Quantum Fokker-Planck modeling of degenerate electrons

Le, Hai P.

doi:10.1016/j.jcp.2021.110230

Quantum Fokker-Planck modeling of degenerate electrons

Journal Article · Thu Feb 25 00:00:00 EST 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110230· OSTI ID:1772702

Le, Hai P. ^[1]

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

In this work, an implicit and conservative numerical scheme is proposed for the isotropic quantum Fokker-Planck equation describing the evolution of degenerate electrons subject to elastic collisions with other electrons and ions. The electron-ion and electron-electron collision operators are discretized using a discontinuous Galerkin method, and the electron energy distribution is updated by an implicit time integration method. The numerical scheme is designed to satisfy all conservation laws exactly. Numerical tests and comparisons with other modeling approaches are shown to demonstrate the accuracy and conservation properties of the proposed method.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1772702

Alternate ID(s):: OSTI ID: 1781956
OSTI ID: 23206118

Report Number(s):: LLNL-JRNL--809582; 1015672

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: na Vol. 434; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (31)

Implicit and Conservative Difference Scheme for the Fokker-Planck Equation Epperlein, E. M. Journal of Computational Physics, Vol. 112, Issue 2 https://doi.org/10.1006/jcph.1994.1101	journal	June 1994
Fast Spectral Methods for the Fokker–Planck–Landau Collision Operator Pareschi, L.; Russo, G.; Toscani, G. Journal of Computational Physics, Vol. 165, Issue 1 https://doi.org/10.1006/jcph.2000.6612	journal	November 2000
A practical difference scheme for Fokker-Planck equations Chang, J. S.; Cooper, G. Journal of Computational Physics, Vol. 6, Issue 1 https://doi.org/10.1016/0021-9991(70)90001-X	journal	August 1970
Nonrelativistic and relativistic Landau/Fokker-Planck equation for arbitrary statistics Danielewicz, P. Physica A: Statistical Mechanics and its Applications, Vol. 100, Issue 1 https://doi.org/10.1016/0378-4371(80)90157-0	journal	January 1980
Thermalization dynamics of primary and secondary electrons in metals Kitamura, Hikaru Journal of Electron Spectroscopy and Related Phenomena, Vol. 232 https://doi.org/10.1016/j.elspec.2018.12.002	journal	April 2019
A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma Thomas, A. G. R.; Tzoufras, M.; Robinson, A. P. L. Journal of Computational Physics, Vol. 231, Issue 3 https://doi.org/10.1016/j.jcp.2011.09.028	journal	February 2012
A Monte Carlo algorithm for degenerate plasmas Turrell, A. E.; Sherlock, M.; Rose, S. J. Journal of Computational Physics, Vol. 249 https://doi.org/10.1016/j.jcp.2013.03.052	journal	September 2013
An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes Taitano, W. T.; Chacón, L.; Simakov, A. N. Journal of Computational Physics, Vol. 318 https://doi.org/10.1016/j.jcp.2016.03.071	journal	August 2016
Modified Monte Carlo method for study of electron transport in degenerate electron gas in the presence of electron–electron interactions, application to graphene Borowik, Piotr; Thobel, Jean-Luc; Adamowicz, Leszek Journal of Computational Physics, Vol. 341 https://doi.org/10.1016/j.jcp.2017.04.011	journal	July 2017
Adaptive spectral solution method for the Landau and Lenard-Balescu equations Scullard, Christian R.; Hickok, Abigail; Sotiris, Justyna O. Journal of Computational Physics, Vol. 402 https://doi.org/10.1016/j.jcp.2019.109110	journal	February 2020
Transport in partially degenerate, magnetized plasmas. Part 1. Collision operators Brown, S. R.; Haines, M. G. Journal of Plasma Physics, Vol. 58, Issue 4 https://doi.org/10.1017/S0022377897006041	journal	December 1997
Transport in partially degenerate, magnetized plasmas. Part 2. Numerical calculation of transport coefficients Brown, S. R.; Haines, M. G. Journal of Plasma Physics, Vol. 62, Issue 2 https://doi.org/10.1017/S0022377899007746	journal	August 1999
