllium layer without +impurities. +to enable us to differentiate the former from inverse +bremsstrahlung. +Regardless of the model applied, the +Thomson scattering’s contribution to the overall opacity +might also be used as an additional density constraint +next to measuring the ablator-hydrogen interface and +applying mass conservation. +Further constraints on the implosion parameters will +be deduced from measuring multiple absorption images +at different times during the implosion in one shot. The +stagnation phase is usually well modeled by a self-similar +description of the conservation laws, [67] which only +allows certain shapes and time evolutions of the density +profiles. +V. +CONCLUSIONS +In summary, we presented a concept to leverage +NIF’s unique capabilities to investigate the deep interiors +of red dwarf stars in the laboratory and shed light +on their internal energy transports mechanisms. +The +proposed experiment has been accepted within NIF’s +Discovery Science Program for upcoming shot days in +2022 and 2023. +The resulting measurement of free- +free absorption and opacity will provide a benchmark +for numerical and analytical approaches, which will in +turn yield an improved description of the Gaunt factor. +Finally, interior structure models for massive hydrogen- +rich astrophysical objects, such as red dwarfs, can be +revisited on the basis of the new opacity constraint. +ACKNOWLEDGMENTS +M.B. +was +supported +by +the +European +Horizon +2020 programme within the Marie Skłodowska-Curie +actions (xICE grant number 894725). +J.L. and D.K. +acknowledge support by the Helmholtz Association +under VH-NG-1141 and by GSI Helmholtzzentrum +für Schwerionenforschung, Darmstadt as part of the +R&D project SI-URDK2224 with the University of +Rostock. +The work of S.S. and D.K. was supported +by Deutsche Forschungsgemeinschaft (DFG – German +Research Foundation) project no. 495324226. The work +of B.B., L.D., G.N.H., S.F.K., N.I., O.L.L., S.A.M, +L.M., M.O.S., P.A.S. and T.D. was performed under the +auspices of the DOE by Lawrence Livermore National +Laboratory under Contract No. DE-AC52-07NA27344. +R.R. and M.S. acknowledge support from the DFG via +the Research Unit FOR 2440. The DFT-MD calculations +were performed at the North-German Supercomputing +Alliance (HLRN) facilities and at the IT- and Media +Center of the University of Rostock. +AUTHOR DECLARATIONS +Conflict of interest +The authors have no conflicts of interest. + +8 +DATA AVAILABILITY +The data that support the findings of this study +are available from the corresponding authors upon +reasonable request. +Appendix A: MESA Simulations +Profiles of temperature, density, and pressure inside +stars with various masses were calculated using the +“Modules for Experiments in Stellar Astrophysics” code +(MESA, release r15140). [6–10] We used the default +MESA equation-of-state (EOS) which is a blend of +the OPAL, [68] SCVH, [69] FreeEOS, [70] HELM, [71] +and PC [72] EOSes. +Radiative opacities are primarily +from OPAL, [73, 74] with low-temperature data from +Ferguson et al. [75] and the high-temperature, Compton- +scattering dominated regime by Buchler and Yueh. [76] +Electron conduction opacities are from Cassisi et al.. [77] +Nuclear reaction rates are from JINA REACLIB [78] +plus additional tabulated weak reaction rates. [79–81] +Screening is included via the prescription of Chugunov +et al.. [82] Thermal neutrino loss rates are from Itoh et +al.. [83] +A pre-main-sequence model has been calculated from +initial parameters of helium mass fraction Yi = 0.2744, +metallicity Zi += 1 − Xi − Yi += 0.01913 (with Xi +being the initial mass fraction of hydrogen), mixing +length parameter αMLT = 1.9179, and including element +diffusion, which has been found to reproduce the solar +model well. [6] The ratio of elements heavier than helium +was taken from Grevesse and Sauval. [84] The time span +of the simulation was chosen so that the star spent a +considerable amount of time on the main sequence. For +stars smaller than the Sun, 10 times the age of the star +when the main sequence was entered has been chosen; +masses M > M⊙ were evolved until tnuc/2 was reached, +were tnuc = (M/M⊙)−2.9 ×1010 a is an approximation for +the lifetime of star on the main sequence. [85] +The decision whether regions of a star were considered +convective or radiative was based on the Schwarzschild +criterion. +Appendix B: Comparing radiative and conductive +opacities +The relation between thermal conductivity through +photon transport (radiation) λrad and the opacity κrad +is given by +λrad = 4acT 3 +3ρκrad +(B1) +where T is the temperature, ρ is the density, a = 7.5657× +10−16 Jm−3K−4 is the radiation density constant, and c is +the speed of light. [17, 85] Eq. (B1) can be used to define +a conductive opacity κc from the thermal conductivity +due to electrons λc by analogy. +This quantity – as +calculated by Hayashi et al. +who reproduce the work +of Mestel [86] and Lee [87] – has been plotted in Fig. 2 +to compare it with radiative opacities. +As +the +two +contributions +to +the +full +thermal +conductivity are additive, the total opacity κtot is given +by 1/κtot = 1/κrad + 1/κc, i.e., in order for κc being the +dominant contribution to the total opacity (see the high +density and low temperature corner of Fig. 2), the former +quantity has to be small compared to κrad. [85] +Appendix C: Radiography predictions +In order to generate the transmission profiles [see +Fig. 7 (b)] from extinction coefficient line-outs [Fig. 7 (c)], +we assumed a perfect, spherically symmetric implosion +and a uniform and monochromatic backlighter emitting +parallel x rays. We calculated +Tν = exp +� +− +� +dxκν(x)ρ(x) +� +(C1) +where the integral runs over the path of the light +and might, therefore, probe different temperature and +density conditions. To account for the limited temporal +resolution of the detector, a series of one-dimensional +transmission profiles at different times was convolved +with a Gaussian gate-function (35 ps FWHM). The +resulting line-out has been rotated, +and a spatial +blur in the form of a two-dimensional Gaussian with +10 µm FWHM in both directions was applied before +the transmission has been multiplied with the expected +backlighter photon flux (240 µm−2 ps−1 (Eph = 5.2 keV) +or 288 µm−2 ps−1 (Eph += +7.2 keV) at the target’s +position), corrected for attenuators shielding various +components and re-binned to the pixel-size of the +detector. +In a last step, noise proportional to the +individual pixels’ intensity has been applied to the data. +[1] I. N. Reid and S. L. Hawley, New Light on Dark Stars +(Springer Berlin-Heidelberg, 2005). +[2] M. J. Heath, L. R. Doyle, M. M. Joshi, +and R. M. +Haberle, Origins of Life and Evolution of the Biosphere + +9 +29, 405 (1999). +[3] D. E. Osterbrock, Astrophysical Journal 118, 529 (1953). +[4] J. E. Bailey, T. Nagayama, G. P. Loisel, G. A. Rochau, +C. Blancard, J. Colgan, P. Cosse, G. Faussurier, C. J. +Fontes, F. Gilleron, I. Golovkin, S. B. Hansen, C. A. +Iglesias, D. P. Kilcrease, J. J. MacFarlane, R. C. Mancini, +S. N. Nahar, C. Orban, J. C. Pain, A. K. Pradhan, +M. Sherrill, and B. G. Wilson, Nature 517, 56 (2015). +[5] N. Vinyoles, A. M. Serenelli, F. L. Villante, S. Basu, +J. Bergström, +M. C. Gonzalez-Garcia, +M. Maltoni, +C. Peña Garay, and N. Song, Astrophysical Journal 835, +202 (2017). +[6] B. Paxton, L. Bildsten, A. Dotter, F. Herwig, P. Lesaffre, +and F. Timmes, ApJS 192, 3 (2011). +[7] B. Paxton, M. Cantiello, P. Arras, L. Bildsten, E. F. +Brown, A. Dotter, C. Mankovich, M. H. Montgomery, +D. Stello, F. X. Timmes, and R. Townsend, ApJS 208, +4 (2013). +[8] B. Paxton, P. Marchant, J. Schwab, E. B. Bauer, +L. Bildsten, M. Cantiello, L. Dessart, R. Farmer, H. Hu, +N. Langer, R. H. D. Townsend, D. M. Townsley, +and +F. X. Timmes, ApJS 220, 15 (2015). +[9] B. Paxton, +J. Schwab, +E. B. Bauer, +L. Bildsten, +S. Blinnikov, P. Duffell, R. Farmer, J. A. Goldberg, +P. Marchant, E. Sorokina, A. Thoul, R. H. D. Townsend, +and F. X. Timmes, ApJS 234, 34 (2018). +[10] B. +Paxton, +R. +Smolec, +J. +Schwab, +A. +Gautschy, +L. Bildsten, M. Cantiello, A. Dotter, R. Farmer, J. A. +Goldberg, A. S. Jermyn, S. M. Kanbur, P. Marchant, +A. Thoul, R. H. D. Townsend, W. M. Wolf, M. Zhang, +and F. X. Timmes, ApJS 243, 10 (2019). +[11] R. Kippenhahn, A. Weigert, +and A. Weiss, Stellar +Structure +and +Evolution +(Springer +Berlin-Heidelber, +2012). +[12] H. W. Babcock, The Astrophysical Journal 133, 572 +(1961). +[13] E. N. Parker, The Astrophysical Journal 198, 205 (1975). +[14] M. Route, The Astrophysical Journal 830, L27 (2016). +[15] R. O. P. Loyd, E. L. Shkolnik, A. C. Schneider, T. S. +Barman, V. S. Meadows, I. Pagano, +and S. Peacock, +The Astrophysical Journal 867, 70 (2018). +[16] F. +Graziani, +M. +P. +Desjarlais, +R. +Redmer, +and +S. B. Trickey, eds., Frontiers and Challenges in Warm +Dense Matter (Springer Cham, Heidelberg, New York, +Dordrecht, London, 2014). +[17] C. Hayashi, R. Hoshi, +and D. Sugimoto, Progress of +Theoretical Physics Supplements 22, 1 (1962). +[18] D. B. Boercker, The Astrophysical Journal 316, L95 +(1987). +[19] W. D. Watson, The Astrophysical Journal 158, 303 +(1969). +[20] I. Hubeny and D. Mihalas, Theory of stellar atmospheres: +An introduction to astrophysical non-equilibrium quanti- +tative spectroscopic analysis (Princeton University Press, +2014). +[21] D. D. Clayton, Principles of Stellar Evolution and +Nucleosynthesis +(The +University +of +Chicago +Press, +Chicago and London, 1983). +[22] H. A. Kramers, Philosophical Magazine 46, 836 (1923). +[23] J. A. Gaunt, Philosophical Transactions of the Royal +Society A 229, 163 (1930). +[24] J. Meyer-ter Vehn and R. Ramis, Physics of Plasmas 26, +113301 (2019). +[25] D. O. Gericke, M. S. Murillo, and M. Schlanges, Physical +Review E 65, 036418 (2002). +[26] A. Grinenko and D. O. Gericke, Physical Review Letters +103, 065005 (2009). +[27] A. Wierling, T. Millat, G. Röpke, +and R. Redmer, +Physics of Plasmas 8, 3810 (2001). +[28] C. E. Starrett, High Energy Density Physics 25, 8 (2017). +[29] M. +Bethkenhagen, +B. +B. +L. +Witte, +M. +Schörner, +G. Röpke, T. Döppner, D. Kraus, S. H. Glenzer, P. A. +Sterne, +and R. Redmer, Physical Review Research 2, +023260 (2020). +[30] P. A. M. van Hoof, +R. J. R. Williams, +K. Volk, +M. Chatzikos, G. J. Ferland, M. Lykins, R. L. Porter, +and Y. Wang, Monthly Notices of the Royal Astronomical +Society 444, 420 (2014). +[31] P. A. M. van Hoof, G. J. Ferland, R. J. R. Williams, +K. Volk, M. Chatzikos, M. Lykins, +and R. L. Porter, +Monthly Notices of the Royal Astronomical Society 449, +2112 (2015). +[32] A. Becker, W. Lorenzen, J. J. Fortney, N. Nettelmann, +M. Schöttler, +and R. Redmer, Astrophysical Journal +Supplement Series 215, 21 (2014). +[33] A. Becker, M. Bethkenhagen, C. Kellermann, J. Wicht, +and R. Redmer, Astron. J. 156, 149 (2018). +[34] B. Holst, M. French, and R. Redmer, Phys. Rev. B 83, +235120 (2011). +[35] G. Kresse and J. Hafner, Physical Review B 47, 558 +(1993). +[36] G. Kresse and J. Hafner, Physical Review B 49, 14251 +(1994). +[37] G. Kresse and J. Furthmüller, Computational Materials +Science 6, 15 (1996). +[38] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 +(1996). +[39] A. Baldereschi, Physical Review B 7, 5212 (1973). +[40] S. Nosé, J. Chem. Phys. 81, 511 (1984). +[41] R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957). +[42] D. A. Greenwood, Proc. Phys. Soc. 71, 585 (1958). +[43] C. E. Starrett and D. Saumon, Physical Review E 87, +013104 (2013). +[44] C. E. Starrett, J. Daligault, +and D. Saumon, Physical +Review E 91, 013104 (2015). +[45] C. E. Starrett and D. Saumon, Physical Review E 93, +063206 (2016). +[46] N. Shaffer, N. Ferris, J. Colgan, D. Kilcrease, +and +C. Starrett, High Energy Density Physics 23, 31 (2017). +[47] W. J. Karzas and R. Latter, The Astrophysical Journal +Supplement Series 6, 167 (1961). +[48] A. M. Serenelli, W. C. Haxton, +and C. Peña Garay, +Astrophysical Journal 743, 24 (2011). +[49] E. I. Moses, R. N. Boyd, B. A. Remington, C. J. Keane, +and R. Al-Ayat, Physics of Plasmas 16, 041006 (2009). +[50] A. L. Kritcher, D. C. Swift, T. Döppner, B. Bachmann, +L. X. Benedict, G. W. Collins, J. L. DuBois, F. Elsner, +G. Fontaine, J. A. Gaffney, S. Hamel, A. Lazicki, W. R. +Johnson, N. Kostinski, D. Kraus, M. J. MacDonald, +B. Maddox, M. E. Martin, P. Neumayer, A. Nikroo, +J. Nilsen, B. A. Remington, D. Saumon, P. A. Sterne, +W. Sweet, A. A. Correa, H. D. Whitley, R. W. Falcone, +and S. H. Glenzer, Nature 584, 51 (2020). +[51] D. Kraus, T. Döppner, A. L. Kritcher, A. Yi, K. Boehm, +B. Bachmann, L. Divol, L. B. Fletcher, S. H. Glenzer, +O. L. Landen, N. Masters, A. M. Saunders, C. Weber, +R. W. Falcone, +and P. Neumayer, J. Phys. Conf. Ser. + +10 +717, 012067 (2016). +[52] G. N. Hall, C. M. Krauland, M. S. Schollmeier, G. E. +Kemp, J. G. Buscho, R. Hibbard, N. Thompson, E. R. +Casco, M. J. Ayers, S. L. Ayers, N. B. Meezan, L. F. B. +Hopkins, R. Nora, B. A. Hammel, L. Masse, J. E. Field, +D. K. Bradley, P. Bell, O. L. Landen, J. D. Kilkenny, +D. Mariscal, J. Park, T. J. McCarville, R. Lowe-Webb, +D. Kalantar, T. Kohut, +and K. Piston, Review of +Scientific Instruments 90, 013702 (2019). +[53] K. Engelhorn, T. J. Hilsabeck, J. Kilkenny, D. Morris, +T. M. Chung, A. Dymoke-Bradshaw, J. D. Hares, P. Bell, +D. Bradley, A. C. Carpenter, M. Dayton, S. R. Nagel, +L. Claus, J. Porter, G. Rochau, M. Sanchez, S. Ivancic, +C. Sorce, +and W. Theobald, Review of Scientific +Instruments 89, 10g123 (2018). +[54] A. B. Zylstra, +S. MacLaren, +S. A. Yi, +J. Kline, +D. Callahan, O. Hurricane, B. Bachmann, G. Kyrala, +L. Masse, P. Patel, J. E. Ralph, J. Salmonson, P. Volegov, +and C. Wilde, Physics of Plasmas 26, 052707 (2019). +[55] A. L. Kritcher, D. Clark, S. Haan, S. A. Yi, A. B. Zylstra, +D. A. Callahan, D. E. Hinkel, L. F. Berzak Hopkins, O. A. +Hurricane, O. L. Landen, S. A. MacLaren, N. B. Meezan, +P. K. Patel, J. Ralph, C. A. Thomas, R. Town, and M. J. +Edwards, Phys. Plasmas 25, 056309 (2018). +[56] A. B. Zylstra, O. A. Hurricane, D. A. Callahan, A. L. +Kritcher, +J. E. Ralph, +H. F. Robey, +J. S. Ross, +C. V. Young, K. L. Baker, D. T. Casey, T. Döppner, +L. Divol, M. Hohenberger, S. Le Pape, A. Pak, P. K. +Patel, R. Tommasini, S. J. Ali, P. A. Amendt, L. J. +Atherton, B. Bachmann, D. Bailey, L. R. Benedetti, +L. Berzak Hopkins, R. Betti, S. D. Bhandarkar, J. Biener, +R. M. Bionta, +N. W. Birge, +E. J. Bond, +D. K. +Bradley, +T. Braun, +T. M. Briggs, +M. W. Bruhn, +P. M. Celliers, +B. Chang, +T. Chapman, +H. Chen, +C. Choate, A. R. Christopherson, D. S. Clark, J. W. +Crippen, E. L. Dewald, T. R. Dittrich, M. J. Edwards, +W. A. Farmer, J. E. Field, D. Fittinghoff, J. Frenje, +J. Gaffney, M. Gatu Johnson, S. H. Glenzer, G. P. +Grim, S. Haan, K. D. Hahn, G. N. Hall, B. A. Hammel, +J. Harte, E. Hartouni, J. E. Heebner, V. J. Hernandez, +H. Herrmann, M. C. Herrmann, D. E. Hinkel, D. D. +Ho, J. P. Holder, W. W. Hsing, H. Huang, K. D. +Humbird, N. Izumi, L. C. Jarrott, J. Jeet, O. Jones, G. D. +Kerbel, S. M. Kerr, S. F. Khan, J. Kilkenny, Y. Kim, +H. Geppert Kleinrath, V. Geppert Kleinrath, C. Kong, +J. M. Koning, J. J. Kroll, M. K. G. Kruse, B. Kustowski, +O. L. Landen, S. Langer, D. Larson, N. C. Lemos, +J. D. Lindl, T. Ma, M. J. MacDonald, B. J. MacGowan, +A. J. Mackinnon, S. A. MacLaren, A. G. MacPhee, +M. M. Marinak, D. A. Mariscal, E. V. Marley, L. Masse, +K. Meaney, N. B. Meezan, P. A. Michel, M. Millot, J. L. +Milovich, J. D. Moody, A. S. Moore, J. W. Morton, +T. Murphy, K. Newman, J.-M. G. Di Nicola, A. Nikroo, +R. Nora, M. V. Patel, L. J. Pelz, J. L. Peterson, Y. Ping, +B. B. Pollock, M. Ratledge, N. G. Rice, H. Rinderknecht, +M. Rosen, M. S. Rubery, J. D. Salmonson, J. Sater, +S. Schiaffino, D. J. Schlossberg, M. B. Schneider, C. R. +Schroeder, H. A. Scott, S. M. Sepke, K. Sequoia, M. W. +Sherlock, S. Shin, V. A. Smalyuk, B. K. Spears, P. T. +Springer, M. Stadermann, S. Stoupin, D. J. Strozzi, L. J. +Suter, C. A. Thomas, R. P. J. Town, E. R. Tubman, +C. Trosseille, P. L. Volegov, C. R. Weber, K. Widmann, +C. Wild, C. H. Wilde, B. M. Van Wonterghem, D. T. +Woods, B. N. Woodworth, M. Yamaguchi, S. T. Yang, +and G. B. Zimmerman, Nature 601, 542 (2022). +[57] K. Hanson, Lect. Notes in Pure and Appl. Math. 115, +363 (1989). +[58] M. Howard, M. Fowler, A. Luttman, S. E. Mitchell, and +M. C. Hock, SIAM Journal on Scientific Computing 38, +B396 (2016). +[59] M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, +D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, +Physics of Plasmas 8, 2275 (2001). +[60] S. H. Glenzer, +D. A. Callahan, +A. J. MacKinnon, +J. L. Kline, G. Grim, E. T. Alger, R. L. Berger, +L. +A. +Bernstein, +R. +Betti, +D. +L. +Bleuel, +T. +R. +Boehly, +D. K. Bradley, +S. C. Burkhart, +R. Burr, +J. A. Caggiano, C. Castro, D. T. Casey, C. Choate, +D. S. Clark, P. Celliers, C. J. Cerjan, G. W. Collins, +E. L. Dewald, P. DiNicola, J. M. DiNicola, L. Divol, +S. Dixit, T. Döppner, R. Dylla-Spears, E. Dzenitis, +M. Eckart, G. Erbert, D. Farley, J. Fair, D. Fittinghoff, +M. Frank, L. J. A. Frenje, S. Friedrich, D. T. Casey, +M. Gatu Johnson, C. Gibson, E. Giraldez, V. Glebov, +S. Glenn, N. Guler, S. W. Haan, B. J. Haid, B. A. +Hammel, A. V. Hamza, C. A. Haynam, G. M. Heestand, +M. Hermann, H. W. Hermann, D. G. Hicks, D. E. Hinkel, +J. P. Holder, D. M. Holunda, J. B. Horner, W. W. +Hsing, H. Huang, N. Izumi, M. Jackson, O. S. Jones, +D. H. Kalantar, R. Kauffman, J. D. Kilkenny, R. K. +Kirkwood, J. Klingmann, T. Kohut, J. P. Knauer, J. A. +Koch, B. Kozioziemki, G. A. Kyrala, A. L. Kritcher, +J. Kroll, K. La Fortune, L. Lagin, O. L. Landen, D. W. +Larson, D. LaTray, R. J. Leeper, S. Le Pape, J. D. Lindl, +R. Lowe-Webb, T. Ma, J. McNaney, A. G. MacPhee, +T. N. Malsbury, E. Mapoles, C. D. Marshall, N. B. +Meezan, F. Merrill, P. Michel, J. D. Moody, A. S. +Moore, M. Moran, K. A. Moreno, D. H. Munro, B. R. +Nathan, A. Nikroo, R. E. Olson, C. D. Orth, A. E. +Pak, P. K. Patel, T. Parham, R. Petrasso, J. E. Ralph, +H. Rinderknecht, S. P. Regan, H. F. Robey, J. S. Ross, +M. D. Rosen, R. Sacks, J. D. Salmonson, R. Saunders, +J. Sater, C. Sangster, M. B. Schneider, F. H. Séguin, +M. J. Shaw, B. K. Spears, P. T. Springer, W. Stoeffl, +L. J. Suter, C. A. Thomas, R. Tommasini, R. P. J. Town, +C. Walters, S. Weaver, S. V. Weber, P. J. Wegner, P. K. +Whitman, K. Widmann, C. C. Widmayer, C. H. Wilde, +D. C. Wilson, B. Van Wonterghem, B. J. MacGowan, +L. J. Atherton, M. J. Edwards, and E. I. Moses, Physics +of Plasmas 19, 056318 (2012). +[61] A. J. Martin, R. J. Simms, +and R. B. Jacobs, Journal +of Vacuum Science & Technology A: Vacuum, Surfaces, +and Films 6, 1885 (1988). +[62] M. T. Mruzek, D. L. Musinski, and J. S. Ankney, Journal +of Applied Physics 63, 2217 (1988). +[63] S. H. Glenzer and R. Redmer, Reviews of Modern Physics +81, 1625 (2009). +[64] G. Dimonte, Physics of Plasmas 7, 2255 (2000). +[65] B. Bachmann, S. A. MacLaren, S. Bhandarkar, T. Briggs, +D. +Casey, +L. +Divol, +T. +Döppner, +D. +Fittinghoff, +M. +Freeman, +S. +Haan, +G. +Hall, +B. +Hammel, +E. Hartouni, N. Izumi, V. Geppert-Kleinrath, S. Khan, +B. Kozioziemski, C. Krauland, O. Landen, D. Mariscal, +E. Marley, L. Masse, K. Meaney, A. Moore, A. Pak, +P. Patel, M. Ratledge, N. Rice, M. Rubery, J. Salmonson, +J. Sater, D. Schlossberg, M. Schneider, V. A. Smalyuk, +C. Trosseille, P. Volegov, C. Weber, J. Williams, +and +A. Wray, submitted (2022). + +11 +[66] D. A. Verner and D. G. Yakovlev, Astronomy and +Astrophysics Supplement Series 109, 125 (1995). +[67] S. Atzeni and J. Meyer-ter Vehn, eds., The Physics of +Inertial Fusion (Clarendon Press, Oxford, 2004). +[68] F. J. Rogers and A. Nayfonov, The Astrophysical Journal +576, 1064 (2002). +[69] D. Saumon, G. Chabrier, +and H. M. van Horn, The +Astrophysical Journal Supplement Series 99, 713 (1995). +[70] A. W. Irwin, “The FreeEOS code for calculating the +equation of state for stellar interiors,” (2004). +[71] F. X. Timmes and F. D. Swesty, The Astrophysical +Journal Supplement Series 126, 501 (2000). +[72] A. Y. Potekhin and G. Chabrier, Contributions to +Plasma Physics 50, 82 (2010). +[73] C. A. Iglesias and F. J. Rogers, The Astrophysical +Journal 412, 752 (1993). +[74] C. A. Iglesias and F. J. Rogers, The Astrophysical +Journal 464, 943 (1996). +[75] J. W. Ferguson, D. R. Alexander, F. Allard, T. Barman, +J. G. Bodnarik, P. H. Hauschildt, A. Heffner-Wong, and +A. Tamanai, The Astrophysical Journal 623, 585 (2005). +[76] J. R. Buchler and W. R. Yueh, The Astrophysical Journal +210, 440 (1976). +[77] S. Cassisi, A. Y. Potekhin, A. Pietrinferni, M. Catelan, +and M. Salaris, The Astrophysical Journal 661, 1094 +(2007). +[78] R. H. Cyburt, A. M. Amthor, R. Ferguson, Z. Meisel, +K. Smith, +S. Warren, +A. Heger, +R. D. Hoffman, +T. Rauscher, A. Sakharuk, H. Schatz, F. K. Thielemann, +and M. Wiescher, The Astrophysical Journal Supplement +Series 189, 240 (2010). +[79] G. M. Fuller, W. A. Fowler, +and M. J. Newman, The +Astrophysical Journal 293, 1 (1985). +[80] T. Oda, M. Hino, K. Muto, M. Takahara, and K. Sato, +Atomic Data and Nuclear Data Tables 56, 231 (1994). +[81] K. Langanke and G. Martínez-Pinedo, Nuclear Physics +A 673, 481 (2000). +[82] A. I. Chugunov, H. E. Dewitt, +and D. G. Yakovlev, +Physical Review D 76, 025028 (2007). +[83] N. Itoh, H. Hayashi, A. Nishikawa, +and Y. Kohyama, +The Astrophysical Journal Supplement Series 102, 411 +(1996). +[84] N. Grevesse and A. J. Sauval, Space Science Reviews 85, +161 (1998). +[85] C. Hansen, +S. Kawaler, +and V. Trimble, Stellar +Interiors: Physical Principles, Structure, and Evolution, +Astronomy and Astrophysics Library (Springer New +York, 2004). +[86] L. Mestel, Mathematical Proceedings of the Cambridge +Philosophical Society 46, 331 (1950). +[87] T. D. Lee, The Astrophysical Journal 111, 625 (1950). + diff --git a/19FAT4oBgHgl3EQfkR2N/content/tmp_files/load_file.txt b/19FAT4oBgHgl3EQfkR2N/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..162b9d6fea3e615358848ae1e41b985e2feb42bd --- /dev/null +++ b/19FAT4oBgHgl3EQfkR2N/content/tmp_files/load_file.txt @@ -0,0 +1,1640 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf,len=1639 +page_content='Platform for Probing Radiation Transport Properties of Hydrogen at Conditions Found in the Deep Interiors of Red Dwarfs J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lütgert,1, 2, 3, ∗ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bethkenhagen,4 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bachmann,5 L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Divol,5 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gericke,6 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glenzer,7 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hall,5 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Izumi,5 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Khan,5 O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Landen,5 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacLaren,5 L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Masse,5, 8 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Redmer,1 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schörner,1 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schölmerich,5 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schumacher,1 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Shaffer,9 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Starrett,10 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sterne,5 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Trosseille,5 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Döppner,5 and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kraus1, 2, † 1Institut für Physik, Universität Rostock, Albert-Einstein-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 18059 Rostock,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Germany 2Helmholtz-Zentrum Dresden-Rossendorf,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bautzner Landstrasse 400,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 01328 Dresden,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Germany 3Institute of Nuclear and Particle Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Technische Universität Dresden,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 01069 Dresden,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Germany 4École Normale Supérieure de Lyon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Université Lyon 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Laboratoire de Géologie de Lyon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' CNRS UMR 5276,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 69364 Lyon Cedex 07,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' France 5Lawrence Livermore National Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Livermore,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' CA 94550,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' USA 6Centre for Fusion,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Space and Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' University of Warwick,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Coventry CV4 7AL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' United Kingdom 7SLAC National Accelerator Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Menlo Park,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' CA 94309,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' USA 8CEA-DAM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' DIF,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' F-91297 Arpajon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' France 9Laboratory for Laser Energetics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' University of Rochester,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 250 East River Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rochester,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' NY 14623,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' USA 10Los Alamos National Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Box 1663, Los Alamos, NM 87545, USA (Dated: January 23, 2023) We describe an experimental concept at the National Ignition Facility for specifically tailored spherical implosions to compress hydrogen to extreme densities (up to ∼ 800× solid density, electron number density ne ∼ 4 × 1025 cm−3) at moderate temperatures (T ∼ 200 eV), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', to conditions, which are relevant to the interiors of red dwarf stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The dense plasma will be probed by laser-generated x-ray radiation of different photon energy to determine the plasma opacity due to collisional (free-free) absorption and Thomson scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The obtained results will benchmark radiation transport models, which in the case for free-free absorption show strong deviations at conditions relevant to red dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' This very first experimental test of free-free opacity models at these extreme states will help to constrain where inside those celestial objects energy transport is dominated by radiation or convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moreover, our study will inform models for other important processes in dense plasmas, which are based on electron-ion collisions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', stopping of swift ions or electron-ion temperature relaxation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' INTRODUCTION Red dwarfs (M dwarfs) are the lightest and coolest main sequence stars and make up ∼ 70 % of all stars in the Sun’s neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [1, 2] Prominent examples are our nearest neighbor Proxima Centauri (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='12 M⊙) or TRAPPIST-1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='089 M⊙), which is only slightly larger than Jupiter, but much more massive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The interiors of red dwarfs mainly consist of hydrogen- helium mixtures, which are progressively shaped by screening effects, ion-ion correlations, and degeneracy as temperature decreases and density increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [3] These many-particle effects are challenging to model, in particular, for calculations of radiation transport, which plays a major role in modeling of sub-stellar objects and stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' From the solar abundance problem, we know that ∼ 20 % changes in opacity have paramount impact on our understanding of stellar interiors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [4, 5] Whether energy can effectively be transported via radiation or, if radiation is not sufficient, convection sets in, is a ∗ julian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='luetgert@uni-rostock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='de † dominik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='kraus@uni-rostock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='de property that is particularly influenced by stellar opacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' In general, the physics of red dwarfs is poorly understood in comparison with the hotter interior of the Sun, which is much closer to the ideal plasma state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Figure 1 shows simulated pressure-temperature profiles of stars on the main sequence, demonstrating the extreme plasma conditions present inside those celestial objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The curves were obtained using the MESA code for stellar evolution [6–10] (see the appendix for details on these simulations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The inset illustrates the schematic interiors of stars from the core (m/M = 0) to the photosphere (m/M = 1) divided into radiative and convective zones for stars with a solar composition of elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Red dwarfs are characterized by masses between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='075 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='5 solar masses so that their typical mass-temperature ratios overall place red dwarfs in a regime, where convection dominates the outer regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Depending on the size of the individual object, a more or less developed radiative core is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The smallest red dwarfs (M ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 M⊙) are thought to be fully convective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' In this case, the fusion reactions in the core are permanently re-fueled by hydrogen from the outer layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Combined with the low fusion rates due to the relatively low core temperatures, convection possibly arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='08610v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='plasm-ph] 20 Jan 2023 2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pressure-temperature profiles for various celestial objects calculated using the MESA package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [6–10] Solid lines denote convective regions while dots indicate a layer of radiative energy transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The gray shaded area shows the conditions, which we intent to generate in our experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Inset: Mass coordinate m/M along stellar interior profiles for objects with solar composition divided into radiative (white, dotted lines) and convective (gray, solid curves) regions over total object mass M relative to the Sun’s mass M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The gray- scale dataset was published by Kippenhahn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [11] while the colored lines show the MESA calculations of the main figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' allows some red dwarfs to last trillions of years until all hydrogen fuel is exhausted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' However, even a small radiative core can strongly change this behavior and its existence crucially depends on the effectiveness of radiation transport in highly compressed matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moreover, the internal structure of a star has a major impact on the activity of its surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [12] The boundary between a radiative core and a convective layer can lead to strong magnetic fields and a turbulent atmosphere, [1, 13, 14] including radiative and plasma outbursts that may threaten life on nearby planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Therefore, understanding the radiative properties of the complex plasmas within a host star is crucial when judging the possibility of an exoplanet to host life – especially for red dwarfs where the habitable zone is thought to be found relatively close to the star itself due to the low surface temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [15] For red dwarf stars, the thermodynamic conditions at the boundary between radiative core and convective envelope are estimated to be in a pressure regime of few Gbars and temperatures of few million Kelvin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [1, 11] Corresponding free electron densities are in the range of few 1025 cm−3, which results in Fermi energies of similar order as the thermal energy of the free electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The energy transport in this so-called warm dense matter regime [16] is extremely difficult to calculate, which gives rise to significant uncertainties in modeling the energy transport inside red dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' THEORY For stellar interiors, the radiative opacity κrad is usually divided into three contributions: [17] κrad = κbf + κff + κT , (1) where κbf is the opacity contribution by bound-free absorption, κff denotes the free-free contribution and κT = ZσT /mi the absorption due to Thomson scattering from free electrons, which is solely dependent on the Thomson scattering transport cross section σT , [18, 19] the average ion charge state Z and the average ion mass mi of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' While Rayleigh scattering might be of interest for the atmosphere of K and M class stars, [20] the high ionization in hotter photospheres and deep within even the smallest stars often justifies to neglect its contribution to κrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' For the solar abundance problem, the bound-free opacity of metals is probably most relevant, but deep in the solar radiation zone as well as for many red dwarfs, particularly those with low metallicity, hydrogen free-free opacity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', absorption due to inverse bremsstrahlung, is the dominant absorption mechanism of radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [17] For these red dwarfs, the absolute values for free-free absorption determine where convection or radiation will be the dominant energy transport mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Figure 2 shows a density-temperature diagram of dominating absorption mechanisms thought to be present for the composition of population I stars in comparison with red dwarf interiors and the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' While bound-free transitions dominate at low densities and temperatures, free-free absorption starts to outrun the bound-free opacity with the increase in density due to increasing electron-ion collision rates as well as pressure ionization of heavier elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [21] At the highest densities, conduction by degenerate electrons becomes more efficient than radiation transport, whereas for low densities and highest temperatures, photon scattering from electrons (Thomson or Compton, depending on photon energy) is most significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Analytical models A classical treatment of the spectral absorption coefficient due to inverse bremsstrahlung, derived from the description of electron-ion collisions in a weakly coupled plasma environment, yields for the absorption coefficient αff, [22] αff(ν) = ρκff(ν) ∝ Z2neni ν3√ T � 1 − exp � − hν kBT �� gff(ν, T), (2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dominating opacities in different regimes of the density-temperature diagram for a composition of elements as in population I stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [17] The colored lines show densities and temperatures realized within main-sequence stars according to the “MESA” stellar evolution code [6–10] with solid lines representing convective layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The proposed experiments will probe conditions similar to the interiors of red dwarf stars where free-free absorption is expected to dominate (indicated by the shaded region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' where ν denotes the x-ray frequency, ρ is the mass density, Z is the average degree of ionization, ne is the free electron number density, ni is the ion number density, T is the plasma temperature, h is Planck’s constant, and kB is Boltzmann’s constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Additional corrections due to quantum and correlation effects are accounted for in a frequency-dependent correction factor gff(ν, T), the so-called Gaunt factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [23] For a weakly coupled ideal plasma, the Gaunt factor can be interpreted as the logarithm of the ratio of maximum impact parameter bmax and minimum impact parameter bmin in the corresponding electron-ion collision (the so-called Coulomb logarithm [24]): gff(ν, T) = √ 3 π ln �bmax bmin � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' (3) This formalism is equivalent to the classical treatment of several other important plasma effects that involve Coulomb collisions of electrons and ions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', stopping power of ions or electron-ion temperature equilibration in dense plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [25] The maximum impact parameter bmax is usually given by min(ve/2πν, λs) where ve is the average velocity of the electrons, ν is the x-ray frequency, and λs is the screening length due to the surrounding plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' On the other hand, bmin can be expressed as max(b⊥, λth), where b⊥ = Ze2/(4πϵ0mev2 e) is the impact parameter for an electron being deflected perpendicular to its direction of incidence and λth denotes the thermal de Broglie wavelength of the electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' However, for conditions relevant to the interiors of red dwarfs [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', ne ∼ few 1025 cm−3, Te ∼ few 100 eV (Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [3])], we find ve/2πν < λth, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', a negative Coulomb logarithm for x-ray frequencies larger than the plasma frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Thus, this simple classical treatment assuming a weakly coupled plasma is not appropriate for such conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Indeed, more sophisticated approaches have been developed to accommodate these conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [26, 27] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Average Atom and Density Functional Theory calculations Figure 3 shows Average Atom calculations with a Mean Force potential (AA-MF) [28] and state-of-the- art Density Functional Theory Molecular Dynamics (DFT-MD) simulations [29] compared to the analytical model for the free-free opacity with constant Gaunt factor and calculations by van Hoof et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [30, 31] The first two simulation methods have previously been applied successfully for calculating the equation- of-state (EOS) and transport properties of dense plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [28, 32–34] The DFT-MD simulations were performed with up to 256 hydrogen atoms using the program package VASP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [35–38] Our considered density range spans 20 −150 g cm−3 at 100, 150, and 200 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The simulations use the Baldereschi mean value point [39] and the Coulomb potential with an energy cutoff of 10 000 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Each DFT-MD point was run for 20 000 time steps with a time step size between 3 as (attoseconds) and 8 as depending on the thermodynamic conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The temperature was controlled with a Nosé-Hoover thermostat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [40] Subsequently, 10 – 20 snapshots were selected from each trajectory to calculate the electrical conductivity and opacity applying the Kubo-Greenwood formalism [41, 42] and the Kramers-Kronig relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' For details on the AA- MF calculations (which were performed for identical temperatures and pressures), we refer to previous publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [28, 43–46] While the DFT-MD simulation naturally includes many-body effects in the description of wavefunctions and the density of states due to the multiple ions included in the simulation, the AA-MF approach, which is strictly speaking also DFT-based, simplifies the calculation by exclusively relying on the atom-in-jellium model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Either of the two formulations calculates opacity from the real part of the electrical conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Both approaches agree on the quantity of extinction remarkably well, supporting each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' This result is particularly noteworthy as the similarity of the AA-MF calculation with DFT-MD – for the specific case of hydrogen – is highly desired: While DFT-MD is generally more accurate, AA-MF is computationally significantly less expensive and should be favored if benchmarks can show good agreement between the two methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' At the same time, the consistency of the computed opacity illustrates impressively that extreme states of matter can be treated by DFT-MD nowadays with the increase :4 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Opacity for a (25 %/75 %) HT mixture at an electron density ne = 5 × 1025 cm−3 and a temperature of T = 100 eV (solid and dotted lines) or T = 150 eV (dashed), respectively, according to different models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The blue and purple lines depict DFT-MD and AA-MF calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The other solid curves show the analytical model for free-free extinction [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' (2)] with a Gaunt factor equal to unity (black line) or values calculated by van Hoof et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [30, 31] (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' For comparison, the opacity due to Thomson scattering for a temperature of T = 100 eV is shown as the dotted black line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The AA-MF calculation at 150 eV and the inset depicting the relative difference between the two results [∆κAA = 2(κ150 eV AA − κ100 eV AA )/(κ150 eV AA + κ100 eV AA )] show that the temperature influence is very small for photon energies above 3 keV due to the degenerate conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' in computational power and, hence, number of energy bands included in the calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Both methods show a discrepancy to the calculation of the free-free opacity from the semi-classical formula [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' (2)], as it can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The simplest approach of setting the Gaunt factor to unity reproduces the classical result of Kramers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [22] Introducing quantum- mechanical corrections, van Hoof et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [30, 31] provide easily applicable, tabulated values for gff by following the seminal work of Karzas and Latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [47] However, this calculation is requiring more assumptions than the AA- MF or the DFT-MD model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', the velocity distribution of the electrons (with is assumed to be Maxwellian) in order to calculate thermally averaged free-free Gaunt factors and from these opacities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [30, 31] Other authors perform similar calculations but integrate over the Fermi distribution of a degenerate electron gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [24] In fact, for dense plasma conditions comparable to the interiors of main sequence stars, even advanced calculations of the Gaunt factor vary by more than 50 % for frequencies larger than the plasma frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [27] In particular, the specific treatment of dynamic screening, strong collisions, and re-normalization due to higher moments can make a significant difference in comparison to widely-used Born approximation treatments of the Gaunt factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [27] Deviations are particularly significant in the photon energy regime from ∼ 500 eV to few keV, which is the dominant contribution when calculating the Rosseland mean opacity for the Sun and smaller stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Indeed, varying the opacity by 50 % can change the radii of the boundaries between convection and radiation zone by up to 10 %, which, given the underlying density and temperature gradients, would significantly impact our general understanding of stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [5, 48] III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' EXPERIMENTAL CONCEPT Using the largest laser system in the world, namely, the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory, [49] it is now possible to create and probe matter states relevant to stellar interiors in the laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [50, 51] To address the questions raised above, we have developed a concept to leverage NIF’s unique capabilities to create relevant conditions and obtain a very first test of free-free opacity models in this very important plasma regime via x-ray absorption measurements of highly compressed hydrogen during the stagnation phase of layered capsule implosions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' In this way, not only the various existing models and resulting tables for the Gaunt factor will be tested, but also modern DFT-MD and AA-MF simulations, which provide the absorption coefficient, can be benchmarked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Finally, due to the equivalent physics involved (electron- ion collisions in dense plasma environments [26]), our results on free-free absorption will inform models for swift ion stopping in warm dense matter as well as corresponding electron-ion equilibration times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Experimental setup A sketch of the experimental setup is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' We will use 184 out of the 192 NIF laser beams to heat a gold Hohlraum creating a quasi-thermal radiation field that implodes a layered fuel capsule at the center of the Hohlraum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The capsule is comprised of a 57 µm thick beryllium ablator shell, containing a 83 µm thick layer of cryogenic solid hydrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The temporally shaped radiation field created by the laser drive will ablate the Be shell and, hence, accelerate the payload inward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Upon stagnation, a high density hydrogen layer with ρ > 100 g cm−3 is formed while most of the Be ablator has been ablated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The implosion design is derived from inertial confinement fusion (ICF) implosions at the NIF [54] and applies a well-tested model that matched a variety of spherical DT implosion experiments in NIF’s ICF 5 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schematic of the experimental setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Using NIF’s laser beams, a nearly Planckian x-ray bath (see bottom right) is created by heating a gold Hohlraum with a fuel capsule at its center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Upon stagnation, the solid hydrogen layer is compressed to mass densities larger than 100 g cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Two Hohlraum windows allow for measuring the transmission of high density hydrogen using x rays created in a stagnating plasma inside the backlighter tube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fielding NIF’s Crystal Backlighter Imager [52] and the single line-of-sight (SLOS) detector [53] enables us to acquire narrow bandwidth high- resolution radiography images of the implosion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [54, 55] In contrast to ICF implosions aiming for high neutron yield,[56] the peak radiation temperature of our Hohlraum drive (Trad = 170 eV) is significantly reduced, deliberately slowing down the implosion to ∼ 200 km s−1 with the goal of creating extreme densities (∼ 150 g cm−3) at moderate temperatures (∼ 200 eV) while reducing x-ray and neutron-related background signals near stagnation that would affect the radiography measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' These conditions are directly relevant to the interiors of red dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The dense plasma states will be probed by x-ray line emission, which is created by the eight remaining NIF beams that heat a backlighter tube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' We will perform 2D-imaging radiography of the implosion and stagnation phase using two different photon energies by varying the backlighter tube material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Vanadium will result in 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV line emission from 1s2p→1s2 (He-α) transitions of helium-like ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' In the same way, helium-like cobalt ions will produce 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' NIF’s Crystal Backlighter Imager (CBI) system [52] will allow for high-resolution, nearly monochromatic radiography images of the imploding and stagnating sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A gated single-line-of-sight (SLOS) detector [53] will provide four images per implosion with a time delay of ∼ 100 ps between consecutive images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' From the radiography images, we will infer radial profiles of the opacity through Abel inversion [57, 58] and forward fitting methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' (a) 1D radiation-hydrodynamics simulations performed using the HYDRA code, [59] showing the mass density ρ at a given radius r and time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Our experiment intends to probe around stagnation when the highest fuel compression is predicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Density, temperature, and ionization profiles around this time (∼ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='5 ns after the start of the drive laser) are plotted in (b) and predict hydrogen mass densities in excess of 150 g cm−3 in the HT mixture with a molar mass of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='5 g mol−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Radiation hydrodynamic simulations The reduced implosion velocity minimizes the hot spot x-ray emission at stagnation to improve the signal- to-noise ratio of the physics measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' For the same reason, we use a (25 %/75 %) HT mixture (which is hydrodynamically equivalent to 50 %/50 % DT) for the ice layer to minimize the neutron yield and the related background signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Tritium is required to enable the hydrogen ice layer formation through beta layering, where self-heating from beta decay leads to a redistribution of HT ice with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [60–62] Figure 5 shows an overview of the ∼ 11 ns implosion trajectory simulated with HYDRA-1D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [59] Compared to previous ICF experiments with Be shells, [54] the ablator thickness is reduced to 57 µm to decrease the remaining ablator mass to near zero, which will maximize the radiography contrast of the hydrogen layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Figure 5(b) illustrates examples of radial density, ionization, and temperature profiles predicted by hydrodynamic simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The high-density portion of the profiles consists of hydrogen (HT) only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Our simulations predict that the material is compressed to mass densities exceeding 150 g cm−3, which corresponds to electron densities of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='6×1025 cm−3, 6 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Beryllium content of the capsule close to stagnation as a function of time t and radius r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The dash-dotted dark line shows the interface of ablator and fuel for a simulation without mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The dashed lines depict contours of constant density in the highly compressed HT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' For the times we intend to probe (around −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='4 ns to −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 ns), the Be is not predicted to contaminate this dense part of the fuel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The values on the abscissa are given relative to the time where the rebounding shock wave coincides with the fuel-ablator interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' at a temperature of ∼ 200 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' These parameters result in Fermi energies of ∼ 400 eV and, thus, ∼ 2× larger than the thermal energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hence, we will probe degenerate plasma conditions as expected in the interiors of red dwarf stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' In addition, these conditions are expected to limit the influence of temperature on the free-free absorption, since the 1/ √ T term in the expression for the inverse bremsstrahlung [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' (2)] can be replaced approximately by 1/√TF , where TF denotes the Fermi temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' This behavior is supported by the results from DFT-MD and the Average Atom Compared to previous ICF experiments with Be shells, [54] the ablator thickness is reduced to 57 µm to decrease the remaining ablator mass to near zero, model, which indicates that the opacity is more sensitive to the Fermi temperature than the electronic temperature under dense degenerate plasma conditions (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 3 and inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The weak dependence on T is highly beneficial for the analysis and interpretation of our data, as we can determine opacity and from there infer density, while a direct measurement of temperature would require additional diagnostics – for example x-ray Thomson scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [63] Reducing the ablator shell thickness and decreasing the remaining mass at stagnation might come with increased risk of hydrodynamic instability at the ablator-ice interface and ablator material mixing into the compressed ice layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' For a more quantitative estimate of mixing, we have performed 1D capsule-only simulations using a buoyancy-drag mix model, [64] which was successful in explaining experimental performance observations of previous layered Be implosions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [54] In addition, more recently the buoyancy-drag mix model has been calibrated in a focused series of experiments using a thin ice layer of varying thickness and detecting neutronic signatures of deuterated plastic, originally located near the inside of a plastic shell, mixing through the ice layer into the hot spot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [65] Figure 6 shows the results for our significantly slower implosion design in terms of atomic Be fraction as function of radius and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The demarcation line between the Be ablator and the HT ice is indicated as a dot-dashed line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' We have labeled the time of minimum radius of this interface by tmin, which coincides with the time when the rebounding shock wave, which leads to the formation of the high-compression HT ice, passes this interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Our simulations clearly show that Be does not mix into the high-compression HT ice layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The radiography measurements are aimed to record transmission images between 400 and 200 ps before tmin, which, hence, is not affected by Be mixing into the high compression HT ice layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' SIMULATED RADIOGRAPHY SIGNAL Synthetic radiography images (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 7 and the appendix for more details) show a clear limb feature at the boundary of the central hydrogen and the beryllium layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Applying mass conservation, this feature will be used as constraint for the density of the encapsulated hydrogen at smaller radii as the total initial fuel mass can be accurately characterized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Toward the outer edges of the radiography field-of-view of 600×600 µm2, we expect the plasma to become fully transmissive to the probe radiation, which will be used to normalize the opacities measured at smaller radii and obtain absolute values of the radial absorption coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' In the investigated density and temperature regime, opacity due to Thomson scattering is expected to reach similar values as free-free absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' As absorption due to Thomson scattering scales linearly with ne and free- free opacity with n2 e, this effect can become particularly significant in the lower density regions of the imploded capsule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' To disentangle both mechanisms, we will perform the absorption measurements at two photon energies (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV as described above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' While disagreeing in the actual magnitude, all but the classical approach (gff = 1) presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 3 find the same proportionality of the free-free opacity with ∼ 1/(hν)(7/2) for high photon energies hν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Classically, the Thomson cross-section is in fist order independent of probing frequency and temperature, which would allow us to separate the two contributions to the signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' While this assumption might give a reasonable first estimate, our AA-MF simulations (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 3) indicate in accordance with previous calculations by Boercker [18] that this description as a constant is not applicable at the extreme conditions we intend to probe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' However, models of the Thomson scattering have to provide only the ratio between the cross-section at the two backlighter energies 7 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' (a) Simulated detector image including free-free (AA-MF calculations) and bound-free [66] absorption as well as Thomson scattering [18] for 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV (top) and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV (bottom) backlighter energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The colorbar indicates the expected number of photons per pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Albeit the limited temporal and spatial resolution of the detector, the interface between the HT mixture and the beryllium ablator is predicted to be visible at least for the lower energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' (c) Absorption coefficient profiles and (b) integrated total capsule transmission T for a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV backlighter close to the time where the highest density in the hydrogen is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' As the lower figure shows, different models for the free-free opacity result in notable changes of the total transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' All presented plots assume a perfectly symmetrical implosion, no mixing between fuel and ablator and a beryllium layer without impurities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' to enable us to differentiate the former from inverse bremsstrahlung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Regardless of the model applied, the Thomson scattering’s contribution to the overall opacity might also be used as an additional density constraint next to measuring the ablator-hydrogen interface and applying mass conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Further constraints on the implosion parameters will be deduced from measuring multiple absorption images at different times during the implosion in one shot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The stagnation phase is usually well modeled by a self-similar description of the conservation laws, [67] which only allows certain shapes and time evolutions of the density profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' CONCLUSIONS In summary, we presented a concept to leverage NIF’s unique capabilities to investigate the deep interiors of red dwarf stars in the laboratory and shed light on their internal energy transports mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The proposed experiment has been accepted within NIF’s Discovery Science Program for upcoming shot days in 2022 and 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The resulting measurement of free- free absorption and opacity will provide a benchmark for numerical and analytical approaches, which will in turn yield an improved description of the Gaunt factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Finally, interior structure models for massive hydrogen- rich astrophysical objects, such as red dwarfs, can be revisited on the basis of the new opacity constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' ACKNOWLEDGMENTS M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' was supported by the European Horizon 2020 programme within the Marie Skłodowska-Curie actions (xICE grant number 894725).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' acknowledge support by the Helmholtz Association under VH-NG-1141 and by GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt as part of the R&D project SI-URDK2224 with the University of Rostock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The work of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' was supported by Deutsche Forschungsgemeinschaft (DFG – German Research Foundation) project no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 495324226.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The work of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='M, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' was performed under the auspices of the DOE by Lawrence Livermore National Laboratory under Contract No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' DE-AC52-07NA27344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' acknowledge support from the DFG via the Research Unit FOR 2440.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The DFT-MD calculations were performed at the North-German Supercomputing Alliance (HLRN) facilities and at the IT- and Media Center of the University of Rostock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' AUTHOR DECLARATIONS Conflict of interest The authors have no conflicts of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 8 DATA AVAILABILITY The data that support the findings of this study are available from the corresponding authors upon reasonable request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Appendix A: MESA Simulations Profiles of temperature, density, and pressure inside stars with various masses were calculated using the “Modules for Experiments in Stellar Astrophysics” code (MESA, release r15140).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [6–10] We used the default MESA equation-of-state (EOS) which is a blend of the OPAL, [68] SCVH, [69] FreeEOS, [70] HELM, [71] and PC [72] EOSes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Radiative opacities are primarily from OPAL, [73, 74] with low-temperature data from Ferguson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [75] and the high-temperature, Compton- scattering dominated regime by Buchler and Yueh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [76] Electron conduction opacities are from Cassisi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='. [77] Nuclear reaction rates are from JINA REACLIB [78] plus additional tabulated weak reaction rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [79–81] Screening is included via the prescription of Chugunov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='. [82] Thermal neutrino loss rates are from Itoh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='. [83] A pre-main-sequence model has been calculated from initial parameters of helium mass fraction Yi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2744, metallicity Zi = 1 − Xi − Yi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='01913 (with Xi being the initial mass fraction of hydrogen), mixing length parameter αMLT = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='9179, and including element diffusion, which has been found to reproduce the solar model well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [6] The ratio of elements heavier than helium was taken from Grevesse and Sauval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [84] The time span of the simulation was chosen so that the star spent a considerable amount of time on the main sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' For stars smaller than the Sun, 10 times the age of the star when the main sequence was entered has been chosen;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' masses M > M⊙ were evolved until tnuc/2 was reached, were tnuc = (M/M⊙)−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='9 ×1010 a is an approximation for the lifetime of star on the main sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [85] The decision whether regions of a star were considered convective or radiative was based on the Schwarzschild criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Appendix B: Comparing radiative and conductive opacities The relation between thermal conductivity through photon transport (radiation) λrad and the opacity κrad is given by λrad = 4acT 3 3ρκrad (B1) where T is the temperature, ρ is the density, a = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='5657× 10−16 Jm−3K−4 is the radiation density constant, and c is the speed of light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [17, 85] Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' (B1) can be used to define a conductive opacity κc from the thermal conductivity due to electrons λc by analogy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' This quantity – as calculated by Hayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' who reproduce the work of Mestel [86] and Lee [87] – has been plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 2 to compare it with radiative opacities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' As the two contributions to the full thermal conductivity are additive, the total opacity κtot is given by 1/κtot = 1/κrad + 1/κc, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', in order for κc being the dominant contribution to the total opacity (see the high density and low temperature corner of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 2), the former quantity has to be small compared to κrad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [85] Appendix C: Radiography predictions In order to generate the transmission profiles [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 7 (b)] from extinction coefficient line-outs [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 7 (c)], we assumed a perfect, spherically symmetric implosion and a uniform and monochromatic backlighter emitting parallel x rays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' We calculated Tν = exp � − � dxκν(x)ρ(x) � (C1) where the integral runs over the path of the light and might, therefore, probe different temperature and density conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' To account for the limited temporal resolution of the detector, a series of one-dimensional transmission profiles at different times was convolved with a Gaussian gate-function (35 ps FWHM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' The resulting line-out has been rotated, and a spatial blur in the form of a two-dimensional Gaussian with 10 µm FWHM in both directions was applied before the transmission has been multiplied with the expected backlighter photon flux (240 µm−2 ps−1 (Eph = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV) or 288 µm−2 ps−1 (Eph = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='2 keV) at the target’s position), corrected for attenuators shielding various components and re-binned to the pixel-size of the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' In a last step, noise proportional to the individual pixels’ intensity has been applied to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [1] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Reid and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hawley, New Light on Dark Stars (Springer Berlin-Heidelberg, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Heath, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Doyle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Joshi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haberle, Origins of Life and Evolution of the Biosphere 9 29, 405 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Osterbrock, Astrophysical Journal 118, 529 (1953).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bailey, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nagayama, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Loisel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rochau, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Blancard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Colgan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Cosse, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Faussurier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fontes, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gilleron, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Golovkin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hansen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Iglesias, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kilcrease, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacFarlane, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mancini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nahar, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Orban, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pain, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pradhan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sherrill, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wilson, Nature 517, 56 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [5] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Vinyoles, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Serenelli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Villante, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Basu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bergström, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gonzalez-Garcia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Maltoni, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Peña Garay, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Song, Astrophysical Journal 835, 202 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [6] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Paxton, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bildsten, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dotter, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Herwig, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lesaffre, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Timmes, ApJS 192, 3 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [7] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Paxton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Cantiello, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Arras, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bildsten, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Brown, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dotter, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mankovich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Montgomery, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Stello, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Timmes, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Townsend, ApJS 208, 4 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Paxton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Marchant, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schwab, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bauer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bildsten, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Cantiello, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dessart, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Farmer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Langer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Townsend, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Townsley, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Timmes, ApJS 220, 15 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [9] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Paxton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schwab, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bauer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bildsten, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Blinnikov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Duffell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Farmer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Goldberg, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Marchant, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sorokina, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Thoul, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Townsend, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Timmes, ApJS 234, 34 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [10] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Paxton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Smolec, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schwab, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gautschy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bildsten, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Cantiello, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dotter, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Farmer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Goldberg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jermyn, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kanbur, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Marchant, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Thoul, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Townsend, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wolf, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Zhang, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Timmes, ApJS 243, 10 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [11] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kippenhahn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Weigert, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Weiss, Stellar Structure and Evolution (Springer Berlin-Heidelber, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [12] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Babcock, The Astrophysical Journal 133, 572 (1961).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [13] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Parker, The Astrophysical Journal 198, 205 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Route, The Astrophysical Journal 830, L27 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [15] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Loyd, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Shkolnik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schneider, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Barman, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meadows, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pagano, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Peacock, The Astrophysical Journal 867, 70 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [16] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Graziani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Desjarlais, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Redmer, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Trickey, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', Frontiers and Challenges in Warm Dense Matter (Springer Cham, Heidelberg, New York, Dordrecht, London, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [17] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hayashi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hoshi, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sugimoto, Progress of Theoretical Physics Supplements 22, 1 (1962).