Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter
Abstract
Here, the influence of finite relaxation times on Thomson scattering from warm dense plasmas is examined within the framework of the average-atom approximation. Presently most calculations use the collision-free Lindhard dielectric function to evaluate the free-electron contribution to the Thomson cross section. In this work, we use the Mermin dielectric function, which includes relaxation time explicitly. The relaxation time is evaluated by treating the average atom as an impurity in a uniform electron gas and depends critically on the transport cross section. The calculated relaxation rates agree well with values inferred from the Ziman formula for the static conductivity and also with rates inferred from a fit to the frequency-dependent conductivity. Transport cross sections determined by the phase-shift analysis in the average-atom potential are compared with those evaluated in the commonly used Born approximation. The Born approximation converges to the exact cross sections at high energies; however, differences that occur at low energies lead to corresponding differences in relaxation rates. The relative importance of including relaxation time when modeling x-ray Thomson scattering spectra is examined by comparing calculations of the free-electron dynamic structure function for Thomson scattering using Lindhard and Mermin dielectric functions. Applications are given to warm dense Bemore »
- Authors:
-
- Univ. of Notre Dame, Notre Dame, IN (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1438706
- Alternate Identifier(s):
- OSTI ID: 1242611
- Report Number(s):
- LLNL-JRNL-680793
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1900494
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 3; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Johnson, W. R., and Nilsen, J. Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter. United States: N. p., 2016.
Web. doi:10.1103/PhysRevE.93.033205.
Johnson, W. R., & Nilsen, J. Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter. United States. https://doi.org/10.1103/PhysRevE.93.033205
Johnson, W. R., and Nilsen, J. Mon .
"Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter". United States. https://doi.org/10.1103/PhysRevE.93.033205. https://www.osti.gov/servlets/purl/1438706.
@article{osti_1438706,
title = {Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter},
author = {Johnson, W. R. and Nilsen, J.},
abstractNote = {Here, the influence of finite relaxation times on Thomson scattering from warm dense plasmas is examined within the framework of the average-atom approximation. Presently most calculations use the collision-free Lindhard dielectric function to evaluate the free-electron contribution to the Thomson cross section. In this work, we use the Mermin dielectric function, which includes relaxation time explicitly. The relaxation time is evaluated by treating the average atom as an impurity in a uniform electron gas and depends critically on the transport cross section. The calculated relaxation rates agree well with values inferred from the Ziman formula for the static conductivity and also with rates inferred from a fit to the frequency-dependent conductivity. Transport cross sections determined by the phase-shift analysis in the average-atom potential are compared with those evaluated in the commonly used Born approximation. The Born approximation converges to the exact cross sections at high energies; however, differences that occur at low energies lead to corresponding differences in relaxation rates. The relative importance of including relaxation time when modeling x-ray Thomson scattering spectra is examined by comparing calculations of the free-electron dynamic structure function for Thomson scattering using Lindhard and Mermin dielectric functions. Applications are given to warm dense Be plasmas, with temperatures ranging from 2 to 32 eV and densities ranging from 2 to 64 g/cc.},
doi = {10.1103/PhysRevE.93.033205},
journal = {Physical Review E},
number = 3,
volume = 93,
place = {United States},
year = {Mon Mar 14 00:00:00 EDT 2016},
month = {Mon Mar 14 00:00:00 EDT 2016}
}
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Figures / Tables:
FIG. 1: Left panel: Transport cross section σtr(p) for a warm-dense Be plasma at density ρ= 8 g/cc and T = 16 eV. Right panel: Electron-ion scattering phase shifts δ(p) in the average-atom potential used to calculate the cross section shown in the left panel.
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