A numerical scheme for the quantum Boltzmann equation with stiff collision terms Filbet, Francis; Hu, Jingwei; Jin, Shi ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 46, Issue 2 https://doi.org/10.1051/m2an/2011051	journal	October 2011
On the quantum Landau collision operator and electron collisions in dense plasmas Daligault, Jérôme Physics of Plasmas, Vol. 23, Issue 3 https://doi.org/10.1063/1.4944392	journal	March 2016
Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C. Physics of Plasmas, Vol. 23, Issue 9 https://doi.org/10.1063/1.4963254	journal	September 2016
Conservative algorithms for non-Maxwellian plasma kinetics Le, Hai P.; Cambier, Jean-Luc Physics of Plasmas, Vol. 24, Issue 12 https://doi.org/10.1063/1.4998242	journal	December 2017
Collisional transport coefficients of dense high-temperature plasmas within the quantum Landau-Fokker-Planck framework Daligault, Jérôme Physics of Plasmas, Vol. 25, Issue 8 https://doi.org/10.1063/1.5045330	journal	August 2018
Kinetic simulation of a plasma collision experiment Larroche, Olivier Physics of Fluids B: Plasma Physics, Vol. 5, Issue 8 https://doi.org/10.1063/1.860670	journal	August 1993
Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker–Planck equation Epperlein, E. M.; Haines, M. G. Physics of Fluids, Vol. 29, Issue 4 https://doi.org/10.1063/1.865901	journal	January 1986
Rational Function Approximations for Fermi-Dirac Integrals Antia, H. M. The Astrophysical Journal Supplement Series, Vol. 84 https://doi.org/10.1086/191748	journal	January 1993
Electron-ion equilibration in a partially degenerate plasma Brysk, H. Plasma Physics, Vol. 16, Issue 10 https://doi.org/10.1088/0032-1028/16/10/005	journal	October 1974
Fast electron transport in laser-produced plasmas and the KALOS code for solution of the Vlasov–Fokker–Planck equation Bell, A. R.; Robinson, A. P. L.; Sherlock, M. Plasma Physics and Controlled Fusion, Vol. 48, Issue 3 https://doi.org/10.1088/0741-3335/48/3/R01	journal	February 2006
Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments Zhang, Xiangxiong; Shu, Chi-Wang Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 467, Issue 2134 https://doi.org/10.1098/rspa.2011.0153	journal	May 2011
Transport Coefficients of Degenerate Plasma Lampe, Martin Physical Review, Vol. 170, Issue 1 https://doi.org/10.1103/PhysRev.170.306	journal	June 1968
Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. I Uehling, E. A.; Uhlenbeck, G. E. Physical Review, Vol. 43, Issue 7 https://doi.org/10.1103/PhysRev.43.552	journal	April 1933
Influence of atomic kinetics on inverse bremsstrahlung heating and nonlocal thermal transport Le, Hai P.; Sherlock, Mark; Scott, Howard A. Physical Review E, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevE.100.013202	journal	July 2019
Crossover from Classical to Fermi Liquid Behavior in Dense Plasmas Daligault, Jérôme Physical Review Letters, Vol. 119, Issue 4 https://doi.org/10.1103/PhysRevLett.119.045002	journal	July 2017
Evolution of the Electron Distribution Function in the Presence of Inverse Bremsstrahlung Heating and Collisional Ionization Milder, A. L.; Le, H. P.; Sherlock, M. Physical Review Letters, Vol. 124, Issue 2 https://doi.org/10.1103/PhysRevLett.124.025001	journal	January 2020
Nonlinear Inverse Bremsstrahlung and Heated-Electron Distributions Langdon, A. Bruce Physical Review Letters, Vol. 44, Issue 9 https://doi.org/10.1103/PhysRevLett.44.575	journal	March 1980
Two-Dimensional Nonlocal Electron Transport in Laser-Produced Plasmas Epperlein, E. M.; Rickard, G. J.; Bell, A. R. Physical Review Letters, Vol. 61, Issue 21 https://doi.org/10.1103/PhysRevLett.61.2453	journal	November 1988
A Numerical Scheme for the Quantum Fokker-Planck-Landau Equation Efficient in the Fluid Regime Hu, Jingwei; Jin, Shi; Yan, Bokai Communications in Computational Physics, Vol. 12, Issue 5 https://doi.org/10.4208/cicp.220411.090112a	journal	November 2012

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