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [18] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Boercker, The Astrophysical Journal 316, L95 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [19] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Watson, The Astrophysical Journal 158, 303 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [20] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hubeny and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mihalas, Theory of stellar atmospheres: An introduction to astrophysical non-equilibrium quanti- tative spectroscopic analysis (Princeton University Press, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [21] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Clayton, Principles of Stellar Evolution and Nucleosynthesis (The University of Chicago Press, Chicago and London, 1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [22] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kramers, Philosophical Magazine 46, 836 (1923).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gaunt, Philosophical Transactions of the Royal Society A 229, 163 (1930).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [24] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meyer-ter Vehn and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ramis, Physics of Plasmas 26, 113301 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gericke, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Murillo, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schlanges, Physical Review E 65, 036418 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Grinenko and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gericke, Physical Review Letters 103, 065005 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wierling, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Millat, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Röpke, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Redmer, Physics of Plasmas 8, 3810 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [28] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Starrett, High Energy Density Physics 25, 8 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [29] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bethkenhagen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Witte, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schörner, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Röpke, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Döppner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kraus, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glenzer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sterne, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Redmer, Physical Review Research 2, 023260 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [30] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' van Hoof, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Williams, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Volk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chatzikos, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ferland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lykins, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Porter, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wang, Monthly Notices of the Royal Astronomical Society 444, 420 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [31] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' van Hoof, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ferland, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Williams, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Volk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chatzikos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lykins, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Porter, Monthly Notices of the Royal Astronomical Society 449, 2112 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Becker, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lorenzen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fortney, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nettelmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schöttler, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Redmer, Astrophysical Journal Supplement Series 215, 21 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Becker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bethkenhagen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kellermann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wicht, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Redmer, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 156, 149 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [34] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Holst, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' French, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Redmer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B 83, 235120 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [35] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kresse and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hafner, Physical Review B 47, 558 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [36] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kresse and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hafner, Physical Review B 49, 14251 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [37] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kresse and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Furthmüller, Computational Materials Science 6, 15 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [38] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kresse and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Furthmüller, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B 54, 11169 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [39] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Baldereschi, Physical Review B 7, 5212 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nosé, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 81, 511 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [41] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kubo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 12, 570 (1957).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [42] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Greenwood, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 71, 585 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [43] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Starrett and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Saumon, Physical Review E 87, 013104 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [44] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Starrett, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Daligault, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Saumon, Physical Review E 91, 013104 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [45] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Starrett and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Saumon, Physical Review E 93, 063206 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [46] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Shaffer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ferris, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Colgan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kilcrease, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Starrett, High Energy Density Physics 23, 31 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [47] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Karzas and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Latter, The Astrophysical Journal Supplement Series 6, 167 (1961).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [48] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Serenelli, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haxton, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Peña Garay, Astrophysical Journal 743, 24 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [49] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moses, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Boyd, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Remington, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Keane, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Al-Ayat, Physics of Plasmas 16, 041006 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [50] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kritcher, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Swift, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Döppner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bachmann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Benedict, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Collins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' DuBois, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Elsner, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fontaine, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gaffney, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hamel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lazicki, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Johnson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kostinski, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kraus, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacDonald, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Maddox, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Martin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Neumayer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nikroo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nilsen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Remington, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Saumon, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sterne, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sweet, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Correa, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Whitley, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Falcone, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glenzer, Nature 584, 51 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [51] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kraus, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Döppner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kritcher, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Yi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Boehm, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bachmann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Divol, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fletcher, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glenzer, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Landen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Masters, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Saunders, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Weber, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Falcone, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Neumayer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 10 717, 012067 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [52] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hall, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Krauland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schollmeier, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kemp, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Buscho, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hibbard, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Thompson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Casco, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ayers, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ayers, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meezan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hopkins, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nora, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hammel, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Masse, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Field, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bradley, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bell, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Landen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kilkenny, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mariscal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Park, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' McCarville, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lowe-Webb, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kalantar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kohut, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Piston, Review of Scientific Instruments 90, 013702 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [53] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Engelhorn, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hilsabeck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kilkenny, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Morris, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chung, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dymoke-Bradshaw, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hares, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bell, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bradley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Carpenter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dayton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nagel, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Claus, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Porter, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rochau, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sanchez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ivancic, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sorce, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Theobald, Review of Scientific Instruments 89, 10g123 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [54] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Zylstra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacLaren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Yi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kline, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Callahan, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hurricane, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bachmann, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kyrala, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Masse, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Patel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ralph, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Salmonson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Volegov, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wilde, Physics of Plasmas 26, 052707 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [55] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kritcher, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Clark, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Yi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Zylstra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Callahan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hinkel, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Berzak Hopkins, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hurricane, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Landen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacLaren, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meezan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Patel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ralph, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Thomas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Town, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Edwards, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Plasmas 25, 056309 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [56] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Zylstra, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hurricane, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Callahan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kritcher, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ralph, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Robey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ross, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Young, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Baker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Casey, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Döppner, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Divol, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hohenberger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Le Pape, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pak, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Patel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Tommasini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ali, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Amendt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Atherton, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bachmann, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bailey, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Benedetti, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Berzak Hopkins, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Betti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bhandarkar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Biener, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bionta, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Birge, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bond, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bradley, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Braun, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Briggs, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bruhn, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Celliers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chapman, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Choate, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Christopherson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Clark, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Crippen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dewald, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dittrich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Edwards, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Farmer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Field, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fittinghoff, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Frenje, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gaffney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gatu Johnson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glenzer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Grim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hahn, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hall, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hammel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Harte, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hartouni, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Heebner, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hernandez, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Herrmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Herrmann, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hinkel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ho, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Holder, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hsing, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Humbird, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Izumi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jarrott, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jeet, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jones, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kerbel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kerr, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Khan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kilkenny, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Geppert Kleinrath, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Geppert Kleinrath, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Koning, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kroll, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kruse, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kustowski, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Landen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Langer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Larson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lemos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lindl, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacDonald, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacGowan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mackinnon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacLaren, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacPhee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Marinak, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mariscal, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Marley, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Masse, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meaney, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meezan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Michel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Millot, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Milovich, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moody, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moore, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Morton, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Murphy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Newman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Di Nicola, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nikroo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nora, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Patel, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pelz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Peterson, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ping, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pollock, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ratledge, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rice, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rinderknecht, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rosen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rubery, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Salmonson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sater, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schiaffino, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schlossberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schneider, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schroeder, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Scott, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sepke, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sequoia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sherlock, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Shin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Smalyuk, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Spears, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Springer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Stadermann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Stoupin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Strozzi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Suter, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Thomas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Town, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Tubman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Trosseille, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Volegov, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Weber, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Widmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wild, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wilde, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Van Wonterghem, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Woods, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Woodworth, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Yamaguchi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Yang, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Zimmerman, Nature 601, 542 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [57] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hanson, Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Notes in Pure and Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 115, 363 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [58] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Howard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fowler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Luttman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mitchell, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hock, SIAM Journal on Scientific Computing 38, B396 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [59] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Marinak, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kerbel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gentile, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jones, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Munro, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pollaine, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dittrich, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haan, Physics of Plasmas 8, 2275 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [60] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glenzer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Callahan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacKinnon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kline, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Grim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Alger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Berger, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bernstein, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Betti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bleuel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Boehly, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bradley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Burkhart, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Burr, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Caggiano, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Castro, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Casey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Choate, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Clark, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Celliers, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Cerjan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Collins, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dewald, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' DiNicola, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' DiNicola, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Divol, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dixit, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Döppner, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dylla-Spears, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dzenitis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Eckart, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Erbert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Farley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fair, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fittinghoff, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Frank, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Frenje, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Friedrich, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Casey, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gatu Johnson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Gibson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Giraldez, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glebov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glenn, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Guler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haid, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hammel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hamza, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haynam, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Heestand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hermann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hermann, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hicks, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hinkel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Holder, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Holunda, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Horner, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hsing, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Huang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Izumi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jackson, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jones, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kalantar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kauffman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kilkenny, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kirkwood, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Klingmann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kohut, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Knauer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Koch, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kozioziemki, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kyrala, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kritcher, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kroll, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' La Fortune, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lagin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Landen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Larson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' LaTray, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Leeper, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Le Pape, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lindl, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lowe-Webb, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ma, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' McNaney, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacPhee, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Malsbury, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mapoles, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Marshall, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meezan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Merrill, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Michel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moody, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moore, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moran, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moreno, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Munro, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nathan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nikroo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Olson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Orth, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pak, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Patel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Parham, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Petrasso, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ralph, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rinderknecht, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Regan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Robey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ross, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rosen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sacks, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Salmonson, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Saunders, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sater, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sangster, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schneider, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Séguin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Shaw, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Spears, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Springer, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Stoeffl, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Suter, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Thomas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Tommasini, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Town, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Walters, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Weaver, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Weber, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wegner, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Whitman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Widmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Widmayer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wilde, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wilson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Van Wonterghem, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacGowan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Atherton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Edwards, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moses, Physics of Plasmas 19, 056318 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [61] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Martin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Simms, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Jacobs, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 6, 1885 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [62] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mruzek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Musinski, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ankney, Journal of Applied Physics 63, 2217 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [63] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Glenzer and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Redmer, Reviews of Modern Physics 81, 1625 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [64] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dimonte, Physics of Plasmas 7, 2255 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [65] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bachmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' MacLaren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bhandarkar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Briggs, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Casey, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Divol, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Döppner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fittinghoff, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Freeman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Haan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hall, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hammel, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hartouni, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Izumi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Geppert-Kleinrath, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Khan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kozioziemski, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Krauland, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Landen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mariscal, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Marley, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Masse, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meaney, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Moore, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pak, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Patel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ratledge, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rice, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rubery, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Salmonson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sater, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schlossberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schneider, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Smalyuk, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Trosseille, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Volegov, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Weber, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Williams, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wray, submitted (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' 11 [66] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Verner and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Yakovlev, Astronomy and Astrophysics Supplement Series 109, 125 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [67] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Atzeni and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meyer-ter Vehn, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=', The Physics of Inertial Fusion (Clarendon Press, Oxford, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [68] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rogers and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nayfonov, The Astrophysical Journal 576, 1064 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [69] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Saumon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chabrier, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' van Horn, The Astrophysical Journal Supplement Series 99, 713 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [70] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Irwin, “The FreeEOS code for calculating the equation of state for stellar interiors,” (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [71] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Timmes and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Swesty, The Astrophysical Journal Supplement Series 126, 501 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [72] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Potekhin and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chabrier, Contributions to Plasma Physics 50, 82 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [73] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Iglesias and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rogers, The Astrophysical Journal 412, 752 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [74] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Iglesias and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rogers, The Astrophysical Journal 464, 943 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [75] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ferguson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Alexander, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Allard, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Barman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Bodnarik, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hauschildt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Heffner-Wong, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Tamanai, The Astrophysical Journal 623, 585 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [76] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Buchler and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Yueh, The Astrophysical Journal 210, 440 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [77] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Cassisi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Potekhin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Pietrinferni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Catelan, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Salaris, The Astrophysical Journal 661, 1094 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [78] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Cyburt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Amthor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Ferguson, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Meisel, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Smith, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Warren, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Heger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hoffman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Rauscher, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sakharuk, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Schatz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Thielemann, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Wiescher, The Astrophysical Journal Supplement Series 189, 240 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [79] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fuller, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Fowler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Newman, The Astrophysical Journal 293, 1 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [80] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Oda, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hino, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Muto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Takahara, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sato, Atomic Data and Nuclear Data Tables 56, 231 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [81] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Langanke and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Martínez-Pinedo, Nuclear Physics A 673, 481 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [82] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Chugunov, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Dewitt, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Yakovlev, Physical Review D 76, 025028 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [83] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Itoh, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hayashi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Nishikawa, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kohyama, The Astrophysical Journal Supplement Series 102, 411 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [84] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Grevesse and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Sauval, Space Science Reviews 85, 161 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [85] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Hansen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Kawaler, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Trimble, Stellar Interiors: Physical Principles, Structure, and Evolution, Astronomy and Astrophysics Library (Springer New York, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [86] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Mestel, Mathematical Proceedings of the Cambridge Philosophical Society 46, 331 (1950).