Numerical solution of the quantum LenardBalescu equation for a nondegenerate onecomponent plasma
Abstract
We present a numerical solution of the quantum LenardBalescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous onecomponent plasma with various initial conditions. Unlike the more usual Landau/FokkerPlanck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the nonlogarithmic orderunity terms. The spectral method can also be used to solve the Landau equation and a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full LenardBalescu solution in the weakcoupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.
 Authors:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Univ. of California, Los Angeles, CA (United States)
 Univ. Autonoma de Barcelona (Spain)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1399709
 Report Number(s):
 LLNLJRNL687277
Journal ID: ISSN 1070664X; TRN: US1703090
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 9; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION
Citation Formats
Scullard, Christian R., Belt, Andrew P., Fennell, Susan C., Janković, Marija R., Ng, Nathan, Serna, Susana, and Graziani, Frank R. Numerical solution of the quantum LenardBalescu equation for a nondegenerate onecomponent plasma. United States: N. p., 2016.
Web. doi:10.1063/1.4963254.
Scullard, Christian R., Belt, Andrew P., Fennell, Susan C., Janković, Marija R., Ng, Nathan, Serna, Susana, & Graziani, Frank R. Numerical solution of the quantum LenardBalescu equation for a nondegenerate onecomponent plasma. United States. doi:10.1063/1.4963254.
Scullard, Christian R., Belt, Andrew P., Fennell, Susan C., Janković, Marija R., Ng, Nathan, Serna, Susana, and Graziani, Frank R. 2016.
"Numerical solution of the quantum LenardBalescu equation for a nondegenerate onecomponent plasma". United States.
doi:10.1063/1.4963254. https://www.osti.gov/servlets/purl/1399709.
@article{osti_1399709,
title = {Numerical solution of the quantum LenardBalescu equation for a nondegenerate onecomponent plasma},
author = {Scullard, Christian R. and Belt, Andrew P. and Fennell, Susan C. and Janković, Marija R. and Ng, Nathan and Serna, Susana and Graziani, Frank R.},
abstractNote = {We present a numerical solution of the quantum LenardBalescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous onecomponent plasma with various initial conditions. Unlike the more usual Landau/FokkerPlanck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the nonlogarithmic orderunity terms. The spectral method can also be used to solve the Landau equation and a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full LenardBalescu solution in the weakcoupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.},
doi = {10.1063/1.4963254},
journal = {Physics of Plasmas},
number = 9,
volume = 23,
place = {United States},
year = 2016,
month = 9
}
Web of Science

The BalescuLenard collision term for a quark plasma. Classical model
The collision term for a classical model of a quark plasma is found. By truncation of the color hierarchy, an approximation for the collision terms in a quantum model without allowance for spin is obtained.