Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; Janković, Marija R.; Ng, Nathan; Serna, Susana; Graziani, Frank R.

doi:10.1063/1.4963254

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

Journal Article · Thu Sep 01 00:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4963254· OSTI ID:1399709

Scullard, Christian R. ^[1]; Belt, Andrew P. ^[2]; ^[2]; Janković, Marija R. ^[2]; Ng, Nathan ^[2]; Serna, Susana ^[3]; ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of California, Los Angeles, CA (United States)
Univ. Autonoma de Barcelona (Spain)

We present a numerical solution of the quantum Lenard-Balescu 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 one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity 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 Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1399709

Alternate ID(s):: OSTI ID: 1327556

Report Number(s):: LLNL--JRNL-687277

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 9 Vol. 23; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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