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' [87] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} +page_content=' Lee, The Astrophysical Journal 111, 625 (1950).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/19FAT4oBgHgl3EQfkR2N/content/2301.08610v1.pdf'} diff --git a/1dAzT4oBgHgl3EQfRfuL/content/2301.01217v1.pdf b/1dAzT4oBgHgl3EQfRfuL/content/2301.01217v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0068b8aeabfd074bb7fbc1d5de84adcbd8206ee1 --- /dev/null +++ b/1dAzT4oBgHgl3EQfRfuL/content/2301.01217v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:eaf060e6bbbe047d158937323204b8227f55c6c9c8afa89bce6e446ab6bed709 +size 1257432 diff --git a/1dAzT4oBgHgl3EQfRfuL/vector_store/index.faiss b/1dAzT4oBgHgl3EQfRfuL/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..649aff5d81d7c7fe1eb2a13ed66511e5fe9ececb --- /dev/null +++ b/1dAzT4oBgHgl3EQfRfuL/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f46a98e5a5b9a5433f7298c2c62f13c0847b1e1cd7d595f91613db6b3f12d08a +size 3211309 diff --git a/1dAzT4oBgHgl3EQfRfuL/vector_store/index.pkl b/1dAzT4oBgHgl3EQfRfuL/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..81206cf715a2f6f54704e6b09382ea95cc44a0cc --- /dev/null +++ b/1dAzT4oBgHgl3EQfRfuL/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e1126aed6c3c7bf7ef5d49949ed5281e2c255f6682ac71ce44995c435ccf7795 +size 125118 diff --git a/29E1T4oBgHgl3EQf5wUG/content/2301.03514v1.pdf b/29E1T4oBgHgl3EQf5wUG/content/2301.03514v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..89bae21bc200498b3051d3e43664c71238ead590 --- /dev/null +++ b/29E1T4oBgHgl3EQf5wUG/content/2301.03514v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c210ac11556216d3310828e94044130ff2845027612479b55e0ced6b3f65e037 +size 515253 diff --git a/29E1T4oBgHgl3EQf5wUG/vector_store/index.pkl b/29E1T4oBgHgl3EQf5wUG/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..80d9d38aa25b94f07ae2a289eb25f9932340e9d8 --- /dev/null +++ b/29E1T4oBgHgl3EQf5wUG/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:70e2d0cedfd091cab91f624c8bf91cef27a2b0ef26c95401367bdbca96bebfb0 +size 124722 diff --git a/2dFAT4oBgHgl3EQfDhxB/content/2301.08416v1.pdf b/2dFAT4oBgHgl3EQfDhxB/content/2301.08416v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6d8394e7657b7f1acd32a7b46227195c472b4556 --- /dev/null +++ b/2dFAT4oBgHgl3EQfDhxB/content/2301.08416v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b4e49ed0fcd8cbc68b1ec7260e4e205bb33b4d983783e0b47b52f34c36f310be +size 1308603 diff --git a/2dFAT4oBgHgl3EQfDhxB/vector_store/index.faiss b/2dFAT4oBgHgl3EQfDhxB/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..e08e0e2d5fbf9bb70c87b3583a4b43c6cebe4c79 --- /dev/null +++ b/2dFAT4oBgHgl3EQfDhxB/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:472eeac83328726ee5e0e9275323be9e06f1aeb44a169620c8f4e559c06963b8 +size 2752557 diff --git a/2tAzT4oBgHgl3EQf9P4T/content/tmp_files/2301.01915v1.pdf.txt b/2tAzT4oBgHgl3EQf9P4T/content/tmp_files/2301.01915v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..a70404b4269cba2b6af5af5fd9d05c5814d17408 --- /dev/null +++ b/2tAzT4oBgHgl3EQf9P4T/content/tmp_files/2301.01915v1.pdf.txt @@ -0,0 +1,1992 @@ +arXiv:2301.01915v1 [cs.IT] 5 Jan 2023 +CHINA COMMUNICATIONS +Sum-Rate Maximization in Active RIS-Assisted Multi-Antenna +WPCN +Jie Jiang, Bin Lyu, Pengcheng Chen, and Zhen Yang +School of Communications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China +Abstract: +In this paper, we propose an active re- +configurable intelligent surface (RIS) enabled hybrid +relaying scheme for a multi-antenna wireless pow- +ered communication network (WPCN), where the ac- +tive RIS is employed to assist both wireless energy +transfer (WET) from the power station (PS) to energy- +constrained users and wireless information transmis- +sion (WIT) from users to the receiving station (RS). +For further performance enhancement, we propose to +employ both transmit beamforming at the PS and re- +ceive beamforming at the RS. We formulate a sum- +rate maximization problem by jointly optimizing the +RIS phase shifts and amplitude reflection coefficients +for both the WET and the WIT, transmit and receive +beamforming vectors, and network resource alloca- +tion. To solve this non-convex problem, we propose an +efficient alternating optimization algorithm with linear +minimum mean squared error criterion, semi-definite +relaxation (SDR) and successive convex approxima- +tion techniques. Specifically, the tightness of apply- +ing the SDR is proved. +Simulation results demon- +strate that our proposed scheme with 10 reflecting el- +ements (REs) and 4 antennas can achieve 17.78% and +415.48% performance gains compared to the single- +antenna scheme with 10 REs and passive RIS scheme +with 100 REs, respectively. +Keywords: Wireless powered communication net- +work, active reconfigurable intelligent surface, beam- +forming, sum-rate maximization. +Received: XX +Revised: XX +Editor: XX +I. INTRODUCTION +With the development of the Internet-of-Things (IoT), +an intelligent society with ubiquitous interconnections +and deep coverage will be truly realized. However, +wireless devices (WDs) in IoT networks are generally +energy-constrained and suffer from limited lifetime +[1], which fundamentally limits the performance of +communication networks. Traditional ways of chang- +ing or recharging the batteries manually are impossi- +ble and unacceptable, especially when the number of +WDs is numerous. Therefore, how to tackle this issue +is a critical problem in the widespread development of +IoT. Wireless powered communication has been pro- +posed as a prospective technology for enhancing the +energy sustainability of WDs, which can be classified +into two directions based on application scenarios [2– +4]. The first one focuses on investigating simultane- +ous wireless information and power transfer (SWIPT), +where the base station (BS) simultaneously transfers +energy and information signals to energy receivers +and information receivers via the common radio fre- +quency (RF) signals in the downlink (DL), resulting +in a pivotal tradeoff between the achievable rate and +harvested energy [5]. In contrast to the SWIPT, wire- +less powered communication network (WPCN) has +been proposed as a novel type of wireless network di- +agram to improve the lifetime of WDs and enhance +the deployment flexibility of IoT. In a WPCN, energy- +constrained WDs first harvest energy in the DL and +then use the harvested energy to transmit independent +information in the uplink (UL) based on the widely +used harvest-then-transmit (HTT) protocol [6]. +WPCN has been widely investigated in the literature +China Communications +1 + +[6–9], which promotes the development of WPCN. +However, WPCN generally suffers from the “doubly +near-far” phenomenon if the power station (PS) and +the receiving station (RS) are co-located at the hybrid +access point (HAP) [6, 8]. Specifically, a WD located +far away from the HAP harvesting less energy in the +DL has to transmit information with more power in +the UL, which results in an unfair time and resource +allocation among the WDs. To deal with the issue, a +promising way is to deploy the PS and RS separately +[10, 11]. In [10], multiple users harvest energy from a +dedicated PS and then communicate with an informa- +tion RS following the HTT protocol. In this scenario, +a user physically close to the PS is naturally far away +from the RS, and vice versa. Considering a similar +scenario, a user-centric energy-efficient (EE) problem +in WPCN is investigated in [11]. However, the perfor- +mance of WPCN is still limited due to the low efficien- +cies caused by the severe path-loss, which seriously +affects its practical applications. +Recently, reconfigurable intelligent surface (RIS), +with the unprecedented ability to reshape the wireless +transmission environment, has drawn widespread at- +tentions from academia and industry [12–18]. RIS is +comprised of a large number of programmable reflect- +ing elements (REs), which can alter the phase shifts +and amplitudes of incident signals. As such, RIS can +adaptively modify the impinging radio waves towards +the appropriate direction [13]. According to the re- +flection patterns, RIS can be classified as passive RIS +and active RIS. Without the property of power amplifi- +cation, the independent diffusive scatterer-based (IDS) +model accounts for the basic properties of passive RIS, +which has been widely adopted in RIS-assisted wire- +less communications [18]. The passive RIS is only +equipped with the phase-shift controller, while the ac- +tive RIS contains both the phase-shift controller and +the active reflection-type amplifier. Hence, the active +RIS can alter both the phase shifts and amplitudes of +the incident signals. It is worth noting that the active +RIS with its novel hardware structure and signal model +has been proposed in [19, 20]. +Different from the +full-duplex amplify-and-forward (FD-AF) relay that +requires power-consuming RF chains, the active RIS +can directly reflect and amplify the incident signals in +the EM level in a FD manner without reception. In this +way, the active RIS exhibits promising qualities, such +as a low power consumption, light weight, conformal +geometry and high flexibility for practical deployment. +Currently, the passive RIS has been widely applied +in WPCNs for performance enhancement [21–24]. In +[21], the passive RIS is employed between the HAP +and users to improve both DL WET and UL WIT effi- +ciencies in single-input-single-output (SISO) WPCN. +To achieve further performance improvement, the +multi-antenna technique is employed in [22], where +the HAP with multi-antenna transmits energy signals +to users in the DL and receives information from users +in the UL by employing transmit bemforming and re- +ceive beamforming, respectively. +In [23], the fully +dynamic RIS beamforming scheme is proposed for +WPCN, for which the phase shift vectors are indepen- +dently designed over different time slots. However, +in the above works [21–23], the PS and RS are also +co-located at the HAP, which results in performance +unfair among users. +To address this issue, the au- +thors in [24] consider the scenario where the PS and +RS are separately deployed, for which the locations of +RIS and users can be carefully considered to achieve a +fair performance among users. However, as mentioned +above, the passive RIS can only reflect incident signals +without amplification, which leads to the limited per- +formance enhancement due to the double-fading ef- +fect suffered by the reflecting links. Thus, the energy- +constrained users still need to consume much time for +harvesting energy in the DL and have less time for in- +formation transmission. +Inspired by the amplification characteristic of the +active RIS, the active RIS is confirmed to be superior +to the passive RIS in terms of performance enhance- +ment, and thus has been considered a promising tech- +nique for IoT networks [19, 20, 25–29]. The authors +in [19] compare the capacity improvement achieved +by the active RIS to the passive RIS, which demon- +strats that the active RIS can fundamentally mitigate +the double-fading effect. In [20], an active RIS is ap- +plied in single input multiple output (SIMO) systems, +for which the joint optimization of phase shifts ma- +trix and receive beamforming is considered to obtain +the maximum achievable rate. In [25], the placement +of the active RIS is optimized to enhance SISO sys- +tems’ performance. The authors in [26] propose to use +the active RIS to achieve secure transmission, which +not only establishes the reliable link from the trans- +mitter to the receiver but also prevents the confidential +information intercepted by the eavesdropper. The ac- +2 +China Communications + +tive RIS-aided multiuser MISO PS-SWIPT is studied +in [27] to minimize the base station transmit power, +which shows significant improvements compared to +the passive RIS-aided system. Similarly, in [28], an +active RIS is employed to assist SWIPT to boost the +efficiency of both WET and WIT, while the conclu- +sions and approaches are inapplicable to the WPCN +system because of thire different system models. +Although the active RIS has received a lot of inter- +ests for wireless communication networks, the appli- +cations of active RIS in WPCN is still at the very early +stage and has not been well studied in the literature. +To the best of our knowledge, there exists only one +paper investigating the usage of active RIS in WPCN +[29]. Specifically, the authors in [29] investigate the +weight sum-rate maximization problem in the active +RIS assisted single-antenna WPCN, where the PS and +RS is co-located at the HAP. As a result, similar to +[21–23], a part of WDs in [29] still suffer from the +“doubly near-far” phenomenon, which is not suitable +for practical applications with high requirement of per- +formance fairness. Moreover, the authors consider a +certain simplified communication scenario where both +the HAP and the WDs have single antenna each. The +transmit beamforming and receive beamforming can- +not be exploited, which is also a key technology for +performance enhancement. +Motivated by the observations above, we propose +an active RIS enabled hybrid relaying scheme for the +multi-antenna WPCN, where the active RIS is em- +ployed to facilitate both the WET from the PS to +energy-constrained users and the WIT from users to +the RS, which is shown in Figure 1. Compared with +the existing works which used the passive RIS in +WPCN [21–24], our proposed active RIS scheme can +amplify the energy signals and information signals to +achieve a satisfying system performance. +Different +from the single-antenna scenario considered in [29], +we propose to employ multi-antenna at both the PS +and RS, which can construct the transmit beamform- +ing and receive beamforming for further performance +enhancement. Specifically, the transmit beamforming +at the PS can be used to enhance the WPT efficiency +from the PS to users. In the meanwhile, the receive +beamforming at the RS can be used to exploit the an- +tenna gain and eliminate the noise caused by the ac- +tive RIS. In the considered system setup, we aim to +maximize the sum-rate problem by jointly optimiz- +ing the transmit beamforming at the PS, the receive +beamforming at the RS, the reflecting coefficients at +the RIS, and network resource allocation. It should +be noted that compared to [21–24, 29], our formulated +problem is much more challenging to solve and the +proposed algorithms in [21–24, 29] cannot be used to +solve our formulated problem. Thus, we propose an +efficient algorithm to solve the formulated problem. +The main contributions of this paper are summarized +as follows: +• We propose an active RIS assisted multi-antenna +WPCN for performance enhancement, where the +active RIS is served as a hybrid relay to achieve +two purposes, i.e., the first one is to assist the +WET from the PS to users, and the second one +is to aid the WIT from users to the RS. To fur- +ther improve system performance, both trans- +mit beamforming and receive beamforming tech- +niques are respectively considered at the PS and +RS. +• We investigate the sum-rate maximization prob- +lem by jointly optimizing transmit beamforming +vector at the PS, receive beamforming vectors at +the RS, phase shifts and amplitude reflection coef- +ficients at the RIS for both the WET and the WIT, +and network resource allocation. To deal with the +non-convexity of the formulated problem, we pro- +pose an efficient alternating optimization (AO) al- +gorithm. Specifically, the original problem can be +divided into four sub-problems, which are solved +sequentially in an alternating manner until con- +vergence is achieved. +• For designing the receive beamforming, we apply +the linear minimum mean squared error (MMSE) +criterion and obtain the closed-form expression. +For the optimization of the transmit beamform- +ing and RIS reflecting coefficient matrices for +the WET, the semidefinite relaxation (SDR) tech- +nique is adopted and the tightness of applying the +SDR is proved. For the optimization of RIS re- +flecting coefficients for the WIT, we obtain the +optimal phase shifts in a closed-form and propose +a successive convex approximation (SCA) algo- +rithm to determine the optimal amplitude reflec- +tion coefficients. In addition, the convergence of +proposed problem is analyzed and confirmed via +numerical simulations. +China Communications +3 + +• Finally, numerical results are provided to evaluate +the performance of proposed scheme, which indi- +cates that compared to the single-antenna scheme +with 10 REs and the passive-RIS scheme with 100 +REs, the proposed scheme with 4 antennas and 10 +REs can achieve 17.78% and 415.48% sum-rate +gain, respectively. +The rest of this paper is organized as follows. Sec- +tion II describes the system model of the active RIS- +assisted multi-antenna WPCN. The sum-rate maxi- +mization problem is formulated in Section III and +solved in Section IV, respectively. In Section V, per- +formance is evaluated by numerical results. Finally, +this paper is concluded in Section VI. +Notations: In this paper, vectors and matrices are +denoted by boldface lowercase and uppercase letters, +respectively. The operators ( · )T, ( · )H, | · | and ∥ · ∥ +denote the transpose, conjugate transpose, absolute +value and the Euclidean norm, respectively. Tr( · ) and +rank( · ) denote the trace and rank of a matrix, respec- +tively. X ⪰ 0 represents that X is a positive semidef- +inite matrix. E[ · ] stands for the statistical expecta- +tion. IN denotes the N-dimensional identity matrix. +0 denotes the zero matrix/vector with appropriate size. +CN×M denotes the set of all N × M complex-valued +matrices. HM denotes the set of all M ×M Hermitian +matrices. RN×1 represents the set of all N × 1 real- +valued vectors. CN +� +µ, σ2� +denotes the distribution of +a circularly symmetric complex Gaussian random vec- +tor with mean µ and variance σ2. arg( · ) denotes the +phase extraction operation. diag(x) denotes a diago- +nal matrix whose diagonal elements are from vector x. +Im( · ) and Re( · ) respectively denotes the imaginary +part and real part of a complex number. +II. SYSTEM MODEL +As shown in Figure 1, we consider an active RIS-aided +multi-antenna WPCN, which consists of a PS with M +antennas, a RS with L antennas, an active RIS, and +K energy-constrained users each with single antenna. +We assume that each user is equipped with an energy +harvesting (EH) circuit for harvesting energy, where +a rectifier is used to convert the received RF signals +to direct current (DC) signals. Then, the net energy +harvested from the DC signals can be stored in the +rechargeable battery. The active RIS consists of N +active REs, which can steer the reflected signals in +��,� +� +��,� +� +��,� +��,� +�� +�� +PS +RS +�� +Active RIS +Energy transfer +Information transmission +EH circuit +Rectifier +RF signal +Rechargeable +battery +DC signal +Figure 1. +System model for an active RIS-assisted multi- +antenna WPCN. +a specific direction and also amplify them by the ac- +tive loads (negative resistance) [20]. In contrast to the +passive RE, each active RE is equipped with an addi- +tionally integrated active reflection-type amplifier sup- +ported by a power supply. By appropriately setting the +effective resistance, it is reasonable to assume that the +reflection amplitude and phase of each element is inde- +pendently [19, 20, 25–29]. To power the operations of +active RIS and users, the PS is equipped with a stable +energy source. In addition, the PS has the capability +for performing computational tasks [21]. In particu- +lar, the users first harvest energy from the RF signals +transmitted by the PS and then use the harvested en- +ergy to deliver information to the RS. To allievate the +severe path-loss suffered by the reflecting links, the ac- +tive RIS is employed to improve the WET efficiency +from the PS to users and the WIT efficiency from the +users to the RS. +The channels are assumed to follow a quasi-static +flat-fading model. +That is, all channel coefficients +are constant throughout each transmission block but +vary from block to block [30]. The downlink base- +band equivalent channels of PS-to-RIS, RIS-to-Uk, +and PS-to-Uk links are denoted by Hr ∈ CN×M, +hH +u,k ∈ C1×N, and hH +d,k ∈ C1×M, respectively, where +Uk denotes the k-th user. Similarly, the uplink base- +band equivalent channels of Uk-to-RIS, RIS-to-RS, +and Uk-to-RS links are respectively denoted by gu,k ∈ +CN×1, Gr ∈ CL×N, and gd,k ∈ CL×1, respectively. +Since there have been many efficient channel estima- +4 +China Communications + +用tion techniques proposed for RIS systems [31–34], we +assume the perfect channel state information can be +available in advance, which is a common assumption +considered in [21, 22, 35] and a prerequisite for inves- +tigating the upper-bound of system performance. It +should be noted that the channel estimation error is +generally inevitable [31]. However, the effect of chan- +nel estimation error on system performance degrada- +tion is out the scope of this paper. +According to the HTT protocol [6], the normalized +transmission block of interest is divided into K + 1 +time slots. The first time slot with duration of τ0 ∈ +[0, 1] is a dedicated slot for WET, in which all users +harvest energy from the PS with the assistance of +active RIS. The remaining K time slots denoted by +τ = [τ1, . . . , τK], are used for UL WIT via the time di- +vision multiple access (TDMA) scheme. Specifically, +during τk, k = 1, · · · , K, Uk delivers its information +to the RS. Without loss of generality, the whole oper- +ation time period is set to a normalized transmission +block. The network time scheduling constraint is thus +given by +τ0 + +K +� +k=1 +τk ≤ 1, ∀k. +(1) +2.1 Wireless Energy Transfer Phase +In the WET phase, the PS transmits energy signals to +all users with the assistance of the active RIS. Denote +the transmitted signal as s = w0s, where s is the +pseudo-random baseband signal transmitted by the PS, +and w0 ∈ CM×1 is the transmit beamforming vector. +The energy constraint at the PS is expressed as +E +� +|s|2� += Tr +� +w0wH +0 +� +≤ P0, +(2) +where P0 denotes the maximum transmit power at the +PS. +The reflecting coefficient matrix of the active +RIS in the WET phase is denoted by Φ0 += +diag {φ0,1, . . . , φ0,N} +∈ +CN×N +with +φ0,n += +a0,nejθ0,n, n = 1, . . . , N, where a0,n and θ0,n rep- +resent the amplitude reflection coefficient and phase +shift of the n-th RE, respectively. Without loss of gen- +erality, we suppose each active RE has the following +constraints +a0,n ≤ an,max, 0 ≤ θ0,n ≤ 2π, ∀n, +(3) +where an,max is the maximum amplitude reflection co- +efficient of n-th RE. It is worth noting that an,max can +be greater than 1 [25], which is a main characteris- +tic distinguishing the active RIS from the passive RIS +since the active load can amplify the reflected signals. +The received signal at Uk during τ0 is given by +yu,k = hH +d,ks +� �� � +direct link ++ hH +u,kΦ0 (Hrs + nv) +� +�� +� +RIS-aided link ++nu,k, ∀k, +(4) +where nu,k ∈ C and nv ∈ CN×1 represent the ad- +ditive white Gaussian noise (AWGN) at Uk and the +RIS, respectively. Without loss of generality, we as- +sume nu,k ∼ CN +� +0, σ2 +u,k +� +and nv ∼ CN +� +0, σ2 +vIN +� +. +Denote the equivalent downlink channel as hH +k += +hH +u,kΦ0Hr + hH +d,k ∈ C1×M and (4) can be rewritten +as +yu,k = hH +k w0s + hH +u,kΦ0nv + nu,k, ∀k. +(5) +Due to the fact that the active RIS not only amplifies +the desired signal, i.e., s, but also amplifies the input +noise, i.e., nv, it is reasonable to consider the second +term of (4) for computing the amount of harvested en- +ergy accurately [20]. However, the noise at Uk is gen- +erally quite small and can be negligible. Accordingly, +the harvested energy by Uk, denoted by Ek, is given +by +Ek = β +��hH +k w0 +��2τ0 + β +��hH +u,kΦ0 +��2σ2 +vτ0, ∀k, +(6) +where β ∈ (0, 1] denotes the energy conversion effi- +ciency of each user. It is practical for us to consider +the linear EH model here, which is also a common as- +sumption in the literature [6, 8, 11, 10, 22, 29]. +It is worth noting that the active RIS can allocate +the available reflecting power to amplify the incident +signals with active loads [20]. In the DL WET phase, +the amplification power of s and nv is limited by the +RIS power budget, which is shown by the following +constraint +P0 ∥Φ0Hr∥2 + σ2 +v ∥Φ0IN∥2 ≤ Pr, +(7) +where Pr is the maximum reflecting power for ampli- +fication at the active RIS and substantially lower than +that of an active RF amplifier [25]. +China Communications +5 + +2.2 Wireless Information Transmission Phase +In the WIT phase, the users utilize the harvested en- +ergy to transmit information to the RS via a TDMA +manner. Let fk denotes the information-carrying sig- +nal of Uk with unit power and then the transmit signal +during τk is denoted by xk = √pkfk, where pk is the +transmit power at Uk. We assume that all the harvested +energy at Uk in the WET phase is used for delivering +its own information. Let p = [p1, . . . , pK] ∈ R1×K, +which satisfies +pkτk ≤ Ek, ∀k. +(8) +Similarly, the reflecting coefficient matrix at the +active RIS for the WIT during τk is denoted by +Φk = diag {φk,1, . . . , φk,N} ∈ CN×N, where φk,n = +ak,nejθk,n, ak,n and θk,n have the following constraints +ak,n ≤ an,max, 0 ≤ θk,n ≤ 2π, ∀k, ∀n. +(9) +The received signal at the RS from Uk with the as- +sistance of active RIS during τk is written as +yr,k = gH +d,kxk +� �� � +direct link ++ GrΦk (gu,kxk + nv) +� +�� +� +RIS-aided link ++nr, ∀k, +(10) +where nr ∈ CL×1 represents the AWGN at the RS and +satisfies nr ∼ CN +� +0, σ2 +rIN +� +. +In the UL WIT phase, we also have the amplification +power constraint at the active RIS as follows +pk ∥Φkgu,k∥2 + σ2 +v ∥ΦkIN∥2 ≤ Pr, ∀k. +(11) +Denote the receive beamforming vector at the RS +during τk as wk ∈ CL×1, which can be used to ex- +tract the desired signal and suppress interference and +noises. Let the equivalent uplink channel be gk = +gd,k + GrΦkgu,k, ∀k. The estimated signal at the RS +during τk is expressed as +uk =wH +k yr,k +=wH +k gkxk + wH +k GrΦknv + wH +k nr, ∀k. +(12) +Then, the signal-noise-ratio (SNR) at the RS during +τk is written as +γk = pk +��wH +k (GrΦkgu,k + gd,k) +��2 +��wH +k GrΦk +��2 σ2v + ∥wk∥2 σ2r +, ∀k. +(13) +Denote the achievable rate from Uk to the RS as Rk, +which is formulated as +Rk = τk log (1 + γk) , ∀k. +(14) +III. PROBLEM FORMULATION +In this section, we formulate the system sum-rate max- +imization problem by jointly optimizing the reflecting +coefficients for both the WET and the WIT at the ac- +tive RIS, the transmit beamforming at the PS, the re- +ceive beamforming at the RS, the transmit power at +each user, and the network time scheduling. The opti- +mization problem is formulated as +(P1) +max +τ0,τ,Φ0,Φk,w0,p,wk +K +� +k=1 +Rk +(15) +s.t. +(1), (2), (3), (7), (8), (9) and (11), +τ0 ≥ 0, τk ≥ 0, pk ≥ 0, ∀k. +(16) +where (16) indicates that the time and power variables +are all nonnegative. +One can observe that the objective function in (15) +is a non-concave function due to the coupled of vari- +ables. In addition, there exists several non-convex con- +straints, i.e., (2), (7), (8) and (11). It is thus challeng- +ing to solve P1 directly by standard optimization tech- +niques. In the next section, we propose an AO algo- +rithm to solve it efficiently. +IV. ALTERNATING OPTIMIZATION SO- +LUTION +In this section, an efficient AO algorithm is proposed +to solve P1. In particular, we decompose P1 into sev- +eral subproblems and iteratively solve them in an al- +ternating manner. To show the procedure of AO algo- +rithm, we summarize a flow chart in Figure 2. Specif- +ically, the variables are partitioned into four blocks, +{wk}, {w0, τ, p}, {Φ0, τ0, τ, p}, and {Φk}. Then, +the variables in each block are alternately solved by +6 +China Communications + +Linear MMSE-based Receive +Beamforming Optimization +SDP-based Transmit +Beamforming Optimization +SDP-based RIS Reflecting Coefficients for the +WET and Resource Allocation Optimization +SCA-based RIS Reflecting Coefficients +Optimization for the WIT +System Variables +�, �, �� , �� +��, ��, �� +�, {��} +{��} +�� , �� , ��, �� +�� +�, � +Discarding +��, �� , �� +��, ��, +�, � +�, �� +�� +AO iteration flow +Update +Input +Figure 2. A flow chart of the proposed algorithm. +its corresponding sub-problem with the other blocks +fixed until the convergence is achieved. +4.1 Linear MMSE-based Receive Beamform- +ing Optimization +With the other variables fixed, we first design the re- +ceive beamforming vectors {wk}. To cope with the +interference caused by nv and nr in (13), we apply +the linear MMSE criterion here. Based on this crite- +rion, the MMSE-based receive beamforming is given +by +w∗ +k = +� +gkgH +k + σ2 +v +pk +GrΦkΦH +k GH +r + σ2 +r +pk +IL +�−1 +gk, ∀k. +(17) +4.2 SDP-based Transmit Beamforming Opti- +mization +We then proceed to optimize {w0, τ, p} with the other +variables {wk, Φ0, τ0, Φk} fixed. Letting ek = pkτk +and e = [e1, . . . , eK] and applying the obtained results +in (17), P1 can be simplified as follows +(P2) max +w0,τ,e +K +� +k=1 +τk log +� +1 + ǫk +ek +τk +� +(18) +s.t. +ek ≤ Ek, ∀k, +(19) +τk ≥ 0, ek ≥ 0, ∀k, +(20) +(1), (2) and (11), +where ǫk += +|(w∗ +k)H(GrΦkgu,k+gd,k)| +2 +∥(w∗ +k)HGrΦk∥ +2σ2v+∥w∗ +k∥ +2σ2r , ∀k. +It +can be found that P2 is highly non-convex. +To +solve it efficiently, the SDR technique [36] is em- +ployed. +Define Hk += +hkhH +k , and Gu,k += +diag +� +|gu,k,1|2 , |gu,k,2|2 , . . . , |gu,k,N|2� +, +∀k. +Let +W0 += +w0wH +0 , which satisfies W0 +⪰ +0 and +rank(W0) = 1. Then, (19) is rewritten as +ek ≤ βτ0[Tr (HkW0) + +��hH +u,kΦ0 +��2 σ2 +v], ∀k. +(21) +Denote the RIS reflecting coefficient vector for the +WET as ϕk = [φk,1, φk,2, . . . , φk,N]T, ∀k, (11) can +be recast as +ekϕH +k Gu,kϕk + τkσ2 +vϕH +k ϕk ≤ τkPr, ∀k. +(22) +Then, P2 can be equivalently transformed into +(P2-1) max +W0,τ,e +K +� +k=1 +τk log +� +1 + ǫk +ek +τk +� +(23) +s.t. +Tr (W0) ≤ P0, +(24) +W0 ⪰ 0, +(25) +rank(W0) = 1, +(26) +(1), (20), (21) and (22). +Since the rank-one constraint in (26) is non-convex, +we employ the SDR technique to relax it. Thus, P2-1 +becomes to be a convex semidefinite program (SDP) +and can be solved with the interior-point method [37]. +Proposition 1. The optimal transmit beamforming +matrix obtained by solving the relaxed version of P2-1, +denoted by W ∗ +0 , is rank-one. +Proof. Please refer to Appendix A. +According to Proposition 1, the tightness of SDR +is guaranteed. Hence, we can employ Cholesky de- +composition to obtain the optimal energy beamform- +ing vector w∗ +0. +4.3 SDP-based RIS Reflecting Coefficients for +the WET and Resource Allocation Opti- +mization +In this sub-section, we focus on optimizing the re- +flecting beamforming at the RIS in the WET phase, +the transmit power at each user, and the network +time scheduling. +Since τ0 and Φ0 are coupled, +we first optimize {Φ0, τ, p} with τ0 given. Define +Ψ0 = ˜ϕ0 ˜ϕH +0 with Ψ0 ⪰ 0 and rank(Ψ0) = 1, +where ˜ϕ0 = [ϕH +0 , 1]H and ϕ0 = [φ0,1, . . . , φ0,N]T . +China Communications +7 + +Let Hu,k = diag {hu,k,1, . . . , hu,k,N} and Qu,k = +diag +� +|hu,k,1|2 , . . . , |hu,k,N|2 , 1 +� +. Then, (7) and (19) +are respectively reformulated as +P0Tr( ˜ +HrΨ0) + σ2 +vTr(Ψ0) ≤ Pr, +(27) +ek ≤ βτ0Tr[(V + σ2 +vQu,k)Ψ0] − βτ0σ2 +v, ∀k, (28) +where +V = +�HH +u,kHrW0HH +r Hu,k +HH +u,kHrW0hd,k +hH +d,kW0HH +r Hu,k +hH +d,kW0hd,k +� +, +and +˜ +Hr = +�HrHH +r +0 +0 +0 +� +. +With the obtained solutions in Sections 4.1 and 4.2, +P1 can be equivalently written as +(P2-2) max +Ψ0,τ,e +K +� +k=1 +τk log +� +1 + ǫk +ek +τk +� +(29) +s.t. +Ψ0 ⪰ 0, rank(Ψ0) = 1, +(30) +[Ψ0]n,n ≤ a2 +max, ∀n, +(31) +[Ψ0]N+1,N+1 = 1, +(32) +(1), (20), (22), (27) and (28). +Similarly, after the relaxation of the rank-one con- +straint in (30), P2-2 is also an SDP and can be solved +by the interior-point method. Recall that the tightness +of optimizing W0 by SDR can be guaranteed, we can +also prove that the obtained solution Ψ0 is rank-one. +Then, ˜ϕ0 can be recovered by implementing Cholesky +decomposition of Ψ0, and the optimal reflection co- +efficient vector for the WET ϕ∗ +0 can be obtanied by +linear operation from ˜ϕ0. Subsequently, the optimal +RIS reflecting coefficient matrix Φ∗ +0 can be obtained +by Φ∗ +0 = diag((ϕH +0 )∗). +Finally, we continue to update the optimal energy +transmission time τ0 ∈ [0, 1] by the one-dimensional +search method. Thus, the maximum sum-rate of this +sub-problem is achieved with the optimal solution +{Φ∗ +0, τ ∗ +0 , τ ∗, p∗}. The procedure is summarized in Al- +gorithm 1. +Algorithm 1. SDP-based RIS reflecting coefficients for the WET +and resource allocation optimization +Input: w0, {wk}, {Φk}, ∀k +Output: Φ∗ +0, τ ∗ +0 , τ ∗, p∗ +1: Initialization: The maximum objective function +value Rmax = 0 and the step size δ. +2: for τ0 = 0 : δ : 1 do +3: +Given w0, {wk}, {Φk}, we obtain τ ′ +0, Ψ′ +0, τ ′ +k, +e′ +k, ∀k by solving P2-2. +4: +Calculate R = �K +k=1 τ ′ +k log +� +1 + ǫk +e′ +k +τ ′ +k +� +. +5: +if R > Rmax then +6: +Update Rmax ← R. +7: +Update τ0 ← τ ′ +0, Ψ0 ← Ψ′ +0, τk ← τ ′ +k, ek ← +e′ +k. +8: +end if +9: end for +10: Obtain ˜ϕ0 from Ψ0 by Cholesky decomposition. +11: Obtain ϕ0 from ˜ϕ0. +12: Set Φ∗ +0 = diag((ϕH +0 )∗). +13: Calculate p∗ +k = e∗ +k/τ ∗ +k. +14: return Φ∗ +0, τ ∗ +0 , τ ∗, p∗. +4.4 SCA-based RIS Reflecting Coefficients +Optimization for the WIT +In this sub-section, we investigate the optimization of +RIS reflecting coefficient matrix Φk in the WIT phase, +which is given by +(P3) max +Φk +K +� +k=1 +Rk +(33) +s.t. +(9) and (11). +Note that P3 is still a non-convex optimization prob- +lem as the active RIS introduces additional noise term +in the denominator of the objective function, which re- +sults in a quadratic fractional programming problem. +In fact, the RIS reflecting coefficients include ampli- +tude reflection coefficients and phase shifts. To sim- +plify this problem, we derive the optimal phase shifts +in the closed-form and then exploit an SCA algorithm +to obtain the near-optimal amplitude reflection coeffi- +cients according to [20]. +It is worth noting that P3 can be decomposed into K +8 +China Communications + +independent subproblems, each of which maximizes +the SNR of Uk at the RS during τk with respect to the +RIS reflection coefficient vector ϕk. Specifically, with +w∗ +k obtained in (17) and introducing some new aux- +iliary variables, the k-th SNR maximization problem +can be formulated as +γk = pk +��bH +k ϕk + gd,k +��2 +ϕH +k Qrϕkσ2v + σ2r +, +(34) +where gd,k += +wH +k gd,k, gH +r,k += +wH +k Gr, bH +k += +gH +r,kdiag (gu,k), Qr = diag +� +|gr,k,1|2 , . . . , |gr,k,N|2� +, +∀k. Let Fk = pkGu,k + σ2 +vIN, ∀k. The subproblem +can be expressed as +(P4) max +ϕk +γk +(35) +s.t. +ϕH +k Fkϕk ≤ Pr, ∀k, +(36) +(9). +To solve P4, we decompose the optimization of RIS +reflecting coefficient vector ϕk into two sub-problems +for the amplitude reflection coefficient design and the +optimal phase shift design, respectively. Let ϕk = +Θk ¯ϕk, where Θk += +diag +� +ejθk,1, . . . , ejθk,N� +∈ +CN×N and ¯ϕk = [ak,1, . . . , ak,N]T ∈ RN×1. +4.4.1 Optimization of phase shifts for the WIT +The optimal design of phase shifts is given in the fol- +lowing proposition. +Proposition 2. The optimal RIS phase shift of the n-th +RE for the WIT during τk is derived as +θ∗ +k,n = arg(gd,k) − arg(gu,k,n) + arg(gr,k,n), (37) +∀k, ∀n, +where gu,k,n and gr,k,n denote the n-th element of the +vector gu,k and gr,k, respectively. +Proof. Please refer to Appendix B. +4.4.2 Optimization of amplitude reflection coeffi- +cients for the WIT +For P4, the optimal design of phase shifts shown in +Proposition 2 holds because the value of the ampli- +fication power in (9) and (36) and the noise power +in the denominator of (34) are independent with the +phase shift of each RE. In addition, optimizing θk,n +is equivalent to maximizing the objective function in +(34) [20]. With the optimal phase shifts in Proposition +2, we proceed to optimize the RIS amplitude reflec- +tion coefficients for the WIT. In particular, P4 can be +simplified as +(P4-1) max +¯ϕk +¯γk = pk +��¯bH +k ¯ϕk + |gd,k| +��2 +¯ϕH +k Qr ¯ϕkσ2v + σ2r +(38) +s.t. +¯ϕH +k Fk ¯ϕk ≤ Pr, ∀k, +(39) +ak,n ≤ an,max, ∀k, ∀n, +(40) +where ¯γk = |γk|, and ¯bk is element-wise modulus +of bk. To deal with the non-convexity of the objec- +tive function (38), we introduce a new auxiliary vari- +able nk = ¯ϕH +k Qr ¯ϕkσ2 +v + σ2 +r, which denotes the noise +power received at the RIS. Then, P4-1 can be con- +verted into the following equivalent form +(P4-2) max +¯γk,nk, ¯ϕk ¯γk +(41) +s.t.