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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Works referenced in this record:
Correlation effects on the temperaturerelaxation rates in dense plasmas
journal, May 2009
 Daligault, Jérôme; Dimonte, Guy
 Physical Review E, Vol. 79, Issue 5
On the Numerical Value of ∫0hex2dx
journal, November 1897
 Dawson, H. G.
 Proceedings of the London Mathematical Society, Vol. s129, Issue 1
An electron conductivity model for dense plasmas
journal, January 1984
 Lee, Y. T.; More, R. M.
 Physics of Fluids, Vol. 27, Issue 5
Dense plasma temperature equilibration in the binary collision approximation
journal, March 2002
 Gericke, D. O.; Murillo, M. S.; Schlanges, M.
 Physical Review E, Vol. 65, Issue 3
Largeeddy and unsteady RANS simulations of a shockaccelerated heavy gas cylinder
journal, April 2015
 Morgan, B. E.; Greenough, J. A.
 Shock Waves, Vol. 26, Issue 4
Ionic transport in highenergydensity matter
journal, April 2016
 Stanton, Liam G.; Murillo, Michael S.
 Physical Review E, Vol. 93, Issue 4
LenardBalescu Calculations and Classical Molecular Dynamics Simulations of Electrical and Thermal Conductivities of Hydrogen Plasmas: LenardBalescu Calculations and Classical Molecular Dynamics Simulations of Electrical and Thermal Conductivities of Hydrogen Plasmas
journal, December 2014
 Whitley, H. D.; Scullard, Ch. R.; Benedict, L. X.
 Contributions to Plasma Physics, Vol. 55, Issue 23
Kinetic approach to temperature relaxation in dense plasmas
journal, January 2005
 Gericke, D. O.
 Journal of Physics: Conference Series, Vol. 11
QuantumMechanical Plasma Transport Theory
journal, January 1969
 Williams, R. H.
 Physics of Fluids, Vol. 12, Issue 11
Molecular dynamics simulations and generalized LenardBalescu calculations of electronion temperature equilibration in plasmas
journal, October 2012
 Benedict, Lorin X.; Surh, Michael P.; Castor, John I.
 Physical Review E, Vol. 86, Issue 4
Coupled mode effects on energy transfer in weakly coupled, twotemperature plasmas
journal, August 2009
 Vorberger, J.; Gericke, D. O.
 Physics of Plasmas, Vol. 16, Issue 8
Theory of interparticle correlations in dense, hightemperature plasmas. I. General formalism
journal, September 1985
 Ichimaru, Setsuo; Mitake, Shinichi; Tanaka, Shigenori
 Physical Review A, Vol. 32, Issue 3
Electronion equilibration in a partially degenerate plasma
journal, October 1974
 Brysk, H.
 Plasma Physics, Vol. 16, Issue 10
Partial ionization in dense plasmas: Comparisons among averageatom density functional models
journal, June 2013
 Murillo, Michael S.; Weisheit, Jon; Hansen, Stephanie B.
 Physical Review E, Vol. 87, Issue 6
Molecular dynamics studies of electronion temperature equilibration in hydrogen plasmas within the coupledmode regime
journal, April 2017
 Benedict, Lorin X.; Surh, Michael P.; Stanton, Liam G.
 Physical Review E, Vol. 95, Issue 4
Electron liquid at any degeneracy
journal, August 1986
 Dandrea, R. G.; Ashcroft, N. W.; Carlsson, A. E.
 Physical Review B, Vol. 34, Issue 4
Reduced coupledmode approach to electronion energy relaxation
journal, July 2013
 Chapman, D. A.; Vorberger, J.; Gericke, D. O.
 Physical Review E, Vol. 88, Issue 1
Numerical solution of the quantum LenardBalescu equation for a nondegenerate onecomponent plasma
journal, September 2016
 Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.
 Physics of Plasmas, Vol. 23, Issue 9
Ignition calculations using a reduced coupledmode electron ion energy exchange model*
journal, March 2016
 Garbett, W. J.; Chapman, D. A.
 Journal of Physics: Conference Series, Vol. 688
HighFrequency Conductivity of a Fully Ionized Plasma
journal, January 1962
 Oberman, Carl; Ron, Amiram; Dawson, John
 Physics of Fluids, Vol. 5, Issue 12
Energy relaxation and the quasiequation of state of a dense twotemperature nonequilibrium plasma
journal, September 1998
 Dharmawardana, M. W. C.; Perrot, François
 Physical Review E, Vol. 58, Issue 3
Works referencing / citing this record:
Development and modeling of a polardirectdrive exploding pusher platform at the National Ignition Facility
journal, July 2018
 Ellison, C. Leland; Whitley, Heather D.; Brown, Colin R. D.
 Physics of Plasmas, Vol. 25, Issue 7
Exploring the crossover between highenergydensity plasma and ultracold neutral plasma physics
journal, October 2019
 Bergeson, Scott D.; Baalrud, Scott D.; Ellison, C. Leland
 Physics of Plasmas, Vol. 26, Issue 10
Figures/Tables have been extracted from DOEfunded journal article accepted manuscripts.