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

Abstract

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.

Authors:
 [1];  [2]; ORCiD logo [2];  [2];  [2];  [3]; ORCiD logo [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of California, Los Angeles, CA (United States)
  3. Univ. Autonoma de Barcelona (Spain)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1399709
Alternate Identifier(s):
OSTI ID: 1327556
Report Number(s):
LLNL-JRNL-687277
Journal ID: ISSN 1070-664X; TRN: US1703090
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 9; Journal ID: ISSN 1070-664X
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 Lenard-Balescu equation for a non-degenerate one-component 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 Lenard-Balescu equation for a non-degenerate one-component plasma. United States. doi:https://doi.org/10.1063/1.4963254
Scullard, Christian R., Belt, Andrew P., Fennell, Susan C., Janković, Marija R., Ng, Nathan, Serna, Susana, and Graziani, Frank R. Thu . "Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma". United States. doi:https://doi.org/10.1063/1.4963254. https://www.osti.gov/servlets/purl/1399709.
@article{osti_1399709,
title = {Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component 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 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.},
doi = {10.1063/1.4963254},
journal = {Physics of Plasmas},
number = 9,
volume = 23,
place = {United States},
year = {2016},
month = {9}
}

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Works referenced in this record:

Carrier-carrier scattering and optical dephasing in highly excited semiconductors
journal, January 1992


A Vlasov–Fokker–Planck code for high energy density physics
journal, July 2011

  • Tzoufras, M.; Bell, A. R.; Norreys, P. A.
  • Journal of Computational Physics, Vol. 230, Issue 17
  • DOI: 10.1016/j.jcp.2011.04.034

Kinetic Equation for Plasma
journal, September 1962


On the quantum Landau collision operator and electron collisions in dense plasmas
journal, March 2016


Theory of interparticle correlations in dense, high-temperature plasmas. V. Electric and thermal conductivities
journal, September 1985


Quantum-Mechanical Plasma Transport Theory
journal, January 1969


A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation
journal, September 2015


Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas
journal, October 2012


Coupled mode effects on energy transfer in weakly coupled, two-temperature plasmas
journal, August 2009

  • Vorberger, J.; Gericke, D. O.
  • Physics of Plasmas, Vol. 16, Issue 8
  • DOI: 10.1063/1.3197136

Accurate spectral numerical schemes for kinetic equations with energy diffusion
journal, August 2015

  • Wilkening, Jon; Cerfon, Antoine J.; Landreman, Matt
  • Journal of Computational Physics, Vol. 294
  • DOI: 10.1016/j.jcp.2015.03.039

Reduced coupled-mode approach to electron-ion energy relaxation
journal, July 2013


A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit
journal, August 2014


High performance computing with a conservative spectral Boltzmann solver
conference, January 2012

  • Haack, Jeffrey R.; Gamba, Irene M.
  • 28TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS 2012, AIP Conference Proceedings
  • DOI: 10.1063/1.4769536

Implicit and Conservative Difference Scheme for the Fokker-Planck Equation
journal, June 1994


Effects of nonequilibrium particle distributions in deuterium-tritium burning
journal, January 2010

  • Michta, David; Graziani, Frank; Luu, Thomas
  • Physics of Plasmas, Vol. 17, Issue 1
  • DOI: 10.1063/1.3276103

Fokker-Planck Equation for an Inverse-Square Force
journal, July 1957

  • Rosenbluth, Marshall N.; MacDonald, William M.; Judd, David L.
  • Physical Review, Vol. 107, Issue 1
  • DOI: 10.1103/PhysRev.107.1

Dynamical Screening and the dc Conductivity in a Fully Ionized Plasma
journal, January 1989

  • Morales, F.; Kilimann, M. K.; Redmer, R.
  • Contributions to Plasma Physics, Vol. 29, Issue 4-5
  • DOI: 10.1002/ctpp.2150290412

New velocity-space discretization for continuum kinetic calculations and Fokker–Planck collisions
journal, June 2013


Correlation effects on the temperature-relaxation rates in dense plasmas
journal, May 2009


On Bogoliubov's kinetic equation for a spatially homogeneous plasma
journal, July 1960


Properties of the Lenard–Balescu collision operator: A numerical study
journal, February 2002

  • Ricci, Paolo; Lapenta, Giovanni
  • Physics of Plasmas, Vol. 9, Issue 2
  • DOI: 10.1063/1.1418720

T-matrix approach to equilibium and nonequilibrium carrier-carrier scattering in semiconductors
journal, April 1999


A Numerical Scheme for the Quantum Fokker-Planck-Landau Equation Efficient in the Fluid Regime
journal, November 2012


The Electrical Conductivity of an Ionized Gas
journal, October 1950

  • Cohen, Robert S.; Spitzer, Lyman; Routly, Paul McR.
  • Physical Review, Vol. 80, Issue 2
  • DOI: 10.1103/PhysRev.80.230

Transport Phenomena in a Completely Ionized Gas
journal, March 1953


Irreversible Processes in Ionized Gases
journal, January 1960


Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas
journal, August 2013


A practical difference scheme for Fokker-Planck equations
journal, August 1970


Numerical Integration of Kinetic Equations
journal, January 1965


On classical orthogonal polynomials and differential operators
journal, June 2005


Table of Integrals, Series, and Products
journal, October 1966

  • S., D.; Gradshteyn, I. S.; Ryzhik, I. M.
  • Mathematics of Computation, Vol. 20, Issue 96
  • DOI: 10.2307/2003554