√pk +�¯bH +k ¯ϕk + |gd,k| +� +≥ √nk¯γk, ∀k, +(42) +¯ϕH +k Qr ¯ϕkσ2 +v + σ2 +r ≤ nk, ∀k, +(43) +(39) and (40). +However, the constraint (42) is still non-convex. To +solve P4-1 efficiently, we exploit the SCA algorithm to +approximate the square root by a convex upper-bound +in each iteration. Define ¯γk(t) and nk(t) as the iter- +ative optimization variables after the t-th step itera- +tion. In terms of {¯γk (t) , nk (t)}, the first-order Tay- +lor polynomial is used to approximate √nk¯γk, which +is given by +√nk¯γk ≤G(¯γk, nk; t) += +� +¯γk(t)nk(t) + 1 +2 +�nk(t) +¯γk(t) +� 1 +2 +[ ¯γk − ¯γk(t)] ++ 1 +2 +� ¯γk(t) +nk(t) +� 1 +2 +[n − nk(t)] . +(44) +Based on (44), (42) can be rewritten as +√pk +�¯bH +k ¯ϕk + |gd,k| +� +≥ G(¯γk, nk; t), ∀k. +(45) +China Communications +9 + +Then, P4-2 can be reformulated as the following +problem +(P4-3) max +¯γk,nk, ¯ϕk ¯γk, +(46) +s.t.(39), (40), (43) and (45). +As P4-3 is convex and can be solved by the inter- +point method. We then discuss the initialization of +¯γk(t) and nk(t). First, we propose an initial solution +¯ϕk(0) by solving a simple feasible version of problem +P4-1, i.e., ¯ϕk(0), satisfying the constraints (39) and +(40). Then, the reasonable initialization of ¯γk(0) and +nk(0) is given by +¯γk(0) = pk +��¯bH +k ¯ϕk(0) + |gd,k| +��2 +σ2v ¯ϕH +k (0)Qr ¯ϕk(0) + σ2r +, +(47) +nk(0) = σ2 +v ¯ϕH +k (0)Qr ¯ϕk(0) + σ2 +r. +(48) +With the initialization described in (47) and (48), the +optimal amplitude reflection coefficients for the WIT, +denoted by ¯ϕ∗ +k, can be obtained by iteratively solving +P4-3 until the convergence is achieved. As a result, the +RIS reflecting coefficients during τk can be calculated +by +Φ∗ +k = diag (Θ∗ +k ¯ϕ∗ +k) , ∀k, +(49) +where Θ∗ +k = diag{ejθ∗ +k,1, . . . , ejθ∗ +k,N}. +The detailed description of optimizing the RIS re- +flecting coefficients in P3 is summarized in the Algo- +rithm 2. +Algorithm 2. SCA-based RIS reflecting coefficients for the WIT +Input: {wk}, p, ∀k +Output: {Φ∗ +k}, ∀k +1: Initialization: ¯γk(t), nk(t), ¯ϕk(t), and t = 0. +2: Obtain θ∗ +k,n in Proposition 2 and have Θ∗ +k. +3: repeat +4: +t = t + 1. +5: +Update ¯γk(t), nk(t), ¯ϕk(t) by solving P4-3. +6: until the convergence is achieved. +7: Obtain Φ∗ +k = diag (Θ∗ +k ¯ϕ∗ +k), where ¯ϕ∗ +k = ¯ϕk(t). +8: return {Φ∗ +k}. +4.5 Algorithm Summarization and Analysis +Based on the above analysis, the algorithm for solving +P1 is summarized in Algorithm 3. Based on the opti- +mality analysis,the objective function of P1 is a non- +decreasing function. Due to the power budget con- +straint (2), (7) and (11), the optimal objective value +of problem P1 is bounded. Hence, the convergence +of Algorithm 2 can be thus guaranteed, which will be +also confirmed by numerical simulations in Section V. +4.5.1 Complexity Analysis +The computational complexity of our proposed AO +algorithm is analyzed as follows, which contains +the linear MMSE-based receive beamforming cal- +culation, the SDR algorithm and the SCA algo- +rithm in each iteration. +For the linear MMSE- +based receive beamforming optimization, we derive +a closed-form solution to the (17), and the approx- +imate worst-case computational complexity is given +by O +� +KL max(N, L)2� +. +According to [36], for +the subproblem of SDP-based transmit beamform- +ing optimization, the worst-case computational com- +plexity is O +� +max(K, M)4.5 log(1/ǫ) +� +, where ǫ is the +computational accuracy of the interior-point method +in CVX. Similarly, for the SDP-based RIS reflect- +ing coefficients for the WET and resource alloca- +tion optimization, the worst-case computational com- +plexity is O +� +Iτ max(N, K)4.5 log(1/ǫ) +� +, where Iτ +is the iteration number for updating τ0. +For the +SCA-based RIS reflecting coefficients optimization in +the WIT, the computational complexity is less than +O +� +ISKN 3.5 log(N/ǫ) +� +, where IS is the iteration +number for the SCA algorithm. Thus, the computa- +tional complexity of the overall AO algorithm is given +by +O +� +IA +� +KL max(N, L)2 + max(K, M)4.5 log(1/ǫ) ++Iτ max(N, K)4.5 log(1/ǫ) + ISKN 3.5 log(N/ǫ) +�� +, +(50) +where IA denotes the number of iterations required for +convergence. +4.5.2 Optimality Analysis +As the formulated problem P1 is extremely non- +convex, it is very difficult to obtain the globally op- +timal solution. To solve P1 efficiently, we propose +10 +China Communications + +an efficient AO algorithm to obtain the suboptimal so- +lutions. Firstly, we obtain the optimal receive beam- +forming {wk} in a closed-form, which are the globally +optimal solutions. With the obtained receive beam- +forming solutions, the formulated problem can be sim- +plified but is still non-convex. +Secondly, the SDR +technique is adopted to optimize the transmit beam- +forming, the RIS reflecting coefficient matrices for +the WET phase, the transmit power at each user, and +the network time scheduling. In particular, we prove +the obtained solutions of P2-1 and P2-2 are rank-one. +Since the tightness of applying SDR can be guaran- +teed, the obtained solutions {w0, Φ0, τ, p} are glob- +ally optimal [23]. Then, we use the one-dimensional +search method to exploit the optimal energy trans- +mission time τ0 by setting an appropriate step size. +Thirdly, for the optimization of RIS reflecting coef- +ficients for the WIT phase, we decompose P4 into two +sub-problems. On the one hand, the optimal phase +shifts have been derived in a closed-form which has +been proved. On the other hand, P4-1 is solved by +Algorithm 2, which obtains the reflection amplitudes +of {Φk} are near-optima of the original problem [38]. +Hence, Algorithm 3 can be used to obtain the near- +optimal solutions to P1 with a high accuracy. +Algorithm 3. AO algorithm for P1 +1: Initialization: w0, {wk}, Φ0, {Φk}, τ0, τ, p, ∀k. +2: repeat +3: +Given Φk and p, update {wk} by (17). +4: +Given Φ0, τ0, {Φk}, {wk}, update w0 with by +solving P2-1. +5: +Given w0, {wk}, {Φk}, update Φ0, τ0, τ and p +by Algorithm 1. +6: +Given {wk} and p, update {Φk} by Algorithm +2. +7: until �K +k=1 Rk converged. +8: return w∗ +0, {w∗ +k}, Φ∗ +0, {Φ∗ +k}, τ ∗ +0 , τ ∗, p∗. +V. NUMERICAL RESULTS +In this section, numerical results are presented to eval- +uate the performance of the proposed scheme. +As +shown in Figure 3, we consider that the simulated net- +work deployment is a 2-D coordinate system, where +��� +�� + (!) +(0,0) +( ", 0) +( #, 0) +$(!) +( %, &) +��������� +�� +Figure 3. Placement model of simulation setup. +the coordinates of the PS, the RIS, and the RS are +given as (0,0), (xr, 0), and (xs,0), respectively, the +users are randomly deployed within a circular area +centered at (xu, xh) with radius 1m. We follow the +channel model considered in [29]. In particular, the +large-scale path-loss is modeled as L = A(d/d0)−α, +where A is the path-loss at the reference distance +d0 = 1m and set as A = −30dB, d denotes the dis- +tance between two nodes, and α is the path-loss expo- +nent. For the RIS related links, the path-loss exponent +is set as 2.2 since the location of RIS can be carefully +designed to avoid the severe signal blockage. While +the path-loss exponents for the RIS unrelated links are +set as 3.5 due to the users’ random deployment. We +assume the direct link channels follow Rayleigh fad- +ing but the RIS related channels follow Rician fading. +Specifically, the small-scale channel from the PS to the +RIS can be expressed as +Hr = +�� +βr +βr + 1 +¯ +HLoS +r ++ +� +1 +βr + 1 +¯ +HNLoS +r +� +(51) +where βr is the Rician factor for the PS-RIS link, +¯ +HLoS +r +denotes the deterministic line of sight (LoS) +component, and ¯ +HNLoS +r +denotes the non-LoS compo- +tent with circularly symmetric complex Gaussian ran- +dom variables with zero mean and unit variance. The +other channels can be similarly defined. Unless oth- +erwise stated, other parameters are given as follows: +βr = 10 [39], ρ = 0.8, σ2 +v = σ2 +r = −90dBm, +P0 = 20dBm [20], Pr = 20dBm, amax = 25dB +[40], N = 10, K = 4, M = 4, L = 4, xr = 10m, +xu = 10m, xs = 20m, and xh = 2m. +For comparisons, we also evaluate the performance +of the following benchmark schemes: +(1) Active RIS-aided single-antenna WPCN scheme +(Active-SA). +China Communications +11 + +(2) Passive RIS-aided multi-antenna WPCN scheme +(Passive-MA). +(3) Active RIS-aided multi-antenna WPCN with uni- +form energy beamforming scheme (Active-MA- +UEBF). +Notice that for the multi-antenna schemes, the num- +ber of antennas is set as 4 in the PS and RS. In addition, +we set the number of REs in the Passive-MA scheme +as N = 100 to show the superiority of the proposed +scheme. +Before performance comparisons, we first show the +convergence performance of the proposed AO algo- +rithm in Figure 4. One can observe that as the num- +ber of iterations increases, the sum-rate first increases +but finally converges to a constant after nearly 8 iter- +ations. This demonstrates that the convergence of the +proposed scheme can be achieved quickly. The other +observation is that the effect of the parameter setting +on convergence is limited. +2 +4 +6 +8 +10 +12 +Number of iterations +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +Sum rate (bps/Hz) +N=10, M=L=4 +N=10, M=L=8 +N=20, M=L=4 +N=20, M=L=8 +N=30, M=L=4 +N=30, M=L=8 +Figure 4. +Convergence behavior of the proposed scheme +under different parameter settings. +Figure 5 shows the impact of the transmit power +at the PS (i.e., P0) on the sum-rate when the RIS’s +maximum reflecting power Pr = 10, 20 dBm and +the RIS’s maximum amplitude reflection coefficient +amax = 10, 25 dB, respectively. In general, the pro- +posed scheme outperforms the Active-SA scheme with +the same parameters, which confirms that the assis- +tance of multiple antennas can achieve a significant +performance gain by constructing the transmit beam- +forming at the PS and the receive beamforming at the +RS. For a given amax = 25 dB, our proposed scheme +with 10 REs can achieve 415.48% performance gain +5 +10 +15 +20 +25 +30 +35 +40 +45 +Transmit power at the PS(dBm) +0 +5 +10 +15 +20 +25 +30 +35 +Sum rate (bps/Hz) +Proposed, Pr=20, amax=25 +Proposed, Pr=20, amax=10 +Proposed, Pr=10, amax=25 +Proposed, Pr=10, amax=10 +Active-SA, Pr=20, amax=25 +Active-SA, Pr=20, amax=10 +Passive-MA, N=100 +Figure 5. Sum-rate versus the transmit power at the PS. +compared to the passive RIS scheme with 100 REs +when P0 = 20 dBm. Indeed, the active RIS can con- +siderably make use of its amplification characteristic +to amplify the energy signals at low transmit power +and thereby realize a superior capability at the cost of +additional power consumption. For a given amax = 10 +dB, it can be seen that the sum-rates achieved by the +proposed scheme with Pr = 20 dBm and Pr = 10 +dBm are almost the same, which implies that the am- +plification power constraints defined in (7) and (11) +are inactive since amax is limited for the small trans- +mit power. Note that, the performance gap is signif- +icant between the scheme with amax = 25 dB and +amax = 10 dB because amax directly limits the ampli- +tude reflection coefficient of the active RIS. In addi- +tion, the sum-rate of the passive-MA scheme is gener- +ally lower than the active RIS schemes with the same +REs and the passive RIS needs to be equipped with +more REs (e.g., 100 REs) to achieve the similar per- +formance. +In Figure 6, we evaluate the sum-rate versus the +number of reflecting elements at the RIS. It can be +seen that the proposed schemes can achieve a higher +performance gain compared with the other benchmark +schemes. With an increasing number of reflecting ele- +ments, the sum-rate increases due to the fact that more +transmission links can be provided for both the WET +and the WIT. In addition, to investigate the best system +performance, the maximum number of users is set to +be equal to the number of REs. Since the active RIS +can amplify the incident signals, a limited number of +REs is sufficient to reach the desired SNR. Therefore, +the size of active RIS can be reduced, making it ap- +12 +China Communications + +5 +10 +15 +20 +25 +30 +35 +Number of REs +10 +12 +14 +16 +18 +20 +22 +24 +Sum rate (bps/Hz) +Proposed, K=4 +Proposed, K=N +Active-SA, K=4 +Active-SA, K=N +Active-MA-UEBF, K=4 +Active-MA-UEBF, K=N +Figure 6. Sum-rate versus number of reflecting elements at +the RIS. +2 +3 +4 +5 +6 +7 +8 +9 +10 +Number of Users +2 +4 +6 +8 +10 +12 +14 +16 +18 +20 +Sum rate (bps/Hz) +Proposed +Active-SA +Active-MA-UEBF +Passive-MA +Figure 7. Sum-rate versus the number of users. +plicable to the scenario where the space for the RIS +deployment is limited. +In Figure 7, we study the effect of number of user +on the sum-rate. As the number of users increases, +the total amount of harvested energy by users im- +proves, which results in a higher sum-rate. Nonethe- +less, when the number of users reaches a threshold, +e.g. +K = 8, the sum-rate achieved by our pro- +posed scheme becomes to be saturated. This is due +to the fact that the increment of number of users re- +duces the energy transfer duration and the time allo- +cated to each user for information transmission, which +makes the sum-rate converge to a constant. Again, +our proposed scheme notably outperforms the other +benchmark schemes. +For example, when the num- +ber of users is K = 4, our proposed scheme can +achieve 17.78% and 415.48% performance gain com- +1 +2.5 +4 +5.5 +7 +8.5 +10 +11.5 +13 +14.5 +16 +17.5 +19 +Location of RIS +0 +5 +10 +15 +20 +25 +Sum rate (bps/Hz) +Proposed +Active-SA +Active-MA-UEBF +Passive-MA +Figure 8. Sum-rate versus x-coordinate of the RIS. +pared with the Active-SA scheme and the Passive-MA +scheme with 100 REs, respectively. +In Figure 8, we plot the sum-rate versus the hori- +zontal ordinate of the RIS. As xr varies, the sum-rates +of all schemes first increase but then decrease. Com- +pared to the scenario that the RIS is close to the RS, +by deploying the RIS near the PS, e.g., xr = 1, the +sum-rate can be improved. +It is because the users +can harvest more energy assisted by the active RIS. +Moreover, we can observe that the sum-rate is maxi- +mized at xr = 10, where the reflecting link between +the active RIS and each user is strongest so the users +can benefit from a larger amplification and reflection +gain. However, when the RIS is neither close to the +PS nor the users, both the PS-RIS link and the RIS- +users links become weak, which results in the reduce +of harvested energy. Furthermore, since the Active- +MA-UEBF scheme adopts the uniform energy beam- +forming, the energy signals cannot adaptively align +with the direction of the desired channels, which re- +sults in a low WET efficiency. In addition, the schemes +with the active RIS can achieve a much better perfor- +mance than the passive RIS scheme, which demon- +strates that the active RIS with the amplification func- +tionality can significantly mitigates the double-fading +effect. The above observation demonstrates that the lo- +cation of the active RIS should be carefully designed. +VI. CONCLUSIONS +In this paper, we have proposed an active RIS as- +sisted relaying scheme to enhance the performance +of multiuser multi-antenna WPCN, which is involved +China Communications +13 + +in both the WET from the PS to users and the WIT +from users to the RS. To further enhance system per- +formance, both transmit beamforming at the PS and +receive beamforming at the RS have been designed. +We have formulated a system sum-rate maximization +problem by jointly optimizing the RIS reflection coef- +ficients for both the WET and the WIT, transmit and +receive beamforming vectors, transmit power at each +user, and network time scheduling. As the formulated +problem is non-convex, we have proposed an AO al- +gorithm with linear MMSE, SDR and SCA techniques +to solve it efficiently. Finally, numerical results have +been provided to confirm the performance superiority +of the proposed scheme. +APPENDIX +A. Proof of Proposition 1 +The Lagrangian function of P2-1 can be expressed as +L = +K +� +k=1 +λkβTr(Hd,kW0) − ξTr(W0) ++ Tr(ΩW) + δ, ∀k, +(52) +where λk ≥ 0, ξ ≥ 0, and Ω ∈ HM are the Lagrange +multipliers associated with constraints (21), (22), and +(24), respectively, δ denotes the term unrelated with +W0. The Karush-Kuhn-Tucker (KKT) conditions of +P2-1 are given as follows +∂L +∂W0 += +K +� +k=1 +λ∗ +kβHd,k − ξ∗IM + Ω∗ = 0, +(53) +Ω∗W ∗ +0 = 0, +(54) +where λ∗ +k, ξ∗ and Ω∗ are the optimal Lagrangian mul- +tipliers for the dual problem of P2-1. It can be proved +that λ∗ +k > 0 and ξ∗ > 0 since the constraints (21) and +(22)are equalities in the optimal condition. Based on +(53) and (54), it is straightforward to obtain the fol- +lowing equality +(ξ∗IM − +K +� +k=1 +λ∗ +kβHd,k)W ∗ +0 = 0 +(55) +According to [41], rank(ξ∗IM −�K +k=1 λ∗ +kβHd,k) ≥ +M − 1 due to the fact that Hd,k for ∀k are indepen- +dently distributed. Thus, from (55), we can obtain that +rank(W0) ≤ 1. It is obvious that W0 = 0 is not +the optimal solution to P2-1. Hence, we derive that +rank(W0) = 1, which thus proves Proposition 1. +B. Proof of Proposition 2 +Since Qr and Fk are diagonal matrices, we observe +that the noise power in the denominator of (35) and the +amplification power in (9) and (36) are independent +of the phase shift of each RE. Therefore, maximizing +γk with respect to Θk is equivalent to the following +optimization problem +(P4-4) max +Θk +��bH +k Θk ¯ϕk + gd,k +��2 +(56) +s.t. +|Θk,n| = 1, ∀k, ∀n. +(57) +We rewrite the objective function as +��bH +k Θk ¯ϕk +��2 + |gd,k|2 + 2 +��bH +k Θk ¯ϕk +�� |gd,k| cos α, +(58) +where α = arctan Im(bH +k Θk ¯ϕk) +Re(bH +k Θk ¯ϕk) − arctan Im(gd,k) +Re(gd,k). +Obviously, the maximum of +��bH +k Θk ¯ϕk + gd,k +��2 is +achieved when arg(bH +k Θk ¯ϕk) = arg(gd,k) ≜ ω. +Let vk = [vk,1, vk,2, ..., vk,N]T ∈ RN×1 and ξk = +diag(bH +k ) ¯ϕk. +As bH +k Θk ¯ϕk = vH +k ξk, P4-4 can be +rewritten as +(P4-5) max +vk +��vH +k ξk +��2 +(59) +s.t. +|vk,n| = 1, ∀k, ∀n, +(60) +arg(vH +k ξk) = ω, ∀k. +(61) +Based on [12], +the optimal solution to P4- +5 can be expressed as v∗ +k += +ej(ω−arg(ξk)) += +ej(ω−arg(diag(bH +k ) ¯ϕk)). +Then, the optimal RIS phase +shift for the n-th RE is expressed as θk,n += +arg(gd,k) − arg(bH +k,n) − arg( ¯ϕk,n). Finally, we ob- +tain that θk,n = arg(gd,k)−arg(gu,k,n)+arg(gr,k,n), +∀k, ∀n. This completes the proof of Proposition 2. +References +[1] SOMOV A, GIAFFREDA R. Powering IoT de- +vices: Technologies and opportunities[J]. IEEE +IoT Newsletter, 2015. +[2] VARSHNEY L R. Transporting information and +energy simultaneously[C]//2008 IEEE Interna- +14 +China Communications + +tional Symposium on Information Theory. IEEE, +2008: 1612-1616. +[3] ZHONG C, SURAWEERA H A, ZHENG G, +et al. Wireless information and power transfer +with full duplex relaying[J]. IEEE Transactions +on Communications, 2014, 62(10): 3447-3461. +[4] WU Q, GUAN X, ZHANG R. Intelligent reflect- +ing surface-aided wireless energy and informa- +tion transmission: An overview[J]. Proceedings +of the IEEE, 2021. +[5] ZHANG R, HO C K. +MIMO broadcasting +for simultaneous wireless information and power +transfer[J]. IEEE Transactions on Wireless Com- +munications, 2013, 12(5): 1989-2001. +[6] JU H, ZHANG R. +Throughput maximization +in wireless powered communication networks +[J]. IEEE Transactions on Wireless Communi- +cations, 2013, 13(1): 418-428. +[7] JU H, ZHANG R. +User cooperation in +wireless powered communication networks[C]// +2014 IEEE Global Communications Conference. +IEEE, 2014: 1430-1435. +[8] JU H, ZHANG R. Optimal resource allocation +in full-duplex wireless-powered communication +network[J]. IEEE Transactions on Communica- +tions, 2014, 62(10): 3528-3540. +[9] KIM J, LEE H, SONG C, et al. Sum through- +put maximization for multi-user MIMO cogni- +tive wireless powered communication networks +[J]. IEEE Transactions on Wireless Communica- +tions, 2016, 16(2): 913-923. +[10] WU Q, TAO M, NG D W K, et al. +Energy- +efficient resource allocation for wireless pow- +ered communication networks[J]. IEEE Trans- +actions on Wireless Communications, 2015, 15 +(3): 2312-2327. +[11] WU Q, CHEN W, LI J. Wireless powered com- +munications with initial energy: QoS guaranteed +energy-efficient resource allocation[J]. +IEEE +Communications Letters, 2015, 19(12): 2278- +2281. +[12] WU Q, ZHANG R. Intelligent Reflecting Sur- +face Enhanced Wireless Network via Joint Ac- +tive and Passive Beamforming[J]. IEEE Trans- +actions on Wireless Communications, 2019, 18 +(11): 5394-5409. +[13] DI RENZO M, ZAPPONE A, DEBBAH M, et al. +Smart radio environments empowered by recon- +figurable intelligent surfaces: How it works, state +of research, and the road ahead[J]. IEEE journal +on selected areas in communications, 2020, 38 +(11): 2450-2525. +[14] KUNDU N K, MCKAY M R. +RIS-Assisted +MISO Communication: +Optimal Beamform- +ers and Performance Analysis[C]//2020 IEEE +Globecom Workshops (GC Wkshps. Taipei, Tai- +wan: IEEE, 2020: 1-6. +[15] ZOU Y, GONG S, XU J, et al. Wireless pow- +ered intelligent reflecting surfaces for enhancing +wireless communications[J]. IEEE Transactions +on Vehicular Technology, 2020, 69(10): 12369- +12373. +[16] ZHANG Z, DAI L. A joint precoding framework +for wideband reconfigurable intelligent surface- +aided cell-free network[J]. IEEE Transactions on +Signal Processing, 2021, 69: 4085-4101. +[17] LIANG Y C, CHEN J, LONG R, et al. Recon- +figurable intelligent surfaces for smart wireless +environments: Channel estimation, system de- +sign and applications in 6G networks[J]. Science +China Information Sciences, 2021, 64(10): 1-21. +[18] YU X, JAMALI V, XU D, et al. Smart and recon- +figurable wireless communications: From IRS +modeling to algorithm design[J]. IEEE Wireless +Communications, 2021, 28(6): 118-125. +[19] ZHANG Z, DAI L, CHEN X, et al. Active RIS +vs. passive RIS: Which will prevail in 6G?[A]. +2021. arXiv: 2103.15154. +[20] LONG R, LIANG Y C, PEI Y, et al. +Active +reconfigurable intelligent surface-aided wireless +communications[J]. IEEE Transactions on Wire- +less Communications, 2021, 20(8): 4962-4975. +[21] LYU B, RAMEZANI P, HOANG D T, et al. +Optimized Energy and Information Relaying +in Self-Sustainable IRS-Empowered WPCN[J]. +IEEE TRANSACTIONS ON COMMUNICA- +TIONS, 2021, 69(1): 15. +[22] ZHENG Y, BI S, ZHANG Y J A, et al. Joint +beamforming and power control for throughput +maximization in IRS-assisted MISO WPCNs[J]. +IEEE Internet of Things Journal, 2021, 8(10): +8399-8410. +[23] HUA M, WU Q, POOR H V. Power-Efficient +Passive Beamforming and Resource Allocation +for IRS-Aided WPCNs[J]. IEEE Transactions on +Communications, 2022. +China Communications +15 + +[24] XU Y, GAO Z, WANG Z, et al. RIS-enhanced +WPCNs: Joint radio resource allocation and pas- +sive beamforming optimization[J]. IEEE Trans- +actions on Vehicular Technology, 2021, 70(8): +7980-7991. +[25] YOU C, ZHANG R. Wireless communication +aided by intelligent reflecting surface: Active +or passive?[J]. IEEE Wireless Communications +Letters, 2021, 10(12): 2659-2663. +[26] DONG L, WANG H M, BAI J. +Active Re- +configurable Intelligent Surface Aided Secure +Transmission[J]. IEEE Transactions on Vehic- +ular Technology, 2021. +[27] ZARGARI S, HAKIMI A, TELLAMBURA C, +et al. Multiuser MISO PS-SWIPT Systems: Ac- +tive or Passive RIS?[J]. IEEE Wireless Commu- +nications Letters, 2022. +[28] GAO Y, WU Q, ZHANG G, et al. Beamform- +ing Optimization for Active Intelligent Reflect- +ing Surface-Aided SWIPT[A]. +2022. +arXiv: +2203.16093. +[29] ZENG P, QIAO D, WU Q, et al. +Throughput +Maximization for Active Intelligent Reflecting +Surface Aided Wireless Powered Communica- +tions[J]. +IEEE Wireless Communications Let- +ters, 2022. +[30] WU Q, ZHANG R. Weighted Sum Power Maxi- +mization for Intelligent Reflecting Surface Aided +SWIPT[J]. IEEE WIRELESS COMMUNICA- +TIONS LETTERS, 2020, 9(5): 5. +[31] HU S, WEI Z, CAI Y, et al. +Robust and se- +cure sum-rate maximization for multiuser MISO +downlink systems with self-sustainable IRS[J]. +IEEE Transactions on Communications, 2021, +69(10): 7032-7049. +[32] ZHENG B, ZHANG R. +Intelligent reflect- +ing surface-enhanced OFDM: Channel estima- +tion and reflection optimization[J]. IEEE Wire- +less Communications Letters, 2019, 9(4): 518- +522. +[33] WU Q, ZHANG S, ZHENG B, et al. +Intel- +ligent reflecting surface-aided wireless commu- +nications: A tutorial[J]. IEEE Transactions on +Communications, 2021, 69(5): 3313-3351. +[34] WANG Z, LIU L, CUI S. +Channel Estima- +tion for Intelligent Reflecting Surface Assisted +Multiuser Communications: Framework, Algo- +rithms, and Analysis[J]. IEEE Transactions on +Wireless Communications, 2020, 19(10): 6607- +6620. +[35] ZHENG Y, BI S, ZHANG Y J, et al. +Intel- +ligent reflecting surface enhanced user cooper- +ation in wireless powered communication net- +works[J]. IEEE Wireless Communications Let- +ters, 2020, 9(6): 901-905. +[36] LUO Z Q, MA W K, SO A, et al. Semidefinite +Relaxation of Quadratic Optimization Problems +[J]. IEEE Signal Processing Magazine, 2010, 27 +(3): 20-34. +[37] BOYD S, BOYD S P, VANDENBERGHE L. +Convex optimization[M]. Cambridge university +press, 2004. +[38] RAZAVIYAYN M. Successive Convex Approx- +imation: Analysis and Applications[D]. Univer- +sity of Minnesota, 2014. +[39] GUO H, LIANG Y C, CHEN J, et al. Weighted +Sum-Rate Maximization for Reconfigurable In- +telligent Surface Aided Wireless Networks[J]. +IEEE Transactions on Wireless Communica- +tions, 2020, 19(5): 3064-3076. +[40] AMATO F, PETERSON C W, DEGNAN B P, +et al. Tunneling RFID tags for long-range and +low-power microwave applications[J]. +IEEE +Journal of Radio Frequency Identification, 2018, +2(2): 93-103. +[41] XU X, LIANG Y C, YANG G, et al. +Recon- +figurable intelligent surface empowered symbi- +otic radio over broadcasting signals[J]. +IEEE +Transactions on Communications, 2021, 69(10): +7003-7016. +16 +China Communications + diff --git a/2tAzT4oBgHgl3EQf9P4T/content/tmp_files/load_file.txt b/2tAzT4oBgHgl3EQf9P4T/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..823da272b6a5c37e7c36f7441bb22f569b176d5b --- /dev/null +++ b/2tAzT4oBgHgl3EQf9P4T/content/tmp_files/load_file.txt @@ -0,0 +1,652 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf,len=651 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='01915v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='IT] 5 Jan 2023 CHINA COMMUNICATIONS Sum-Rate Maximization in Active RIS-Assisted Multi-Antenna WPCN Jie Jiang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Bin Lyu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Pengcheng Chen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' and Zhen Yang School of Communications and Information Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Nanjing University of Posts and Telecommunications,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Nanjing 210003,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' China Abstract: In this paper,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' we propose an active re- configurable intelligent surface (RIS) enabled hybrid relaying scheme for a multi-antenna wireless pow- ered communication network (WPCN),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' where the ac- tive RIS is employed to assist both wireless energy transfer (WET) from the power station (PS) to energy- constrained users and wireless information transmis- sion (WIT) from users to the receiving station (RS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For further performance enhancement, we propose to employ both transmit beamforming at the PS and re- ceive beamforming at the RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' We formulate a sum- rate maximization problem by jointly optimizing the RIS phase shifts and amplitude reflection coefficients for both the WET and the WIT, transmit and receive beamforming vectors, and network resource alloca- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To solve this non-convex problem, we propose an efficient alternating optimization algorithm with linear minimum mean squared error criterion, semi-definite relaxation (SDR) and successive convex approxima- tion techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specifically, the tightness of apply- ing the SDR is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Simulation results demon- strate that our proposed scheme with 10 reflecting el- ements (REs) and 4 antennas can achieve 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='78% and 415.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='48% performance gains compared to the single- antenna scheme with 10 REs and passive RIS scheme with 100 REs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Keywords: Wireless powered communication net- work, active reconfigurable intelligent surface, beam- forming, sum-rate maximization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Received: XX Revised: XX Editor: XX I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' INTRODUCTION With the development of the Internet-of-Things (IoT), an intelligent society with ubiquitous interconnections and deep coverage will be truly realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, wireless devices (WDs) in IoT networks are generally energy-constrained and suffer from limited lifetime [1], which fundamentally limits the performance of communication networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Traditional ways of chang- ing or recharging the batteries manually are impossi- ble and unacceptable, especially when the number of WDs is numerous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Therefore, how to tackle this issue is a critical problem in the widespread development of IoT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Wireless powered communication has been pro- posed as a prospective technology for enhancing the energy sustainability of WDs, which can be classified into two directions based on application scenarios [2– 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The first one focuses on investigating simultane- ous wireless information and power transfer (SWIPT), where the base station (BS) simultaneously transfers energy and information signals to energy receivers and information receivers via the common radio fre- quency (RF) signals in the downlink (DL), resulting in a pivotal tradeoff between the achievable rate and harvested energy [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In contrast to the SWIPT, wire- less powered communication network (WPCN) has been proposed as a novel type of wireless network di- agram to improve the lifetime of WDs and enhance the deployment flexibility of IoT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In a WPCN, energy- constrained WDs first harvest energy in the DL and then use the harvested energy to transmit independent information in the uplink (UL) based on the widely used harvest-then-transmit (HTT) protocol [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' WPCN has been widely investigated in the literature China Communications 1 [6–9], which promotes the development of WPCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, WPCN generally suffers from the “doubly near-far” phenomenon if the power station (PS) and the receiving station (RS) are co-located at the hybrid access point (HAP) [6, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specifically, a WD located far away from the HAP harvesting less energy in the DL has to transmit information with more power in the UL, which results in an unfair time and resource allocation among the WDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To deal with the issue, a promising way is to deploy the PS and RS separately [10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In [10], multiple users harvest energy from a dedicated PS and then communicate with an informa- tion RS following the HTT protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In this scenario, a user physically close to the PS is naturally far away from the RS, and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Considering a similar scenario, a user-centric energy-efficient (EE) problem in WPCN is investigated in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, the perfor- mance of WPCN is still limited due to the low efficien- cies caused by the severe path-loss, which seriously affects its practical applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Recently, reconfigurable intelligent surface (RIS), with the unprecedented ability to reshape the wireless transmission environment, has drawn widespread at- tentions from academia and industry [12–18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' RIS is comprised of a large number of programmable reflect- ing elements (REs), which can alter the phase shifts and amplitudes of incident signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As such, RIS can adaptively modify the impinging radio waves towards the appropriate direction [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' According to the re- flection patterns, RIS can be classified as passive RIS and active RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Without the property of power amplifi- cation, the independent diffusive scatterer-based (IDS) model accounts for the basic properties of passive RIS, which has been widely adopted in RIS-assisted wire- less communications [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The passive RIS is only equipped with the phase-shift controller, while the ac- tive RIS contains both the phase-shift controller and the active reflection-type amplifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Hence, the active RIS can alter both the phase shifts and amplitudes of the incident signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It is worth noting that the active RIS with its novel hardware structure and signal model has been proposed in [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Different from the full-duplex amplify-and-forward (FD-AF) relay that requires power-consuming RF chains, the active RIS can directly reflect and amplify the incident signals in the EM level in a FD manner without reception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In this way, the active RIS exhibits promising qualities, such as a low power consumption, light weight, conformal geometry and high flexibility for practical deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Currently, the passive RIS has been widely applied in WPCNs for performance enhancement [21–24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In [21], the passive RIS is employed between the HAP and users to improve both DL WET and UL WIT effi- ciencies in single-input-single-output (SISO) WPCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To achieve further performance improvement, the multi-antenna technique is employed in [22], where the HAP with multi-antenna transmits energy signals to users in the DL and receives information from users in the UL by employing transmit bemforming and re- ceive beamforming, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In [23], the fully dynamic RIS beamforming scheme is proposed for WPCN, for which the phase shift vectors are indepen- dently designed over different time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, in the above works [21–23], the PS and RS are also co-located at the HAP, which results in performance unfair among users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To address this issue, the au- thors in [24] consider the scenario where the PS and RS are separately deployed, for which the locations of RIS and users can be carefully considered to achieve a fair performance among users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, as mentioned above, the passive RIS can only reflect incident signals without amplification, which leads to the limited per- formance enhancement due to the double-fading ef- fect suffered by the reflecting links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Thus, the energy- constrained users still need to consume much time for harvesting energy in the DL and have less time for in- formation transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Inspired by the amplification characteristic of the active RIS, the active RIS is confirmed to be superior to the passive RIS in terms of performance enhance- ment, and thus has been considered a promising tech- nique for IoT networks [19, 20, 25–29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The authors in [19] compare the capacity improvement achieved by the active RIS to the passive RIS, which demon- strats that the active RIS can fundamentally