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Title: Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation

Abstract

In this paper, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly coupled plasma from the Lenard-Balescu equation. With some minor approximations, we derive an analytic formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electron-ion temperature ratios and arbitrary electron degeneracy. Lastly, for large temperature ratios, we derive the necessary correction to account for the coupled-mode effect, which can be evaluated very efficiently using ordinary Gaussian quadrature.

Authors:
 [1];  [2];  [1];  [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Autonomous University of Barcelona (Spain). Department of Mathematics
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1458674
Alternate Identifier(s):
OSTI ID: 1418883
Report Number(s):
LLNL-JRNL-737460
Journal ID: ISSN 2470-0045; PLEEE8; 890285; TRN: US1901501
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 97; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING

Citation Formats

Scullard, Christian R., Serna, Susana, Benedict, Lorin X., Ellison, C. Leland, and Graziani, Frank R. Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation. United States: N. p., 2018. Web. doi:10.1103/PhysRevE.97.013205.
Scullard, Christian R., Serna, Susana, Benedict, Lorin X., Ellison, C. Leland, & Graziani, Frank R. Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation. United States. doi:10.1103/PhysRevE.97.013205.
Scullard, Christian R., Serna, Susana, Benedict, Lorin X., Ellison, C. Leland, and Graziani, Frank R. Wed . "Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation". United States. doi:10.1103/PhysRevE.97.013205. https://www.osti.gov/servlets/purl/1458674.
@article{osti_1458674,
title = {Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation},
author = {Scullard, Christian R. and Serna, Susana and Benedict, Lorin X. and Ellison, C. Leland and Graziani, Frank R.},
abstractNote = {In this paper, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly coupled plasma from the Lenard-Balescu equation. With some minor approximations, we derive an analytic formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electron-ion temperature ratios and arbitrary electron degeneracy. Lastly, for large temperature ratios, we derive the necessary correction to account for the coupled-mode effect, which can be evaluated very efficiently using ordinary Gaussian quadrature.},
doi = {10.1103/PhysRevE.97.013205},
journal = {Physical Review E},
number = 1,
volume = 97,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 1 work
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Figures / Tables:

TABLE I TABLE I: Fitting coefficients for the special functions U1(μ), U2(μ) and U3(μ).

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