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

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 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):
 LLNLJRNL737460
Journal ID: ISSN 24700045; PLEEE8; 890285; TRN: US1901501
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review E
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 1; Journal ID: ISSN 24700045
 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 electronion temperature equilibration rates from the LenardBalescu equation. United States: N. p., 2018.
Web. https://doi.org/10.1103/PhysRevE.97.013205.
Scullard, Christian R., Serna, Susana, Benedict, Lorin X., Ellison, C. Leland, & Graziani, Frank R. Analytic expressions for electronion temperature equilibration rates from the LenardBalescu equation. United States. https://doi.org/10.1103/PhysRevE.97.013205
Scullard, Christian R., Serna, Susana, Benedict, Lorin X., Ellison, C. Leland, and Graziani, Frank R. Wed .
"Analytic expressions for electronion temperature equilibration rates from the LenardBalescu equation". United States. https://doi.org/10.1103/PhysRevE.97.013205. https://www.osti.gov/servlets/purl/1458674.
@article{osti_1458674,
title = {Analytic expressions for electronion temperature equilibration rates from the LenardBalescu 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 electronion temperature equilibration time for a homogeneous weakly coupled plasma from the LenardBalescu equation. With some minor approximations, we derive an analytic formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electronion temperature ratios and arbitrary electron degeneracy. Lastly, for large temperature ratios, we derive the necessary correction to account for the coupledmode 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}
}
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Figures / Tables:
TABLE I: Fitting coefficients for the special functions U_{1}(μ), U_{2}(μ) and U_{3}(μ).
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