mitigate the double-fading effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In [20], an active RIS is ap- plied in single input multiple output (SIMO) systems, for which the joint optimization of phase shifts ma- trix and receive beamforming is considered to obtain the maximum achievable rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In [25], the placement of the active RIS is optimized to enhance SISO sys- tems’ performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The authors in [26] propose to use the active RIS to achieve secure transmission, which not only establishes the reliable link from the trans- mitter to the receiver but also prevents the confidential information intercepted by the eavesdropper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The ac- 2 China Communications tive RIS-aided multiuser MISO PS-SWIPT is studied in [27] to minimize the base station transmit power, which shows significant improvements compared to the passive RIS-aided system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Similarly, in [28], an active RIS is employed to assist SWIPT to boost the efficiency of both WET and WIT, while the conclu- sions and approaches are inapplicable to the WPCN system because of thire different system models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Although the active RIS has received a lot of inter- ests for wireless communication networks, the appli- cations of active RIS in WPCN is still at the very early stage and has not been well studied in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To the best of our knowledge, there exists only one paper investigating the usage of active RIS in WPCN [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specifically, the authors in [29] investigate the weight sum-rate maximization problem in the active RIS assisted single-antenna WPCN, where the PS and RS is co-located at the HAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As a result, similar to [21–23], a part of WDs in [29] still suffer from the “doubly near-far” phenomenon, which is not suitable for practical applications with high requirement of per- formance fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Moreover, the authors consider a certain simplified communication scenario where both the HAP and the WDs have single antenna each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The transmit beamforming and receive beamforming can- not be exploited, which is also a key technology for performance enhancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Motivated by the observations above, we propose an active RIS enabled hybrid relaying scheme for the multi-antenna WPCN, where the active RIS is em- ployed to facilitate both the WET from the PS to energy-constrained users and the WIT from users to the RS, which is shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Compared with the existing works which used the passive RIS in WPCN [21–24], our proposed active RIS scheme can amplify the energy signals and information signals to achieve a satisfying system performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Different from the single-antenna scenario considered in [29], we propose to employ multi-antenna at both the PS and RS, which can construct the transmit beamform- ing and receive beamforming for further performance enhancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specifically, the transmit beamforming at the PS can be used to enhance the WPT efficiency from the PS to users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In the meanwhile, the receive beamforming at the RS can be used to exploit the an- tenna gain and eliminate the noise caused by the ac- tive RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In the considered system setup, we aim to maximize the sum-rate problem by jointly optimiz- ing the transmit beamforming at the PS, the receive beamforming at the RS, the reflecting coefficients at the RIS, and network resource allocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It should be noted that compared to [21–24, 29], our formulated problem is much more challenging to solve and the proposed algorithms in [21–24, 29] cannot be used to solve our formulated problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Thus, we propose an efficient algorithm to solve the formulated problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The main contributions of this paper are summarized as follows: We propose an active RIS assisted multi-antenna WPCN for performance enhancement, where the active RIS is served as a hybrid relay to achieve two purposes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', the first one is to assist the WET from the PS to users, and the second one is to aid the WIT from users to the RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To fur- ther improve system performance, both trans- mit beamforming and receive beamforming tech- niques are respectively considered at the PS and RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' We investigate the sum-rate maximization prob- lem by jointly optimizing transmit beamforming vector at the PS, receive beamforming vectors at the RS, phase shifts and amplitude reflection coef- ficients at the RIS for both the WET and the WIT, and network resource allocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To deal with the non-convexity of the formulated problem, we pro- pose an efficient alternating optimization (AO) al- gorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specifically, the original problem can be divided into four sub-problems, which are solved sequentially in an alternating manner until con- vergence is achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For designing the receive beamforming, we apply the linear minimum mean squared error (MMSE) criterion and obtain the closed-form expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For the optimization of the transmit beamform- ing and RIS reflecting coefficient matrices for the WET, the semidefinite relaxation (SDR) tech- nique is adopted and the tightness of applying the SDR is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For the optimization of RIS re- flecting coefficients for the WIT, we obtain the optimal phase shifts in a closed-form and propose a successive convex approximation (SCA) algo- rithm to determine the optimal amplitude reflec- tion coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In addition, the convergence of proposed problem is analyzed and confirmed via numerical simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' China Communications 3 Finally, numerical results are provided to evaluate the performance of proposed scheme, which indi- cates that compared to the single-antenna scheme with 10 REs and the passive-RIS scheme with 100 REs, the proposed scheme with 4 antennas and 10 REs can achieve 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='78% and 415.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='48% sum-rate gain, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Sec- tion II describes the system model of the active RIS- assisted multi-antenna WPCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The sum-rate maxi- mization problem is formulated in Section III and solved in Section IV, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In Section V, per- formance is evaluated by numerical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Finally, this paper is concluded in Section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Notations: In this paper, vectors and matrices are denoted by boldface lowercase and uppercase letters, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The operators ( · )T, ( · )H, | · | and ∥ · ∥ denote the transpose, conjugate transpose, absolute value and the Euclidean norm, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Tr( · ) and rank( · ) denote the trace and rank of a matrix, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' X ⪰ 0 represents that X is a positive semidef- inite matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' E[ · ] stands for the statistical expecta- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IN denotes the N-dimensional identity matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 0 denotes the zero matrix/vector with appropriate size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' CN×M denotes the set of all N × M complex-valued matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' HM denotes the set of all M ×M Hermitian matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' RN×1 represents the set of all N × 1 real- valued vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' CN � µ, σ2� denotes the distribution of a circularly symmetric complex Gaussian random vec- tor with mean µ and variance σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' arg( · ) denotes the phase extraction operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' diag(x) denotes a diago- nal matrix whose diagonal elements are from vector x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Im( · ) and Re( · ) respectively denotes the imaginary part and real part of a complex number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' SYSTEM MODEL As shown in Figure 1, we consider an active RIS-aided multi-antenna WPCN, which consists of a PS with M antennas, a RS with L antennas, an active RIS, and K energy-constrained users each with single antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' We assume that each user is equipped with an energy harvesting (EH) circuit for harvesting energy, where a rectifier is used to convert the received RF signals to direct current (DC) signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then, the net energy harvested from the DC signals can be stored in the rechargeable battery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The active RIS consists of N active REs, which can steer the reflected signals in ��,� � ��,� � ��,� ��,� �� �� PS RS �� Active RIS Energy transfer Information transmission EH circuit Rectifier RF signal Rechargeable battery DC signal Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' System model for an active RIS-assisted multi- antenna WPCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' a specific direction and also amplify them by the ac- tive loads (negative resistance) [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In contrast to the passive RE, each active RE is equipped with an addi- tionally integrated active reflection-type amplifier sup- ported by a power supply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' By appropriately setting the effective resistance, it is reasonable to assume that the reflection amplitude and phase of each element is inde- pendently [19, 20, 25–29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To power the operations of active RIS and users, the PS is equipped with a stable energy source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In addition, the PS has the capability for performing computational tasks [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In particu- lar, the users first harvest energy from the RF signals transmitted by the PS and then use the harvested en- ergy to deliver information to the RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To allievate the severe path-loss suffered by the reflecting links, the ac- tive RIS is employed to improve the WET efficiency from the PS to users and the WIT efficiency from the users to the RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The channels are assumed to follow a quasi-static flat-fading model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' That is, all channel coefficients are constant throughout each transmission block but vary from block to block [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The downlink base- band equivalent channels of PS-to-RIS, RIS-to-Uk, and PS-to-Uk links are denoted by Hr ∈ CN×M, hH u,k ∈ C1×N, and hH d,k ∈ C1×M, respectively, where Uk denotes the k-th user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Similarly, the uplink base- band equivalent channels of Uk-to-RIS, RIS-to-RS, and Uk-to-RS links are respectively denoted by gu,k ∈ CN×1, Gr ∈ CL×N, and gd,k ∈ CL×1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Since there have been many efficient channel estima- 4 China Communications 用tion techniques proposed for RIS systems [31–34], we assume the perfect channel state information can be available in advance, which is a common assumption considered in [21, 22, 35] and a prerequisite for inves- tigating the upper-bound of system performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It should be noted that the channel estimation error is generally inevitable [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, the effect of chan- nel estimation error on system performance degrada- tion is out the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' According to the HTT protocol [6], the normalized transmission block of interest is divided into K + 1 time slots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The first time slot with duration of τ0 ∈ [0, 1] is a dedicated slot for WET, in which all users harvest energy from the PS with the assistance of active RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The remaining K time slots denoted by τ = [τ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , τK], are used for UL WIT via the time di- vision multiple access (TDMA) scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specifically, during τk, k = 1, · · · , K, Uk delivers its information to the RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Without loss of generality, the whole oper- ation time period is set to a normalized transmission block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The network time scheduling constraint is thus given by τ0 + K � k=1 τk ≤ 1, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (1) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='1 Wireless Energy Transfer Phase In the WET phase, the PS transmits energy signals to all users with the assistance of the active RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Denote the transmitted signal as s = w0s, where s is the pseudo-random baseband signal transmitted by the PS, and w0 ∈ CM×1 is the transmit beamforming vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The energy constraint at the PS is expressed as E � |s|2� = Tr � w0wH 0 � ≤ P0, (2) where P0 denotes the maximum transmit power at the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The reflecting coefficient matrix of the active RIS in the WET phase is denoted by Φ0 = diag {φ0,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , φ0,N} ∈ CN×N with φ0,n = a0,nejθ0,n, n = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , N, where a0,n and θ0,n rep- resent the amplitude reflection coefficient and phase shift of the n-th RE, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Without loss of gen- erality, we suppose each active RE has the following constraints a0,n ≤ an,max, 0 ≤ θ0,n ≤ 2π, ∀n, (3) where an,max is the maximum amplitude reflection co- efficient of n-th RE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It is worth noting that an,max can be greater than 1 [25], which is a main characteris- tic distinguishing the active RIS from the passive RIS since the active load can amplify the reflected signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The received signal at Uk during τ0 is given by yu,k = hH d,ks � �� � direct link + hH u,kΦ0 (Hrs + nv) � �� � RIS-aided link +nu,k, ∀k, (4) where nu,k ∈ C and nv ∈ CN×1 represent the ad- ditive white Gaussian noise (AWGN) at Uk and the RIS, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Without loss of generality, we as- sume nu,k ∼ CN � 0, σ2 u,k � and nv ∼ CN � 0, σ2 vIN � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Denote the equivalent downlink channel as hH k = hH u,kΦ0Hr + hH d,k ∈ C1×M and (4) can be rewritten as yu,k = hH k w0s + hH u,kΦ0nv + nu,k, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (5) Due to the fact that the active RIS not only amplifies the desired signal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', s, but also amplifies the input noise, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', nv, it is reasonable to consider the second term of (4) for computing the amount of harvested en- ergy accurately [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, the noise at Uk is gen- erally quite small and can be negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Accordingly, the harvested energy by Uk, denoted by Ek, is given by Ek = β ��hH k w0 ��2τ0 + β ��hH u,kΦ0 ��2σ2 vτ0, ∀k, (6) where β ∈ (0, 1] denotes the energy conversion effi- ciency of each user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It is practical for us to consider the linear EH model here, which is also a common as- sumption in the literature [6, 8, 11, 10, 22, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It is worth noting that the active RIS can allocate the available reflecting power to amplify the incident signals with active loads [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In the DL WET phase, the amplification power of s and nv is limited by the RIS power budget, which is shown by the following constraint P0 ∥Φ0Hr∥2 + σ2 v ∥Φ0IN∥2 ≤ Pr, (7) where Pr is the maximum reflecting power for ampli- fication at the active RIS and substantially lower than that of an active RF amplifier [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' China Communications 5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='2 Wireless Information Transmission Phase In the WIT phase, the users utilize the harvested en- ergy to transmit information to the RS via a TDMA manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Let fk denotes the information-carrying sig- nal of Uk with unit power and then the transmit signal during τk is denoted by xk = √pkfk, where pk is the transmit power at Uk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' We assume that all the harvested energy at Uk in the WET phase is used for delivering its own information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Let p = [p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , pK] ∈ R1×K, which satisfies pkτk ≤ Ek, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (8) Similarly, the reflecting coefficient matrix at the active RIS for the WIT during τk is denoted by Φk = diag {φk,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , φk,N} ∈ CN×N, where φk,n = ak,nejθk,n, ak,n and θk,n have the following constraints ak,n ≤ an,max, 0 ≤ θk,n ≤ 2π, ∀k, ∀n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (9) The received signal at the RS from Uk with the as- sistance of active RIS during τk is written as yr,k = gH d,kxk � �� � direct link + GrΦk (gu,kxk + nv) � �� � RIS-aided link +nr, ∀k, (10) where nr ∈ CL×1 represents the AWGN at the RS and satisfies nr ∼ CN � 0, σ2 rIN � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In the UL WIT phase, we also have the amplification power constraint at the active RIS as follows pk ∥Φkgu,k∥2 + σ2 v ∥ΦkIN∥2 ≤ Pr, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (11) Denote the receive beamforming vector at the RS during τk as wk ∈ CL×1, which can be used to ex- tract the desired signal and suppress interference and noises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Let the equivalent uplink channel be gk = gd,k + GrΦkgu,k, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The estimated signal at the RS during τk is expressed as uk =wH k yr,k =wH k gkxk + wH k GrΦknv + wH k nr, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (12) Then, the signal-noise-ratio (SNR) at the RS during τk is written as γk = pk ��wH k (GrΦkgu,k + gd,k) ��2 ��wH k GrΦk ��2 σ2v + ∥wk∥2 σ2r , ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (13) Denote the achievable rate from Uk to the RS as Rk, which is formulated as Rk = τk log (1 + γk) , ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (14) III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' PROBLEM FORMULATION In this section, we formulate the system sum-rate max- imization problem by jointly optimizing the reflecting coefficients for both the WET and the WIT at the ac- tive RIS, the transmit beamforming at the PS, the re- ceive beamforming at the RS, the transmit power at each user, and the network time scheduling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The opti- mization problem is formulated as (P1) max τ0,τ,Φ0,Φk,w0,p,wk K � k=1 Rk (15) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (1), (2), (3), (7), (8), (9) and (11), τ0 ≥ 0, τk ≥ 0, pk ≥ 0, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (16) where (16) indicates that the time and power variables are all nonnegative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' One can observe that the objective function in (15) is a non-concave function due to the coupled of vari- ables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In addition, there exists several non-convex con- straints, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', (2), (7), (8) and (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It is thus challeng- ing to solve P1 directly by standard optimization tech- niques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In the next section, we propose an AO algo- rithm to solve it efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' ALTERNATING OPTIMIZATION SO- LUTION In this section, an efficient AO algorithm is proposed to solve P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In particular, we decompose P1 into sev- eral subproblems and iteratively solve them in an al- ternating manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To show the procedure of AO algo- rithm, we summarize a flow chart in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specif- ically, the variables are partitioned into four blocks, {wk}, {w0, τ, p}, {Φ0, τ0, τ, p}, and {Φk}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' the variables in each block are alternately solved by 6 China Communications Linear MMSE-based Receive Beamforming Optimization SDP-based Transmit Beamforming Optimization SDP-based RIS Reflecting Coefficients for the WET and Resource Allocation Optimization SCA-based RIS Reflecting Coefficients Optimization for the WIT System Variables �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �� ��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' ��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �� �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' {��} {��} �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' ��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �� �� �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' � Discarding ��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �� ��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' ��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' � �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' �� �� AO iteration flow Update Input Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' A flow chart of the proposed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' its corresponding sub-problem with the other blocks fixed until the convergence is achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='1 Linear MMSE-based Receive Beamform- ing Optimization With the other variables fixed, we first design the re- ceive beamforming vectors {wk}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To cope with the interference caused by nv and nr in (13), we apply the linear MMSE criterion here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Based on this crite- rion, the MMSE-based receive beamforming is given by w∗ k = � gkgH k + σ2 v pk GrΦkΦH k GH r + σ2 r pk IL �−1 gk, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (17) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='2 SDP-based Transmit Beamforming Opti- mization We then proceed to optimize {w0, τ, p} with the other variables {wk, Φ0, τ0, Φk} fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Letting ek = pkτk and e = [e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , eK] and applying the obtained results in (17), P1 can be simplified as follows (P2) max w0,τ,e K � k=1 τk log � 1 + ǫk ek τk � (18) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' ek ≤ Ek, ∀k, (19) τk ≥ 0, ek ≥ 0, ∀k, (20) (1), (2) and (11), where ǫk = |(w∗ k)H(GrΦkgu,k+gd,k)| 2 ∥(w∗ k)HGrΦk∥ 2σ2v+∥w∗ k∥ 2σ2r , ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It can be found that P2 is highly non-convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To solve it efficiently, the SDR technique [36] is em- ployed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Define Hk = hkhH k , and Gu,k = diag � |gu,k,1|2 , |gu,k,2|2 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , |gu,k,N|2� , ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Let W0 = w0wH 0 , which satisfies W0 ⪰ 0 and rank(W0) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then, (19) is rewritten as ek ≤ βτ0[Tr (HkW0) + ��hH u,kΦ0 ��2 σ2 v], ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (21) Denote the RIS reflecting coefficient vector for the WET as ϕk = [φk,1, φk,2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , φk,N]T, ∀k, (11) can be recast as ekϕH k Gu,kϕk + τkσ2 vϕH k ϕk ≤ τkPr, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (22) Then, P2 can be equivalently transformed into (P2-1) max W0,τ,e K � k=1 τk log � 1 + ǫk ek τk � (23) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Tr (W0) ≤ P0, (24) W0 ⪰ 0, (25) rank(W0) = 1, (26) (1), (20), (21) and (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Since the rank-one constraint in (26) is non-convex, we employ the SDR technique to relax it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Thus, P2-1 becomes to be a convex semidefinite program (SDP) and can be solved with the interior-point method [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The optimal transmit beamforming matrix obtained by solving the relaxed version of P2-1, denoted by W ∗ 0 , is rank-one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Please refer to Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' According to Proposition 1, the tightness of SDR is guaranteed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Hence, we can employ Cholesky de- composition to obtain the optimal energy beamform- ing vector w∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='3 SDP-based RIS Reflecting Coefficients for the WET and Resource Allocation Opti- mization In this sub-section, we focus on optimizing the re- flecting beamforming at the RIS in the WET phase, the transmit power at each user, and the network time scheduling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Since τ0 and Φ0 are coupled, we first optimize {Φ0, τ, p} with τ0 given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Define Ψ0 = ˜ϕ0 ˜ϕH 0 with Ψ0 ⪰ 0 and rank(Ψ0) = 1, where ˜ϕ0 = [ϕH 0 , 1]H and ϕ0 = [φ0,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , φ0,N]T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' China Communications 7 Let Hu,k = diag {hu,k,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , hu,k,N} and Qu,k = diag � |hu,k,1|2 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , |hu,k,N|2 , 1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then, (7) and (19) are respectively reformulated as P0Tr( ˜ HrΨ0) + σ2 vTr(Ψ0) ≤ Pr, (27) ek ≤ βτ0Tr[(V + σ2 vQu,k)Ψ0] − βτ0σ2 v, ∀k, (28) where V = �HH u,kHrW0HH r Hu,k HH u,kHrW0hd,k hH d,kW0HH r Hu,k hH d,kW0hd,k � , and ˜ Hr = �HrHH r 0 0 0 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' With the obtained solutions in Sections 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='1 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='2, P1 can be equivalently written as (P2-2) max Ψ0,τ,e K � k=1 τk log � 1 + ǫk ek τk � (29) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Ψ0 ⪰ 0, rank(Ψ0) = 1, (30) [Ψ0]n,n ≤ a2 max, ∀n, (31) [Ψ0]N+1,N+1 = 1, (32) (1), (20), (22), (27) and (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Similarly, after the relaxation of the rank-one con- straint in (30), P2-2 is also an SDP and can be solved by the interior-point method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Recall that the tightness of optimizing W0 by SDR can be guaranteed, we can also prove that the obtained solution Ψ0 is rank-one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then, ˜ϕ0 can be recovered by implementing Cholesky decomposition of Ψ0, and the optimal reflection co- efficient vector for the WET ϕ∗ 0 can be obtanied by linear operation from ˜ϕ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Subsequently, the optimal RIS reflecting coefficient matrix Φ∗ 0 can be obtained by Φ∗ 0 = diag((ϕH 0 )∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Finally, we continue to update the optimal energy transmission time τ0 ∈ [0, 1] by the one-dimensional search method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Thus, the maximum sum-rate of this sub-problem is achieved with the optimal solution {Φ∗ 0, τ ∗ 0 , τ ∗, p∗}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The procedure is summarized in Al- gorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' SDP-based RIS reflecting coefficients for the WET and resource allocation optimization Input: w0, {wk}, {Φk}, ∀k Output: Φ∗ 0, τ ∗ 0 , τ ∗, p∗ 1: Initialization: The maximum objective function value Rmax = 0 and the step size δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 2: for τ0 = 0 : δ : 1 do 3: Given w0, {wk}, {Φk}, we obtain τ ′ 0, Ψ′ 0, τ ′ k, e′ k, ∀k by solving P2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4: Calculate R = �K k=1 τ ′ k log � 1 + ǫk e′ k τ ′ k � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 5: if R > Rmax then 6: Update Rmax ← R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 7: Update τ0 ← τ ′ 0, Ψ0 ← Ψ′ 0, τk ← τ ′ k, ek ← e′ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 8: end if 9: end for 10: Obtain ˜ϕ0 from Ψ0 by Cholesky decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 11: Obtain ϕ0 from ˜ϕ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 12: Set Φ∗ 0 = diag((ϕH 0 )∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 13: Calculate p∗ k = e∗ k/τ ∗ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 14: return Φ∗ 0, τ ∗ 0 , τ ∗, p∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='4 SCA-based RIS Reflecting Coefficients Optimization for the WIT In this sub-section, we investigate the optimization of RIS reflecting coefficient matrix Φk in the WIT phase, which is given by (P3) max Φk K � k=1 Rk (33) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (9) and (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Note that P3 is still a non-convex optimization prob- lem as the active RIS introduces additional noise term in the denominator of the objective function, which re- sults in a quadratic fractional programming problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In fact, the RIS reflecting coefficients include ampli- tude reflection coefficients and phase shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To sim- plify this problem, we derive the optimal phase shifts in the closed-form and then exploit an SCA algorithm to obtain the near-optimal amplitude reflection coeffi- cients according to [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It is worth noting that P3 can be decomposed into K 8 China Communications independent subproblems, each of which maximizes the SNR of Uk at the RS during τk with respect to the RIS reflection coefficient vector ϕk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specifically, with w∗ k obtained in (17) and introducing some new aux- iliary variables, the k-th SNR maximization problem can be formulated as γk = pk ��bH k ϕk + gd,k ��2 ϕH k Qrϕkσ2v + σ2r , (34) where gd,k = wH k gd,k, gH r,k = wH k Gr, bH k = gH r,kdiag (gu,k), Qr = diag � |gr,k,1|2 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , |gr,k,N|2� , ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Let Fk = pkGu,k + σ2 vIN, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The subproblem can be expressed as (P4) max ϕk γk (35) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' ϕH k Fkϕk ≤ Pr, ∀k, (36) (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To solve P4, we decompose the optimization of RIS reflecting coefficient vector ϕk into two sub-problems for the amplitude reflection coefficient design and the optimal phase shift design, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Let ϕk = Θk ¯ϕk, where Θk = diag � ejθk,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , ejθk,N� ∈ CN×N and ¯ϕk = [ak,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , ak,N]T ∈ RN×1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='1 Optimization of phase shifts for the WIT The optimal design of phase shifts is given in the fol- lowing proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The optimal RIS phase shift of the n-th RE for the WIT during τk is derived as θ∗ k,n = arg(gd,k) − arg(gu,k,n) + arg(gr,k,n), (37) ∀k, ∀n, where gu,k,n and gr,k,n denote the n-th element of the vector gu,k and gr,k, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Please refer to Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='2 Optimization of amplitude reflection coeffi- cients for the WIT For P4, the optimal design of phase shifts shown in Proposition 2 holds because the value of the ampli- fication power in (9) and (36) and the noise power in the denominator of (34) are independent with the phase shift of each RE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In addition, optimizing θk,n is equivalent to maximizing the objective function in (34) [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' With the optimal phase shifts in Proposition 2, we proceed to optimize the RIS amplitude reflec- tion coefficients for the WIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In particular, P4 can be simplified as (P4-1) max ¯ϕk ¯γk = pk ��¯bH k ¯ϕk + |gd,k| ��2 ¯ϕH k Qr ¯ϕkσ2v + σ2r (38) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' ¯ϕH k Fk ¯ϕk ≤ Pr, ∀k, (39) ak,n ≤ an,max, ∀k, ∀n, (40) where ¯γk = |γk|, and ¯bk is element-wise modulus of bk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To deal with the non-convexity of the objec- tive function (38), we introduce a new auxiliary vari- able nk = ¯ϕH k Qr ¯ϕkσ2 v + σ2 r, which denotes the noise power received at the RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then, P4-1 can be con- verted into the following equivalent form (P4-2) max ¯γk,nk, ¯ϕk ¯γk (41) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='√pk �¯bH k ¯ϕk + |gd,k| � ≥ √nk¯γk, ∀k, (42) ¯ϕH k Qr ¯ϕkσ2 v + σ2 r ≤ nk, ∀k, (43) (39) and (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, the constraint (42) is still non-convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To solve P4-1 efficiently, we exploit the SCA algorithm to approximate the square root by a convex upper-bound in each iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Define ¯γk(t) and nk(t) as the iter- ative optimization variables after the t-th step itera- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In terms of {¯γk (t) , nk (t)}, the first-order Tay- lor polynomial is used to approximate √nk¯γk, which is given by √nk¯γk ≤G(¯γk, nk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' t) = � ¯γk(t)nk(t) + 1 2 �nk(t) ¯γk(t) � 1 2 [ ¯γk − ¯γk(t)] + 1 2 � ¯γk(t) nk(t) � 1 2 [n − nk(t)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (44) Based on (44), (42) can be rewritten as √pk �¯bH k ¯ϕk + |gd,k| � ≥ G(¯γk, nk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' t), ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (45) China Communications 9 Then, P4-2 can be reformulated as the following problem (P4-3) max ¯γk,nk, ¯ϕk ¯γk, (46) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (39), (40), (43) and (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As P4-3 is convex and can be solved by the inter- point method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' We then discuss the initialization of ¯γk(t) and nk(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' First, we propose an initial solution ¯ϕk(0) by solving a simple feasible version of problem P4-1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', ¯ϕk(0), satisfying the constraints (39) and (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then, the reasonable initialization of ¯γk(0) and nk(0) is given by ¯γk(0) = pk ��¯bH k ¯ϕk(0) + |gd,k| ��2 σ2v ¯ϕH k (0)Qr ¯ϕk(0) + σ2r , (47) nk(0) = σ2 v ¯ϕH k (0)Qr ¯ϕk(0) + σ2 r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (48) With the initialization described in (47) and (48), the optimal amplitude reflection coefficients for the WIT, denoted by ¯ϕ∗ k, can be obtained by iteratively solving P4-3 until the convergence is achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As a result, the RIS reflecting coefficients during τk can be calculated by Φ∗ k = diag (Θ∗ k ¯ϕ∗ k) , ∀k, (49) where Θ∗ k = diag{ejθ∗ k,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' , ejθ∗ k,N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The detailed description of optimizing the RIS re- flecting coefficients in P3 is summarized in the Algo- rithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' SCA-based RIS reflecting coefficients for the WIT Input: {wk}, p, ∀k Output: {Φ∗ k}, ∀k 1: Initialization: ¯γk(t), nk(t), ¯ϕk(t), and t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 2: Obtain θ∗ k,n in Proposition 2 and have Θ∗ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 3: repeat 4: t = t + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 5: Update ¯γk(t), nk(t), ¯ϕk(t) by solving P4-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 6: until the convergence is achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 7: Obtain Φ∗ k = diag (Θ∗ k ¯ϕ∗ k), where ¯ϕ∗ k = ¯ϕk(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 8: return {Φ∗ k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 Algorithm Summarization and Analysis Based on the above analysis, the algorithm for solving P1 is summarized in Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Based on the opti- mality analysis,the objective function of P1 is a non- decreasing function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Due to the power budget con- straint (2), (7) and (11), the optimal objective value of problem P1 is bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Hence, the convergence of Algorithm 2 can be thus guaranteed, which will be also confirmed by numerical simulations in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='1 Complexity Analysis The computational complexity of our proposed AO algorithm is analyzed as follows, which contains the linear MMSE-based receive beamforming cal- culation, the SDR algorithm and the SCA algo- rithm in each iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For the linear MMSE- based receive beamforming optimization, we derive a closed-form solution to the (17), and the approx- imate worst-case computational complexity is given by O � KL max(N, L)2� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' According to [36], for the subproblem of SDP-based transmit beamform- ing optimization, the worst-case computational com- plexity is O � max(K, M)4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 log(1/ǫ) � , where ǫ is the computational accuracy of the interior-point method in CVX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Similarly, for the SDP-based RIS reflect- ing coefficients for the WET and resource alloca- tion optimization, the worst-case computational com- plexity is O � Iτ max(N, K)4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 log(1/ǫ) � , where Iτ is the iteration number for updating τ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For the SCA-based RIS reflecting coefficients optimization in the WIT, the computational complexity is less than O � ISKN 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 log(N/ǫ) � , where IS is the iteration number for the SCA algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Thus, the computa- tional complexity of the overall AO algorithm is given by O � IA � KL max(N, L)2 + max(K, M)4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 log(1/ǫ) +Iτ max(N, K)4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 log(1/ǫ) + ISKN 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 log(N/ǫ) �� , (50) where IA denotes the number of iterations required for convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='2 Optimality Analysis As the formulated problem P1 is extremely non- convex, it is very difficult to obtain the globally op- timal solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To solve P1 efficiently, we propose 10 China Communications an efficient AO algorithm to obtain the suboptimal so- lutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Firstly, we obtain the optimal receive beam- forming {wk} in a closed-form, which are the globally optimal solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' With the obtained receive beam- forming solutions, the formulated problem can be sim- plified but is still non-convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Secondly, the SDR technique is adopted to optimize the transmit beam- forming, the RIS reflecting coefficient matrices for the WET phase, the transmit power at each user, and the network time scheduling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In particular, we prove the obtained solutions of P2-1 and P2-2 are rank-one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Since the tightness of applying SDR can be guaran- teed, the obtained solutions {w0, Φ0, τ, p} are glob- ally optimal [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then, we use the one-dimensional search method to exploit the optimal energy trans- mission time τ0 by setting an appropriate step size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Thirdly, for the optimization of RIS reflecting coef- ficients for the WIT phase, we decompose P4 into two sub-problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' On the one hand, the optimal phase shifts have been derived in a closed-form which has been proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' On the other hand, P4-1 is solved by Algorithm 2, which obtains the reflection amplitudes of {Φk} are near-optima of the original problem [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Hence, Algorithm 3 can be used to obtain the near- optimal solutions to P1 with a high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Algorithm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' AO algorithm for P1 1: Initialization: w0, {wk}, Φ0, {Φk}, τ0, τ, p, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 2: repeat 3: Given Φk and p, update {wk} by (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 4: Given Φ0, τ0, {Φk}, {wk}, update w0 with by solving P2-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 5: Given w0, {wk}, {Φk}, update Φ0, τ0, τ and p by Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 6: Given {wk} and p, update {Φk} by Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 7: until �K k=1 Rk converged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 8: return w∗ 0, {w∗ k}, Φ∗ 0, {Φ∗ k}, τ ∗ 0 , τ ∗, p∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' NUMERICAL RESULTS In this section, numerical results are presented to eval- uate the performance of the proposed scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As shown in Figure 3, we consider that the simulated net- work deployment is a 2-D coordinate system, where ��� �� (!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=') (0,0) ( ", 0) ( #, 0) $(!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=') ( %, &) ��������� �� Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Placement model of simulation setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' the coordinates of the PS, the RIS, and the RS are given as (0,0), (xr, 0), and (xs,0), respectively, the users are randomly deployed within a circular area centered at (xu, xh) with radius 1m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' We follow the channel model considered in [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In particular, the large-scale path-loss is modeled as L = A(d/d0)−α, where A is the path-loss at the reference distance d0 = 1m and set as A = −30dB, d denotes the dis- tance between two nodes, and α is the path-loss expo- nent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For the RIS related links, the path-loss exponent is set as 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='2 since the location of RIS can be carefully designed to avoid the severe signal blockage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' While the path-loss exponents for the RIS unrelated links are set as 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 due to the users’ random deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' We assume the direct link channels follow Rayleigh fad- ing but the RIS related channels follow Rician fading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Specifically, the small-scale channel from the PS to the RIS can be expressed as Hr = �� βr βr + 1 ¯ HLoS r + � 1 βr + 1 ¯ HNLoS r � (51) where βr is the Rician factor for the PS-RIS link, ¯ HLoS r denotes the deterministic line of sight (LoS) component, and ¯ HNLoS r denotes the non-LoS compo- tent with circularly symmetric complex Gaussian ran- dom variables with zero mean and unit variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The other channels can be similarly defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Unless oth- erwise stated, other parameters are given as follows: βr = 10 [39], ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='8, σ2 v = σ2 r = −90dBm, P0 = 20dBm [20], Pr = 20dBm, amax = 25dB [40], N = 10, K = 4, M = 4, L = 4, xr = 10m, xu = 10m, xs = 20m, and xh = 2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For comparisons, we also evaluate the performance of the following benchmark schemes: (1) Active RIS-aided single-antenna WPCN scheme (Active-SA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' China Communications 11 (2) Passive RIS-aided multi-antenna WPCN scheme (Passive-MA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (3) Active RIS-aided multi-antenna WPCN with uni- form energy beamforming scheme (Active-MA- UEBF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Notice that for the multi-antenna schemes, the num- ber of antennas is set as 4 in the PS and RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In addition, we set the number of REs in the Passive-MA scheme as N = 100 to show the superiority of the proposed scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Before performance comparisons, we first show the convergence performance of the proposed AO algo- rithm in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' One can observe that as the num- ber of iterations increases, the sum-rate first increases but finally converges to a constant after nearly 8 iter- ations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' This demonstrates that the convergence of the proposed scheme can be achieved quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The other observation is that the effect of the parameter setting on convergence is limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 2 4 6 8 10 12 Number of iterations 13 14 15 16 17 18 19 20 21 22 23 Sum rate (bps/Hz) N=10, M=L=4 N=10, M=L=8 N=20, M=L=4 N=20, M=L=8 N=30, M=L=4 N=30, M=L=8 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Convergence behavior of the proposed scheme under different parameter settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Figure 5 shows the impact of the transmit power at the PS (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', P0) on the sum-rate when the RIS’s maximum reflecting power Pr = 10, 20 dBm and the RIS’s maximum amplitude reflection coefficient amax = 10, 25 dB, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In general, the pro- posed scheme outperforms the Active-SA scheme with the same parameters, which confirms that the assis- tance of multiple antennas can achieve a significant performance gain by constructing the transmit beam- forming at the PS and the receive beamforming at the RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For a given amax = 25 dB, our proposed scheme with 10 REs can achieve 415.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='48% performance gain 5 10 15 20 25 30 35 40 45 Transmit power at the PS(dBm) 0 5 10 15 20 25 30 35 Sum rate (bps/Hz) Proposed, Pr=20, amax=25 Proposed, Pr=20, amax=10 Proposed, Pr=10, amax=25 Proposed, Pr=10, amax=10 Active-SA, Pr=20, amax=25 Active-SA, Pr=20, amax=10 Passive-MA, N=100 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Sum-rate versus the transmit power at the PS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' compared to the passive RIS scheme with 100 REs when P0 = 20 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Indeed, the active RIS can con- siderably make use of its amplification characteristic to amplify the energy signals at low transmit power and thereby realize a superior capability at the cost of additional power consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For a given amax = 10 dB, it can be seen that the sum-rates achieved by the proposed scheme with Pr = 20 dBm and Pr = 10 dBm are almost the same, which implies that the am- plification power constraints defined in (7) and (11) are inactive since amax is limited for the small trans- mit power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Note that, the performance gap is signif- icant between the scheme with amax = 25 dB and amax = 10 dB because amax directly limits the ampli- tude reflection coefficient of the active RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In addi- tion, the sum-rate of the passive-MA scheme is gener- ally lower than the active RIS schemes with the same REs and the passive RIS needs to be equipped with more REs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', 100 REs) to achieve the similar per- formance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In Figure 6, we evaluate the sum-rate versus the number of reflecting elements at the RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It can be seen that the proposed schemes can achieve a higher performance gain compared with the other benchmark schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' With an increasing number of reflecting ele- ments, the sum-rate increases due to the fact that more transmission links can be provided for both the WET and the WIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In addition, to investigate the best system performance, the maximum number of users is set to be equal to the number of REs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Since the active RIS can amplify the incident signals, a limited number of REs is sufficient to reach the desired SNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Therefore, the size of active RIS can be reduced, making it ap- 12 China Communications 5 10 15 20 25 30 35 Number of REs 10 12 14 16 18 20 22 24 Sum rate (bps/Hz) Proposed, K=4 Proposed, K=N Active-SA, K=4 Active-SA, K=N Active-MA-UEBF, K=4 Active-MA-UEBF, K=N Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Sum-rate versus number of reflecting elements at the RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 2 3 4 5 6 7 8 9 10 Number of Users 2 4 6 8 10 12 14 16 18 20 Sum rate (bps/Hz) Proposed Active-SA Active-MA-UEBF Passive-MA Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Sum-rate versus the number of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' plicable to the scenario where the space for the RIS deployment is limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In Figure 7, we study the effect of number of user on the sum-rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As the number of users increases, the total amount of harvested energy by users im- proves, which results in a higher sum-rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Nonethe- less, when the number of users reaches a threshold, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' K = 8, the sum-rate achieved by our pro- posed scheme becomes to be saturated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' This is due to the fact that the increment of number of users re- duces the energy transfer duration and the time allo- cated to each user for information transmission, which makes the sum-rate converge to a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Again, our proposed scheme notably outperforms the other benchmark schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' For example, when the num- ber of users is K = 4, our proposed scheme can achieve 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='78% and 415.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='48% performance gain com- 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 4 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 7 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 10 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 13 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 16 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='5 19 Location of RIS 0 5 10 15 20 25 Sum rate (bps/Hz) Proposed Active-SA Active-MA-UEBF Passive-MA Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Sum-rate versus x-coordinate of the RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' pared with the Active-SA scheme and the Passive-MA scheme with 100 REs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In Figure 8, we plot the sum-rate versus the hori- zontal ordinate of the RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As xr varies, the sum-rates of all schemes first increase but then decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Com- pared to the scenario that the RIS is close to the RS, by deploying the RIS near the PS, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', xr = 1, the sum-rate can be improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It is because the users can harvest more energy assisted by the active RIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Moreover, we can observe that the sum-rate is maxi- mized at xr = 10, where the reflecting link between the active RIS and each user is strongest so the users can benefit from a larger amplification and reflection gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' However, when the RIS is neither close to the PS nor the users, both the PS-RIS link and the RIS- users links become weak, which results in the reduce of harvested energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Furthermore, since the Active- MA-UEBF scheme adopts the uniform energy beam- forming, the energy signals cannot adaptively align with the direction of the desired channels, which re- sults in a low WET efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' In addition, the schemes with the active RIS can achieve a much better perfor- mance than the passive RIS scheme, which demon- strates that the active RIS with the amplification func- tionality can significantly mitigates the double-fading effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The above observation demonstrates that the lo- cation of the active RIS should be carefully designed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' CONCLUSIONS In this paper, we have proposed an active RIS as- sisted relaying scheme to enhance the performance of multiuser multi-antenna WPCN, which is involved China Communications 13 in both the WET from the PS to users and the WIT from users to the RS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' To further enhance system per- formance, both transmit beamforming at the PS and receive beamforming at the RS have been designed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' We have formulated a system sum-rate maximization problem by jointly optimizing the RIS reflection coef- ficients for both the WET and the WIT, transmit and receive beamforming vectors, transmit power at each user, and network time scheduling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As the formulated problem is non-convex, we have proposed an AO al- gorithm with linear MMSE, SDR and SCA techniques to solve it efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Finally, numerical results have been provided to confirm the performance superiority of the proposed scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' APPENDIX A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Proof of Proposition 1 The Lagrangian function of P2-1 can be expressed as L = K � k=1 λkβTr(Hd,kW0) − ξTr(W0) + Tr(ΩW) + δ, ∀k, (52) where λk ≥ 0, ξ ≥ 0, and Ω ∈ HM are the Lagrange multipliers associated with constraints (21), (22), and (24), respectively, δ denotes the term unrelated with W0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' The Karush-Kuhn-Tucker (KKT) conditions of P2-1 are given as follows ∂L ∂W0 = K � k=1 λ∗ kβHd,k − ξ∗IM + Ω∗ = 0, (53) Ω∗W ∗ 0 = 0, (54) where λ∗ k, ξ∗ and Ω∗ are the optimal Lagrangian mul- tipliers for the dual problem of P2-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It can be proved that λ∗ k > 0 and ξ∗ > 0 since the constraints (21) and (22)are equalities in the optimal condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Based on (53) and (54), it is straightforward to obtain the fol- lowing equality (ξ∗IM − K � k=1 λ∗ kβHd,k)W ∗ 0 = 0 (55) According to [41], rank(ξ∗IM −�K k=1 λ∗ kβHd,k) ≥ M − 1 due to the fact that Hd,k for ∀k are indepen- dently distributed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Thus, from (55), we can obtain that rank(W0) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' It is obvious that W0 = 0 is not the optimal solution to P2-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Hence, we derive that rank(W0) = 1, which thus proves Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Proof of Proposition 2 Since Qr and Fk are diagonal matrices, we observe that the noise power in the denominator of (35) and the amplification power in (9) and (36) are independent of the phase shift of each RE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Therefore, maximizing γk with respect to Θk is equivalent to the following optimization problem (P4-4) max Θk ��bH k Θk ¯ϕk + gd,k ��2 (56) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' |Θk,n| = 1, ∀k, ∀n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (57) We rewrite the objective function as ��bH k Θk ¯ϕk ��2 + |gd,k|2 + 2 ��bH k Θk ¯ϕk �� |gd,k| cos α, (58) where α = arctan Im(bH k Θk ¯ϕk) Re(bH k Θk ¯ϕk) − arctan Im(gd,k) Re(gd,k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Obviously, the maximum of ��bH k Θk ¯ϕk + gd,k ��2 is achieved when arg(bH k Θk ¯ϕk) = arg(gd,k) ≜ ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Let vk = [vk,1, vk,2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=', vk,N]T ∈ RN×1 and ξk = diag(bH k ) ¯ϕk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' As bH k Θk ¯ϕk = vH k ξk, P4-4 can be rewritten as (P4-5) max vk ��vH k ξk ��2 (59) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' |vk,n| = 1, ∀k, ∀n, (60) arg(vH k ξk) = ω, ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' (61) Based on [12], the optimal solution to P4- 5 can be expressed as v∗ k = ej(ω−arg(ξk)) = ej(ω−arg(diag(bH k ) ¯ϕk)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Then, the optimal RIS phase shift for the n-th RE is expressed as θk,n = arg(gd,k) − arg(bH k,n) − arg( ¯ϕk,n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Finally, we ob- tain that θk,n = arg(gd,k)−arg(gu,k,n)+arg(gr,k,n), ∀k, ∀n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' This completes the proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' References [1] SOMOV A, GIAFFREDA R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Powering IoT de- vices: Technologies and opportunities[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE IoT Newsletter, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [2] VARSHNEY L R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Transporting information and energy simultaneously[C]//2008 IEEE Interna- 14 China Communications tional Symposium on Information Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE, 2008: 1612-1616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [3] ZHONG C, SURAWEERA H A, ZHENG G, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Wireless information and power transfer with full duplex relaying[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Communications, 2014, 62(10): 3447-3461.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [4] WU Q, GUAN X, ZHANG R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Intelligent reflect- ing surface-aided wireless energy and informa- tion transmission: An overview[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Proceedings of the IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [5] ZHANG R, HO C K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' MIMO broadcasting for simultaneous wireless information and power transfer[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Wireless Com- munications, 2013, 12(5): 1989-2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [6] JU H, ZHANG R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Throughput maximization in wireless powered communication networks [J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Wireless Communi- cations, 2013, 13(1): 418-428.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [7] JU H, ZHANG R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' User cooperation in wireless powered communication networks[C]// 2014 IEEE Global Communications Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE, 2014: 1430-1435.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [8] JU H, ZHANG R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Optimal resource allocation in full-duplex wireless-powered communication network[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Communica- tions, 2014, 62(10): 3528-3540.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [9] KIM J, LEE H, SONG C, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Sum through- put maximization for multi-user MIMO cogni- tive wireless powered communication networks [J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Wireless Communica- tions, 2016, 16(2): 913-923.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [10] WU Q, TAO M, NG D W K, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Energy- efficient resource allocation for wireless pow- ered communication networks[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Trans- actions on Wireless Communications, 2015, 15 (3): 2312-2327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [11] WU Q, CHEN W, LI J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Wireless powered com- munications with initial energy: QoS guaranteed energy-efficient resource allocation[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Communications Letters, 2015, 19(12): 2278- 2281.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [12] WU Q, ZHANG R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Intelligent Reflecting Sur- face Enhanced Wireless Network via Joint Ac- tive and Passive Beamforming[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Trans- actions on Wireless Communications, 2019, 18 (11): 5394-5409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [13] DI RENZO M, ZAPPONE A, DEBBAH M, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Smart radio environments empowered by recon- figurable intelligent surfaces: How it works, state of research, and the road ahead[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE journal on selected areas in communications, 2020, 38 (11): 2450-2525.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [14] KUNDU N K, MCKAY M R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' RIS-Assisted MISO Communication: Optimal Beamform- ers and Performance Analysis[C]//2020 IEEE Globecom Workshops (GC Wkshps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Taipei, Tai- wan: IEEE, 2020: 1-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [15] ZOU Y, GONG S, XU J, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Wireless pow- ered intelligent reflecting surfaces for enhancing wireless communications[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Vehicular Technology, 2020, 69(10): 12369- 12373.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [16] ZHANG Z, DAI L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' A joint precoding framework for wideband reconfigurable intelligent surface- aided cell-free network[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Signal Processing, 2021, 69: 4085-4101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [17] LIANG Y C, CHEN J, LONG R, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Recon- figurable intelligent surfaces for smart wireless environments: Channel estimation, system de- sign and applications in 6G networks[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Science China Information Sciences, 2021, 64(10): 1-21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [18] YU X, JAMALI V, XU D, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Smart and recon- figurable wireless communications: From IRS modeling to algorithm design[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Wireless Communications, 2021, 28(6): 118-125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [19] ZHANG Z, DAI L, CHEN X, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Active RIS vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' passive RIS: Which will prevail in 6G?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [A].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' arXiv: 2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='15154.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [20] LONG R, LIANG Y C, PEI Y, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Active reconfigurable intelligent surface-aided wireless communications[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Wire- less Communications, 2021, 20(8): 4962-4975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [21] LYU B, RAMEZANI P, HOANG D T, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Optimized Energy and Information Relaying in Self-Sustainable IRS-Empowered WPCN[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE TRANSACTIONS ON COMMUNICA- TIONS, 2021, 69(1): 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [22] ZHENG Y, BI S, ZHANG Y J A, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Joint beamforming and power control for throughput maximization in IRS-assisted MISO WPCNs[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Internet of Things Journal, 2021, 8(10): 8399-8410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [23] HUA M, WU Q, POOR H V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Power-Efficient Passive Beamforming and Resource Allocation for IRS-Aided WPCNs[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Communications, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' China Communications 15 [24] XU Y, GAO Z, WANG Z, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' RIS-enhanced WPCNs: Joint radio resource allocation and pas- sive beamforming optimization[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Trans- actions on Vehicular Technology, 2021, 70(8): 7980-7991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [25] YOU C, ZHANG R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Wireless communication aided by intelligent reflecting surface: Active or passive?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Wireless Communications Letters, 2021, 10(12): 2659-2663.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [26] DONG L, WANG H M, BAI J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Active Re- configurable Intelligent Surface Aided Secure Transmission[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Vehic- ular Technology, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [27] ZARGARI S, HAKIMI A, TELLAMBURA C, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Multiuser MISO PS-SWIPT Systems: Ac- tive or Passive RIS?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Wireless Commu- nications Letters, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [28] GAO Y, WU Q, ZHANG G, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Beamform- ing Optimization for Active Intelligent Reflect- ing Surface-Aided SWIPT[A].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' arXiv: 2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content='16093.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [29] ZENG P, QIAO D, WU Q, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Throughput Maximization for Active Intelligent Reflecting Surface Aided Wireless Powered Communica- tions[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Wireless Communications Let- ters, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [30] WU Q, ZHANG R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Weighted Sum Power Maxi- mization for Intelligent Reflecting Surface Aided SWIPT[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE WIRELESS COMMUNICA- TIONS LETTERS, 2020, 9(5): 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [31] HU S, WEI Z, CAI Y, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Robust and se- cure sum-rate maximization for multiuser MISO downlink systems with self-sustainable IRS[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Communications, 2021, 69(10): 7032-7049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [32] ZHENG B, ZHANG R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Intelligent reflect- ing surface-enhanced OFDM: Channel estima- tion and reflection optimization[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Wire- less Communications Letters, 2019, 9(4): 518- 522.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [33] WU Q, ZHANG S, ZHENG B, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Intel- ligent reflecting surface-aided wireless commu- nications: A tutorial[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Communications, 2021, 69(5): 3313-3351.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [34] WANG Z, LIU L, CUI S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Channel Estima- tion for Intelligent Reflecting Surface Assisted Multiuser Communications: Framework, Algo- rithms, and Analysis[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Wireless Communications, 2020, 19(10): 6607- 6620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [35] ZHENG Y, BI S, ZHANG Y J, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Intel- ligent reflecting surface enhanced user cooper- ation in wireless powered communication net- works[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Wireless Communications Let- ters, 2020, 9(6): 901-905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [36] LUO Z Q, MA W K, SO A, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Semidefinite Relaxation of Quadratic Optimization Problems [J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Signal Processing Magazine, 2010, 27 (3): 20-34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [37] BOYD S, BOYD S P, VANDENBERGHE L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Convex optimization[M].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Cambridge university press, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [38] RAZAVIYAYN M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Successive Convex Approx- imation: Analysis and Applications[D].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Univer- sity of Minnesota, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [39] GUO H, LIANG Y C, CHEN J, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Weighted Sum-Rate Maximization for Reconfigurable In- telligent Surface Aided Wireless Networks[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Wireless Communica- tions, 2020, 19(5): 3064-3076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [40] AMATO F, PETERSON C W, DEGNAN B P, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Tunneling RFID tags for long-range and low-power microwave applications[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Journal of Radio Frequency Identification, 2018, 2(2): 93-103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' [41] XU X, LIANG Y C, YANG G, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' Recon- figurable intelligent surface empowered symbi- otic radio over broadcasting signals[J].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' IEEE Transactions on Communications, 2021, 69(10): 7003-7016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} +page_content=' 16 China Communications' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAzT4oBgHgl3EQf9P4T/content/2301.01915v1.pdf'} diff --git a/2tAzT4oBgHgl3EQffPw3/content/2301.01448v1.pdf b/2tAzT4oBgHgl3EQffPw3/content/2301.01448v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..482e340113d40574d744d76eeb18c819f9f67b81 --- /dev/null +++ b/2tAzT4oBgHgl3EQffPw3/content/2301.01448v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:52e3119012d28abcb3e31e3a4c4d7e3c4ce978b7eca9465e40953ebdeae5f93c +size 2705653 diff --git a/2tAzT4oBgHgl3EQffPw3/vector_store/index.pkl b/2tAzT4oBgHgl3EQffPw3/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..6e6f1dde01f7112e1332c56921a53389927a2bdd --- /dev/null +++ b/2tAzT4oBgHgl3EQffPw3/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d2e0733b8a2cae6fef03ecad865e1bb553559562789b707c812a45b8511caeba +size 262850 diff --git a/39AyT4oBgHgl3EQfo_il/vector_store/index.faiss b/39AyT4oBgHgl3EQfo_il/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..fdad318efa8f991543f9506775e2cc8548cd65a5 --- /dev/null +++ b/39AyT4oBgHgl3EQfo_il/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a9e9abf03196fda13fc079c01130ca85a966551d2fb0c027572d70be6b148f08 +size 3670061 diff --git a/49FKT4oBgHgl3EQfSC3u/content/tmp_files/2301.11774v1.pdf.txt b/49FKT4oBgHgl3EQfSC3u/content/tmp_files/2301.11774v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..c38fe60da6f20364d0fbfcefef949edf48f45414 --- /dev/null +++ b/49FKT4oBgHgl3EQfSC3u/content/tmp_files/2301.11774v1.pdf.txt @@ -0,0 +1,1133 @@ +Reinforcement Learning from Diverse Human Preferences +Wanqi Xue * 1 Bo An 1 Shuicheng Yan 2 Zhongwen Xu 2 +Abstract +The complexity of designing reward functions +has been a major obstacle to the wide application +of deep reinforcement learning (RL) techniques. +Describing an agent’s desired behaviors and prop- +erties can be difficult, even for experts. A new +paradigm called reinforcement learning from hu- +man preferences (or preference-based RL) has +emerged as a promising solution, in which reward +functions are learned from human preference la- +bels among behavior trajectories. However, ex- +isting methods for preference-based RL are lim- +ited by the need for accurate oracle preference +labels. This paper addresses this limitation by de- +veloping a method for crowd-sourcing preference +labels and learning from diverse human prefer- +ences. The key idea is to stabilize reward learning +through regularization and correction in a latent +space. To ensure temporal consistency, a strong +constraint is imposed on the reward model that +forces its latent space to be close to the prior distri- +bution. Additionally, a confidence-based reward +model ensembling method is designed to generate +more stable and reliable predictions. The pro- +posed method is tested on a variety of tasks in +DMcontrol and Meta-world and has shown con- +sistent and significant improvements over existing +preference-based RL algorithms when learning +from diverse feedback, paving the way for real- +world applications of RL methods. +1. Introduction +Recent advances in reinforcement learning (RL) have +achieved remarkable success in simulated environments +such as board games (Silver et al., 2016; 2018; Moravˇc´ık +et al., 2017) and video games (Mnih et al., 2015; Vinyals +et al., 2019; Wurman et al., 2022). However, the application +*This work was done during an internship at Sea AI +Lab, Singapore 1Nanyang Technological University, Singapore +2Sea AI Lab, Singapore. +Correspondence to: +Wanqi Xue +, Zhongwen Xu . +Preprint. +of RL to real-world problems remains a challenge due to +the lack of a suitable reward function (Leike et al., 2018). +On the one hand, designing a reward function to provide +dense and instructive learning signals is difficult in complex +real-world tasks (Christiano et al., 2017; Lee et al., 2021b). +On the other hand, RL agents are likely to exploit a reward +function by achieving high return in an unexpected and un- +intended manner (Leike et al., 2018; Ouyang et al., 2022). +To alleviate the problems, preference-based RL is proposed +to convey human-preferred objectives to agents (Christiano +et al., 2017; Stiennon et al., 2020), in which a (human) +teacher is requested to provide his/her preferences over pairs +of agents’ historical trajectories. Based on human feedback, +a reward model is learned and applied to provide learning +signals to agents (see Fig. 1(a)). Preference-based RL pro- +vides an effective way to learn from human intentions, rather +than explicitly designed rewards, and has demonstrated its +effectiveness in areas such as robotics control (Lee et al., +2021b) and dialogue systems (Ouyang et al., 2022). +Though promising, the learning of preference-based RL +heavily relies on plenty of expert feedback, which could +be prohibitively expensive. Existing works typically focus +on feedback-efficient algorithms. They investigate several +sampling and exploration strategies with the aim of finding +the most deserving queries to be labelled (Biyik & Sadigh, +2018; Lee et al., 2021a; Liang et al., 2022). Some other +works improve feedback efficiency by learning good policy +initialization with imitation learning (Ibarz et al., 2018) and +unsupervised pre-training (Lee et al., 2021b). In addition, +semi-supervised reward learning is also used for better effi- +ciency (Park et al., 2022). Although these methods reduce +the demand for human feedback, scaling preference-based +RL to large-scale real-world problems is still difficult be- +cause the need for feedback increases significantly with the +complexity of problems. +Recently, there has been a trend to replace expensive expert +feedback with crowd-sourced data for scalability (Gerst- +grasser et al., 2022; Ouyang et al., 2022). For example, +in ChatGPT, a group of annotators are hired for providing +affordable human feedback to RL agents. The impressive +results show that preference-based RL has great potential +when sufficient human feedback is provided. Obtaining hu- +man feedback from various sources can effectively address +the issue of data scarcity in preference-based RL. However, +arXiv:2301.11774v1 [cs.LG] 27 Jan 2023 + +Reinforcement Learning from Diverse Human Preferences +Annotation +Reward learning +Encoder +Decoder +(a) +(b) +Figure 1. Illustration of our method. (a) There is a team of different annotators with bounded rationality to provide their preferences. +Based on the preference data, a reward model is learned and used to provide rewards to an RL agent for policy optimization. (b) The +reward models encode an input into a latent space where a strong distribution constraint is applied to address inconsistency issues. +Following that, a novel reward model ensembling method is applied to the decoders to aggregate their predictions. +this approach also brings some challenges, as the collected +preferences may be unreliable, inconsistent, or even adver- +sarial, making it difficult to optimize the policy. The diverse +nature of the feedback can make it challenging to deter- +mine the true underlying preferences and to learn from them +effectively. +In this paper, we propose a simple yet effective method to +help existing preference-based RL algorithms learn from +diverse human preferences. The key idea is to stabilize the +reward learning by regularizing and correcting its predic- +tions in a latent space. Concretely, we first map the inputs +of the reward model to a latent space, enabling the predicted +rewards to be easily manipulated by varying them in this +space. Second, to ensure temporal consistency throughout +the learning process, we impose a strong constraint on the +latent space by forcing it to be close to a prior distribution. +This prior distribution serves as a reference point, providing +a way to measure the consistency of the predicted rewards +over time. Lastly, we measure the confidence of the re- +ward model in its predictions by calculating the divergence +between its latent space and the prior distribution. Based +on this divergence, we design a confidence-based reward +model ensembling method to generate more stable and reli- +able predictions. We demonstrate the effectiveness of our +method on a variety of complex locomotion and robotic +manipulation tasks from DeepMind Control Suite (DM- +Control) (Tassa et al., 2018; Tunyasuvunakool et al., 2020) +and Meta-world (Yu et al., 2020). The results show that +our method is able to effectively recover the performance +of existing preference-based RL algorithms under diverse +preferences in all the tasks. +2. Preliminaries +We consider the reinforcement learning (RL) framework +which is defined as a Markov Decision Process (MDP). For- +mally, an MDP is defined by a tuple ⟨S, A, r, P, γ⟩, where +S and A denote the state and action space, r(s, a) is the +reward function, P(s′|s, a) denotes the transition dynam- +ics, and γ ∈ [0, 1) is the discount factor. At each timestep +t, the agent receives the current state st ∈ S from the +environment and makes an action at ∈ A based on its +policy π(at|st). Subsequently, the environment returns a +reward rt and the next state st+1 to the agent. RL seeks +to learn a policy such that the expected cumulative return, +E +��∞ +k=0 γkr(st+k, at+k) +� +, is maximized. +In realistic applications, designing the reward function to +capture human intent is rather difficult. Preference-based +RL is therefore proposed to address this issue by learning +a reward function from human preferences (Akrour et al., +2011; Wilson et al., 2012; Christiano et al., 2017; Ibarz +et al., 2018). Specifically, there is a human teacher indi- +cating his/her preferences over pairs of segments (σ0, σ1), +where a segment is a part of the trajectory of length H, i.e., +σ = {(s1, a1), . . . , (sH, aH)}. The preferences y could +be (0, 1), (1, 0) and (0.5, 0.5), where (0, 1) indicates σ1 is +preferred to σ0, i.e., σ1 ≻ σ0; (1, 0) indicates σ0 ≻ σ1; +and (0.5, 0.5) implies an equally preferable case. Each feed- +back is stored as a triple (σ0, σ1, y) in a preference buffer +Dp = {((σ0, σ1, y))i}N +i=1. +To learn a reward function ˆr from the labeled preferences, +similar to most prior work (Ibarz et al., 2018; Lee et al., +2021b;a; Liang et al., 2022; Park et al., 2022; Hejna III & +Sadigh, 2022), we define a preference predictor by following + +(s, a, r(s, a), s')(s, a, s')AReinforcement Learning from Diverse Human Preferences +the Bradley-Terry model (Bradley & Terry, 1952): +Pψ +� +σ1 ≻ σ0� += +exp +��H +t=1 ˆr +� +s1 +t, a1 +t; ψ +�� +� +i∈{0,1} exp +��H +t=1 ˆr +� +si +t, ai +t; ψ +��. +(1) +Given the preference buffer Dp, we can train the reward +function ˆr by minimizing the cross-entropy loss between the +preference predictor and the actually labeled preferences: +Ls = − +E +(σ0,σ1,y)∼Dp +� +y(0) log Pψ +� +σ0 ≻ σ1� ++ y(1) log Pψ +� +σ1 ≻ σ0�� +. +(2) +where y(0) and y(1) are the first and second element of y, +respectively. With the learned rewards, we can optimize a +policy π using any RL algorithm to maximize the expected +return (Christiano et al., 2017). +3. Preference-based Reinforcement Learning +from Diverse Human Feedback +Preference-based RL provides an effective framework to +deliver human intentions to RL agents. In this section, we +present our algorithm which helps RL agents to learn from +human preferences that possess high diversity and incon- +sistency. The key idea of our algorithm is to stabilize the +reward learning by regularizing and correcting it in a latent +space. Specifically, we first map the input of the reward +model to a latent space so that the predicted reward can +be easily manipulated by modifying it in the latent space. +Second, to achieve temporal consistency throughout the +learning process, we impose a strong constraint on the latent +space by forcing it to be close to a prior distribution. Last, +we measure the confidence of a reward model in its predic- +tion by calculating the divergence between its latent space +and the prior distribution. Based on the divergence, we de- +sign a confidence-based reward model ensembling method +to generate more reliable and stable predictions. The overall +framework of our algorithm is presented in Figure 1. +3.1. Manipulating Rewards within a Latent Space +Reward learning is a key problem in preference-based RL +because RL agents rely on the guidance of the learned re- +ward model for policy optimization (Silver et al., 2021). +However, learning an instructive and stable reward model +is rather difficult when human preferences possess high +diversity. If we simply minimize the loss in Eq. 2, the +generated rewards will have severe fluctuations and incon- +sistencies because the supervised signal, i.e., the collected +preferences (y), can be noisy, self-contradictory, or even +adversarial. As a result, RL agents cannot converge to a rea- +sonable policy since the learning objectives always change. +Algorithm 1 RL from Diverse Human Preferences +1: Input: Strength of constraint φ, number of reward mod- +els N, frequency of feedback session K +2: Initialize parameters of policy π(s, a) and the reward +model ˆr(s, a; ψ) +3: Initialize preferences buffer Dp ← ∅ and replay buffer +Dr ← ∅ +4: for each iteration do +5: +if iteration % K == 0 then +6: +Sample (σ0, σ1) and query annotators for y +7: +Store preference Dp ← Dp ∪ {(σ0, σ1, y)} +8: +for each reward model updating step do +9: +Sample a minibatch of preferences (σ0, σ1, y) +10: +Optimize the reward model (Eq. 7) +11: +end for +12: +end if +13: +for each timestep do +14: +Collect s′ by taking action a ∼ π(s, a) +15: +Store transition Dr ← Dr ∪ {(s, a, s′)} +16: +end for +17: +for each policy updating step do +18: +Sample a minibatch of transitions (s, a, s′). +19: +Measure the confidence of reward models (Eq. 8) +20: +Relabel the transitions with ˆr(s, a; ψ) (Eq. 9) +21: +Update the policy π(s, a) on {(s, a, ˆr(s, a), s′)} +22: +end for +23: end for +To deal with the problem, an intuitive solution is to correct +the predicted rewards before feeding them to the agent. Con- +ventionally, methods such as reward shaping involve adding +additional rewards or penalties to the original rewards to +guide the agent toward the desired behavior. However, the +added rewards usually introduce unintended side effects or +inconsistencies in the learning process. As a mitigation, we +propose to manipulate the rewards within a latent space, +which avoids directly changing the predictions. We adopt +an encoder-decoder structure where the encoder is used to +map the input, i.e., a state-action pair, to latent space. After +sampling a representation vector from the latent space, the +decoder is applied to map the vector back to a reward. +Formally, the encoder p(z|s, a; ψe), parameterized by ψe, is +in the form of +p(z|s, a; ψe) = N(z|f µ(s, a; ψe), f Σ(s, a; ψe)), +(3) +where N(µ, Σ) denotes a Gaussian distribution with mean +vector µ and covariance matrix Σ. The encoder consists of +two multi-layer perceptrons (MLPs) whose output gener- +ates the K-dimensional mean µ and the K × K covariance +matrix Σ, respectively. The decoder d(r|z; ψd), with pa- +rameters ψd, takes as input a sampled latent variable z and +outputs a reward. Such an encoder-decoder structure enjoys + +Reinforcement Learning from Diverse Human Preferences +Figure 2. Examples for locomotion tasks and robotic manipulation +tasks we test on. +benefits under diverse human preferences: i) we can control +the fluctuations of the rewards by adjusting the distribution +of the latent space; ii) the confidence of the reward model +to its predictions can be easily measured by calculating the +divergence between different latent spaces. In the following +sections, we will elaborate on how to leverage the aforemen- +tioned advantages. +3.2. Achieving Consistency by Imposing a Strong +Constraint +As previously mentioned, the reward model is learned under +the supervision of human feedback, which could have high +diversity if they are collected from different crowds. As a +consequence, the rewards will demonstrate severe fluctua- +tions and inconsistencies throughout the learning process. +For example, at the beginning of the training, the reward +model learns some patterns, and the policy is optimized to- +ward the corresponding objective. As the training processes, +more labeled preferences are added to the dataset and the +updated reward model can be completely different. As a +result, the reward model will make distinct predictions for +the same input at the different training stages. We found +that it is the temporal inconsistency that causes the collapse +of a policy. To alleviate the problem, we propose to impose +a constraint on the latent space so that the reward model +has a fixed optimization direction throughout the training +process. Concretely, we assume that the latent space fol- +lows a prior distribution r(z), and we try to minimize the +Kullback-Leibler (KL) divergence between the latent space +and its prior: +Lc = E(s,a) +� +KL(p(z|s, a; ψe)||r(z)) +� +. +(4) +Since r(z) is pre-defined, the optimization of the encoder +will be guided toward a fixed direction, independent of how +diverse the human preferences are. +Remark 3.1. Minimizing the loss in Eq. 4 is equivalent to +minimizing the mutual information between (S, A) and Z, +which leads to a concise representation of the input. +Proof: To simplify the notation, we let variable X denote the +input pairs (S, A). Then by the definition of KL-divergence: +Lc = +�� +dx dz p(x) +� +p(z|x) log p(z|x) +r(z) +� += +�� +dx dz p(x, z) log p(z|x) − +� +dz p(z) log r(z). +(5) +Since KL(p(z)|r(z)) ≥ 0, we have +� +dz p(z) log p(z) ≥ +� +dz p(z) log r(z). As a result, +Lc ≥ +�� +dx dz p(x, z) log p(z|x) − +� +dz p(z) log p(z) += I(Z, X). +(6) +Eq. 6 shows that minimizing Lc is equivalent to minimizing +an upper bound of I(Z, X). +Overall, the loss function for the reward model is +L = φ ∗ Lc + Ls, +(7) +where φ is a parameter controlling the strength of the con- +straint. Conventionally, φ is set as a small value to confirm +that the supervised signals will not be dominated. However, +counterintuitively, we found that a large φ is crucial for +good performance. Larger φ will lead to a stronger con- +straint on the latent space. As a result, the latent space for +different inputs will be similar, and the predicted rewards +will be controlled into a smaller range. Considering that it +is relative values of rewards, not absolute values, that affect +a policy, a reward model with a smaller value range can +lead to more accurate, stable, and effective outcomes, and +therefore benefit the learning process. +3.3. Confidence-based Reward Model Ensembling +It is common that diverse human preferences contain out- +lier data. To reduce the influence of a single data point on +the reward model, we adopt reward model ensembling to +reduce overfitting and improve stability (Lee et al., 2021b; +Liang et al., 2022). Instead of simply averaging, we design +a confidence-based ensembling mechanism to improve per- +formance. The key idea is to aggregate the predicted results +by up-weighting the reward models with higher confidence +and down-weighting those with less confidence. We first +measure the confidence level of each reward model and then +perform a weighted summation to generate the final result. +Specifically, the confidence of a reward model is measured +by calculating the KL divergence from the predicted latent +space to its prior distribution. If the KL divergence is small +which means the reward model cannot tell too much input- +specific information, the reward model has low confidence +about the input (a model tends to output the prior directly + +Reinforcement Learning from Diverse Human Preferences +0 +0.1M +0.2M +0.3M +0.4M +0.5M +Environment Steps +0 +250 +500 +750 +1000 +Episode Return +Walker +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +200 +400 +600 +Cheetah +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +200 +400 +600 +800 +Quadruped +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +25 +50 +75 +100 +Success Rate (%) +Button Press +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +25 +50 +75 +100 +Sweep Into +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +25 +50 +75 +100 +Hammer +Oracle +Ours +PEBBLE +Figure 3. Learning curves on locomotion tasks (first row) and robotic manipulation tasks (second row). The locomotion tasks are measured +on the ground truth episode return while the robotic manipulation tasks are measured on the success rate. The solid line and shaded +regions represent the mean and standard deviation, respectively, across five runs. +if it knows nothing about the input). On the contrary, a +large KL divergence indicates a high confidence level. We +assume that the confidence is proportional to the exponent +of the KL divergence: +Gi(s, a) = +exp(KL(pi(z|s, a)||r(z))) +�N +j=1 exp(KL(pj(z|s, a)||r(z))) +, +(8) +where Gi(s, a) denotes the confidence of the i-th reward +model to an input (s, a), N is the number of reward mod- +els. After determining the confidence of each model, we +calculate the reward by: +ˆr(s, a; ψ) = +N +� +i=1 +Gi(s, a) × +� +di ◦ qi(r|s, a) +� +, +(9) +where di and qi are the decoder and the encoder of the i-th +reward model, respectively. With the reword model, we +can use any preference-based RL algorithm to learn the +policy. The full procedure of our method is summarized in +Algorithm 1. +4. Experiments +We conduct experiments to answer the following questions: +Q1: Whether the proposed method can effectively help ex- +isting preference-based RL algorithms to learn from +diverse preferences? +Q2: How does each component of the method contribute to +the effectiveness? +Q3: How will latent spaces affect the predicted rewards? +Q4: How will the method be affected by the number of +annotators? +4.1. Setup +We evaluate our method on several complex locomotion +tasks and robotic manipulation tasks from DeepMind Con- +trol Suite (DMControl) (Tassa et al., 2018; Tunyasuvu- +nakool et al., 2020) and Meta-world (Yu et al., 2020), respec- +tively (see Fig. 2). In order to justify the effectiveness of our +method, we train an agent to solve the tasks without observ- +ing the true rewards from the environment. Instead, several +scripted annotators are generated to provide their prefer- +ences between two trajectory segments for the agent to learn +its policy. Unlike existing preference-based RL algorithms +which interact with a single perfect scripted teacher (Chris- +tiano et al., 2017; Lee et al., 2021b; Park et al., 2022), we +consider the situation where there is a team of different an- +notators with bounded rationality to provide the preferences. +Despite being imperfect, the annotators’ preferences are +also calculated from ground truth rewards. Therefore, we +can quantitatively evaluate the method by measuring the +true episode return or success rate from the environments. +Our method can be integrated into any preference-based +RL algorithm to recover their performance under diverse +preferences. In our experiments, we choose one of the most +popular approaches, PEBBLE (Lee et al., 2021b), as the +backbone algorithm. We examine the performance of PEB- +BLE under i) a perfect scripted teacher who provides the +ground true feedback (oracle); ii) a team of randomly sam- +pled annotators whose feedback is imperfect and anisotropic. +The goal of our method is to recover the performance of +PEBBLE under the annotators as much as possible, to ap- + +Reinforcement Learning from Diverse Human Preferences +0 +0.1M +0.2M +0.3M +0.4M +0.5M +Environment Steps +0 +500 +1000 +Episode Return +Walker +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +200 +400 +600 +Cheetah +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +200 +400 +600 +Quadruped +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +25 +50 +75 +100 +Success Rate (%) +Button Press +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +25 +50 +75 +100 +Sweep Into +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +25 +50 +75 +100 +Hammer += 1 += 10 += 100 +Figure 4. Ablation study on the strength of the latent space constraint. The locomotion tasks (first row) are measured on the ground +truth episode return while the robotic manipulation (second row) tasks are measured on the success rate. The results show the mean and +standard deviation averaged over five runs. +proach the oracle case. +Simulating the annotators. We generate the bounded ratio- +nal scripted annotators by following the previous stochastic +preference model (Lee et al., 2021a): +P +� +σ1 ≻ σ0� += +exp +� +β �H +t=1 γH−tr +� +s1 +t, a1 +t +�� +� +i∈{0,1} exp +� +β �H +t=1 γH−tr +� +si +t, ai +t +��. +(10) +r(s, a) is the ground truth reward provided by the envi- +ronment. A scripted annotator is determined by a tuple +⟨β, γ, ϵ, δequal⟩: β is the temperature parameter that con- +trols the randomness of the stochastic preference model. +An annotator becomes perfectly rational and deterministic +as β → ∞, whereas β = 0 produces uniformly random +choices. γ controls the myopic (short-sighted) behavior of +an annotator. Annotators with small γ will emphasize more +on immediate rewards and down-weight long-term return. ϵ +describes the probability that an annotator makes a mistake, +i.e., we flip the preference with the probability of ϵ. δequal de- +notes the threshold that an annotator marks the segments as +equally preferable, i.e., an annotator provides (0.5, 0.5) as a +response if | � +t r(s1 +t, a1 +t) − � +t r(s0 +t, a0 +t)| ≤ δequal. Practi- +cally, we sample a tuple from β ∈ {∞, 1, 5}, γ ∼ U(0.8, 1), +ϵ ∼ U(0, 0.2), δequal ∼ U(0, 0.2) to generate a scripted an- +notator. For each task, we randomly generate 100 annotators +to provide feedback. Each annotator has the same probabil- +ity of being selected for annotation. +Implementation details. For all tasks, we use the same +hyperparameters used by PEBBLE, such as learning rates, +architectures of the neuron networks, and reward model +updating frequency. We adopt an uniform sampling strat- +egy, which selects queries with the same probability. At +each feedback session, a batch of 256 trajectory segments +(σ0, σ1) is sampled for annotation. The strength of con- +straint φ is set as 100 for all tasks. For simplicity, we set the +prior distribution of the latent space as standard Gaussian +where the KL-divergence from a latent space to its prior can +be easily calculated. All experimental results are reported +with the mean and standard deviation across five runs. +4.2. Experimental Results +Locomotion tasks from DMControl. +We select three +complex environments from DMControl, +which are +Walker walk, Cheetah run, and Quadruped walk, to eval- +uate our method. As previously mentioned, PEBBLE is +used as the backbone algorithm and our method is com- +bined with PEBBLE to recover its performance under di- +verse human preferences. The first row of Fig. 3 shows the +learning curves of PEBBLE and our method when learning +from bounded rational annotators. We can find that, com- +pared to learning from a single perfect teacher (oracle), the +performance of PEBBLE (measure on true episode return) +decreases dramatically in all three tasks. For example, in +Walker walk, PEBBLE is able to achieve 1000 scores if +it learns from a single expert, whereas the value is nearly +half of the preferences are from different annotators. Such +failures show that existing preference-based RL algorithms +do not work well when the provided preferences contain +diversity and inconsistency. After integrating our method +(the red line), we can find significant performance increases +in all three tasks: our method is able to achieve almost the +same performance as the oracle in Walker walk, while the +performance gap between our method and its upper bound + +Reinforcement Learning from Diverse Human Preferences +Figure 5. Analysis about the influence of φ on the reward model. First row: increasing the strength of the constraint will narrow the +value range of the predicted rewards. The reward model will also generate more distinct predictions if φ is large. Second row: the t-SNE +visualization of the latent vectors. A large φ leads to a more compact and concise pattern. +(oracle) is very narrow in Cheetah run. In Quadruped walk, +PEBBLE is unable to learn a feasible policy, while our +proposed method still achieves near-optimal performance. +Robotic manipulation tasks from Meta-world. +Meta- +world consists of 50 tasks that cover a range of fundamental +robotic manipulation skills. We consider three challenging +environments to evaluate the effectiveness of our method. +The performance is measured on success rate, i.e., if the +trained agent is able to successfully finish a task or not. Fig 3 +(second row) shows the learning curves of our method as +the baselines. We can find that there is a significant perfor- +mance increase after integrating our method into PEBBLE. +The performance can be almost restored to approach the +oracles in Button Press and Hammer, while in Sweep Into, +the improvement is also non-trivial. These results again +demonstrate that our proposed method is able to effectively +help the existing preference-based RL algorithms learn from +diverse preferences. +4.3. Ablation and Analysis +Effects of the latent space constraint. As previously in- +troduced, to achieve temporal consistency and set a fixed +optimization direction for the reward model, our method +imposes a constraint on the latent space by forcing its dis- +tribution to be close to the prior. To justify the effect of +the constraint, we implement our method with different +strengths of constraint on all six tasks. As shown in Fig. 4, +there is a significant and consistent improvement in all the +tasks as we gradually increase the strength of the constraint. +For example, in Cheetah run, when we set the strength of +0 +100K +200K +300K +400K +500K +Environment Steps +0 +200 +400 +600 +800 +1000 +Episode Return +w/ ensembling +w/o ensembling +0 +100K +200K +300K +400K +500K +Environment Steps +0 +200 +400 +600 +800 +1000 +KL-based +mean +Figure 6. Ablation study on reward model ensembling. +Left: +Learning curves of Walker walk with and without reward model +ensembling. Right: Learning curves of Walker walk with KL- +based model ensembling and simply averaging. The results show +the mean and standard deviation averaged over five runs. +constraint ψ to 1, 10, and 100, the performance increases +from around 200 to 400 and finally reaches near 600. This +phenomenon is a little bit counter-intuitive because, con- +ventionally, a too strong constraint is likely to misguide +the reward model and prevent it from learning from super- +vised signals. However, we found that a strong constraint on +the latent space is compulsory to help an agent learn from +diverse feedback. +Analysis about the reward model. To understand why a +strong constraint is crucial for the performance, we ana- +lyze the effect of the latent space constraint on the reward +model. Specifically, we collect 100,000 state-action pairs +from Cheetah run at different training stages and use the +reward model trained with different strengths of constraint +to predict the rewards. The predictions are presented in + +Φ=l +Φ=10 +Φ= 100 +Predicted Rewards +0.2 +0.0 +0.0 +0.0 +-0.2 +-0.2 +-0.2 +-0.4 +-0.4 +-0.4 +-0.6 +-0.6 +100 +100 +100 +50 +50 +50 +tSNE2 +0 +0 +-50 +-50 +-50 +-100 +-100 +-100 +-100 +-50 +0 +50 +100 +-100 +-50 +50 +100 +-100 +-50 +0 +50 +100 +0 +tSNE1 +tSNE1 +tSNE1Reinforcement Learning from Diverse Human Preferences +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +200 +400 +600 +800 +Episode Return +Num_annotators=1 +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +200 +400 +600 +800 +Num_annotators=10 +0 +0.2M +0.4M +0.6M +0.8M +1.0M +Environment Steps +0 +200 +400 +600 +800 +Num_annotators=100 +Oracle +Ours +PEBBLE +Figure 7. Learning curves of Cheetah run (a locomotion task) with preferences provided by a different number of annotators. The results +are measured on the ground truth episode return, with the solid line and shaded regions representing the mean and standard deviation, +respectively, across five runs. +the first row of Fig. 5. We can find that as we increase the +strength of constraint, the range of reward values decreases +gradually. For example, when φ = 1, the predicted rewards +are between -0.6 and 0.15, while the range is narrowed to +[−0.5, 0] when we set φ = 100. Moreover, the predicted +rewards are more distinct when φ becomes larger, which +indicates that only really good state-action pairs are given +high rewards. We also use t-SNE (Van der Maaten & Hin- +ton, 2008) to visualize the latent vector of those state-action +pairs. As in Fig. 5 (second row), the distribution of the +embeddings becomes more compact as we increase φ. Fur- +thermore, the pattern of the embeddings is more clear and +more concise when φ is large. +Effects of reward model ensembling. We investigate how +well the reward ensembling affects the performance of +our method. Fig. 6 (left) shows the learning curves of +Walker walk with and without reward model ensembling. +We can find that there is a clear performance drop if using a +single reward model. The results demonstrate that ensem- +bling the predictions of several models is helpful to stabilize +the training process if the preferences are diverse. We fur- +ther investigate whether the proposed KL-based aggregation +method is better than simply averaging. As shown in Fig. 6 +(right), simply averaging will suffer severe fluctuations in +the training process, while the performance of our method +is significantly more stable and consistent. +Responses to the number of annotators. To examine how +will our algorithm respond to the number of annotators, we +implement Cheetah run with preferences provided by dif- +ferent numbers of annotators. As shown in Fig 7, when +there is only one annotator which is bounded rational, both +PEBBLE and our method perform worse than the oracle. In +these cases, the preferences are not diverse but just partially +correct. If we slightly increase the number of annotators +to ten, which introduces some diversity, our method is able +to achieve obvious improvement over PEBBLE. The per- +formance gain becomes quite significant when there are +one hundred annotators. The experiments demonstrate that +our method is suitable for situations where the provided +preferences are diverse. +5. Related Work +The main focus in the paper is on one promising direction +which utilizes human preferences (Akrour et al., 2011; Chris- +tiano et al., 2017; Ibarz et al., 2018; Leike et al., 2018; Lee +et al., 2021b; Ouyang et al., 2022; Park et al., 2022; Liang +et al., 2022) to perform policy optimization. Christiano +et al. (2017) introduced modern deep learning techniques +to preference-based learning. Since the learning of the re- +ward function, modeled by deep neural networks, requires +a large number of preferences, recent works have typically +focused on improving the feedback efficiency of a method. +PEBBLE (Lee et al., 2021b) proposed a novel unsupervised +exploration method to pre-train the policy. SURF (Park +et al., 2022) adopted a semi-supervised reward learning +framework to leverage a large number of unlabeled samples. +Some other works improved data efficiency by introducing +additional types of feedback such as demonstrations (Ibarz +et al., 2018) or non-binary rankings (Cao et al., 2021). In +addition to that, designing intrinsic rewards to encourage +effective exploration is also investigated (Liang et al., 2022). +Despite being efficient, previous methods mainly focus on +learning from a single expert, which will severely limit the +scalability of an algorithm. In this work, we focus on learn- +ing from human preferences collected from different types +of annotators. Our method emphasizes addressing the issue +of diversity rather than feedback efficiency. +6. Conclusion +In this work, we propose a simple yet effective method +to improve the performance of preference-based RL algo- +rithms under diverse feedback. The method maps inputs to +a latent space imposes a constraint on the latent space to + +Reinforcement Learning from Diverse Human Preferences +maintain temporal consistency, and uses a confidence-based +ensembling method to generate more stable predictions. Ex- +tensive experiments are conducted in various environments. +The results show that our method can significantly improve +performance under diverse preferences in all the tasks. +References +Akrour, R., Schoenauer, M., and Sebag, M. Preference- +based policy learning. In Joint European Conference +on Machine Learning and Knowledge Discovery in +Databases, pp. 12–27. Springer, 2011. +Biyik, E. and Sadigh, D. Batch active preference-based +learning of reward functions. In Conference on Robot +Learning, pp. 519–528. PMLR, 2018. +Bradley, R. A. and Terry, M. E. Rank analysis of incom- +plete block designs: I. the method of paired comparisons. +Biometrika, 39(3/4):324–345, 1952. +Cao, Z., Wong, K., and Lin, C.-T. Weak human preference +supervision for deep reinforcement learning. IEEE Trans- +actions on Neural Networks and Learning Systems, 32 +(12):5369–5378, 2021. +Christiano, P. F., Leike, J., Brown, T., Martic, M., Legg, +S., and Amodei, D. Deep reinforcement learning from +human preferences. Advances in neural information pro- +cessing systems, 30, 2017. +Gerstgrasser, M., Trivedi, R., and Parkes, D. C. Crowdplay: +Crowdsourcing human demonstrations for offline learn- +ing. In International Conference on Learning Represen- +tations, 2022. URL https://openreview.net/ +forum?id=qyTBxTztIpQ. +Hejna III, D. J. and Sadigh, D. Few-shot preference learning +for human-in-the-loop rl. In 6th Annual Conference on +Robot Learning, 2022. +Ibarz, B., Leike, J., Pohlen, T., Irving, G., Legg, S., and +Amodei, D. Reward learning from human preferences and +demonstrations in atari. Advances in Neural Information +Processing Systems, 31, 2018. +Lee, K., Smith, L., Dragan, A., and Abbeel, P. B-pref: +Benchmarking preference-based reinforcement learning. +In Thirty-fifth Conference on Neural Information Process- +ing Systems Datasets and Benchmarks Track (Round 1), +2021a. +Lee, K., Smith, L. M., and Abbeel, P. Pebble: Feedback- +efficient interactive reinforcement learning via relabeling +experience and unsupervised pre-training. In Proceed- +ings of the 38th International Conference on Machine +Learning, pp. 6152–6163, 2021b. +Leike, J., Krueger, D., Everitt, T., Martic, M., Maini, V., and +Legg, S. Scalable agent alignment via reward modeling: +a research direction. arXiv preprint arXiv:1811.07871, +2018. +Liang, X., Shu, K., Lee, K., and Abbeel, P. Reward uncer- +tainty for exploration in preference-based reinforcement +learning. In International Conference on Learning Rep- +resentations, 2022. +Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A. A., Veness, +J., Bellemare, M. G., Graves, A., Riedmiller, M., Fidje- +land, A. K., Ostrovski, G., et al. Human-level control +through deep reinforcement learning. Nature, 518(7540): +529–533, 2015. +Moravˇc´ık, M., Schmid, M., Burch, N., Lis`y, V., Morrill, D., +Bard, N., Davis, T., Waugh, K., Johanson, M., and Bowl- +ing, M. Deepstack: Expert-level artificial intelligence in +heads-up no-limit poker. Science, 356(6337):508–513, +2017. +Ouyang, L., Wu, J., Jiang, X., Almeida, D., Wainwright, +C. L., Mishkin, P., Zhang, C., Agarwal, S., Slama, +K., Ray, A., et al. +Training language models to fol- +low instructions with human feedback. arXiv preprint +arXiv:2203.02155, 2022. +Park, J., Seo, Y., Shin, J., Lee, H., Abbeel, P., and Lee, +K. SURF: Semi-supervised reward learning with data +augmentation for feedback-efficient preference-based re- +inforcement learning. In International Conference on +Learning Representations, 2022. +Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L., +Van Den Driessche, G., Schrittwieser, J., Antonoglou, I., +Panneershelvam, V., Lanctot, M., et al. Mastering the +game of go with deep neural networks and tree search. +Nature, 529(7587):484–489, 2016. +Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, +M., Guez, A., Lanctot, M., Sifre, L., Kumaran, D., Grae- +pel, T., et al. A general reinforcement learning algorithm +that masters chess, shogi, and go through self-play. Sci- +ence, 362(6419):1140–1144, 2018. +Silver, D., Singh, S., Precup, D., and Sutton, R. S. Reward +is enough. Artificial Intelligence, 299:103535, 2021. +Stiennon, N., Ouyang, L., Wu, J., Ziegler, D., Lowe, R., +Voss, C., Radford, A., Amodei, D., and Christiano, +P. F. Learning to summarize with human feedback. Ad- +vances in Neural Information Processing Systems, 33: +3008–3021, 2020. +Tassa, Y., Doron, Y., Muldal, A., Erez, T., Li, Y., Casas, D. +d. L., Budden, D., Abdolmaleki, A., Merel, J., Lefrancq, +A., et al. +Deepmind control suite. +arXiv preprint +arXiv:1801.00690, 2018. + +Reinforcement Learning from Diverse Human Preferences +Tunyasuvunakool, S., Muldal, A., Doron, Y., Liu, S., Bohez, +S., Merel, J., Erez, T., Lillicrap, T., Heess, N., and Tassa, +Y. dm control: Software and tasks for continuous control. +Software Impacts, 6:100022, 2020. +Van der Maaten, L. and Hinton, G. Visualizing data using +t-sne. Journal of Machine Learning Research, 9(11), +2008. +Vinyals, O., Babuschkin, I., Czarnecki, W. M., Mathieu, M., +Dudzik, A., Chung, J., Choi, D. H., Powell, R., Ewalds, +T., Georgiev, P., et al. Grandmaster level in starcraft ii +using multi-agent reinforcement learning. Nature, 575 +(7782):350–354, 2019. +Wilson, A., Fern, A., and Tadepalli, P. A bayesian approach +for policy learning from trajectory preference queries. +Advances in Neural Information Processing Systems, 25, +2012. +Wurman, P. R., Barrett, S., Kawamoto, K., MacGlashan, J., +Subramanian, K., Walsh, T. J., Capobianco, R., Devlic, +A., Eckert, F., Fuchs, F., et al. Outracing champion gran +turismo drivers with deep reinforcement learning. Nature, +602(7896):223–228, 2022. +Yu, T., Quillen, D., He, Z., Julian, R., Hausman, K., Finn, +C., and Levine, S. Meta-world: A benchmark and evalua- +tion for multi-task and meta reinforcement learning. In +Conference on Robot Learning, pp. 1094–1100. PMLR, +2020. + diff --git a/49FKT4oBgHgl3EQfSC3u/content/tmp_files/load_file.txt b/49FKT4oBgHgl3EQfSC3u/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..88db539bf3bd17b1b39063ea29648c088f7e5fa7 --- /dev/null +++ b/49FKT4oBgHgl3EQfSC3u/content/tmp_files/load_file.txt @@ -0,0 +1,756 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf,len=755 +page_content='Reinforcement Learning from Diverse Human Preferences Wanqi Xue * 1 Bo An 1 Shuicheng Yan 2 Zhongwen Xu 2 Abstract The complexity of designing reward functions has been a major obstacle to the wide application of deep reinforcement learning (RL) techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' Describing an agent’s desired behaviors and prop- erties can be difficult, even for experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' A new paradigm called reinforcement learning from hu- man preferences (or preference-based RL) has emerged as a promising solution, in which reward functions are learned from human preference la- bels among behavior trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' However, ex- isting methods for preference-based RL are lim- ited by the need for accurate oracle preference labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' This paper addresses this limitation by de- veloping a method for crowd-sourcing preference labels and learning from diverse human prefer- ences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' The key idea is to stabilize reward learning through regularization and correction in a latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' To ensure temporal consistency, a strong constraint is imposed on the reward model that forces its latent space to be close to the prior distri- bution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' Additionally, a confidence-based reward model ensembling method is designed to generate more stable and reliable predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' The pro- posed method is tested on a variety of tasks in DMcontrol and Meta-world and has shown con- sistent and significant improvements over existing preference-based RL algorithms when learning from diverse feedback, paving the way for real- world applications of RL methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' Introduction Recent advances in reinforcement learning (RL) have achieved remarkable success in simulated environments such as board games (Silver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' Moravˇc´ık et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=', 2017) and video games (Mnih et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' Vinyals et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' Wurman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' However, the application This work was done during an internship at Sea AI Lab, Singapore 1Nanyang Technological University, Singapore 2Sea AI Lab, Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'} +page_content=' Correspondence to: Wanqi Xue