Collisional transport coefficients of dense hightemperature plasmas within the quantum LandauFokkerPlanck framework
Abstract
In this paper, we extend the longestablished formulas for the transport coefficients of classical plasmas inside the dense plasma regime for temperatures and densities where the classical Landau equation breaks down but its quantum extension that includes quantum degeneracy effects is valid. To this end, the quantum Landau kinetic equation is solved by the ChapmanEnskog method. The mathematical derivation is done in full generality, i.e., for multicomponent systems and to all orders of the polynomials expansion used to approximate the distribution functions. We apply the general results to two important examples, the electron gas model and an electronion plasma model consisting of one type of ions of any charge. We discuss the combined effects of the Pauli exclusion principle, of the electronelectron, and of the electronion collisions on the transport coefficients and on the convergence of the ChapmanEnskog method. For the electron gas model, the effect of the Pauli exclusion principle on the transport coefficients rapidly becomes nonnegligible outside the domain of validity of the classical Landau equation. For the electronion plasmas, the effect of the Pauli exclusion principle depends sensitively on the ion charge Z and varies nonmonotonically with Θ. For instance, for ion charge Z = 1, the electrical conductivity is increased by up to ~30% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~9%, and the shear viscosity coefficient is increased by up to ~13%. Finally, in the Lorentz gas ( $Z\to \infty $) limit, the electrical conductivity is reduced by up to ~14% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~39%, and the shear viscosity coefficient is not affected.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE; LANL Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1467341
 Alternate Identifier(s):
 OSTI ID: 1463382
 Report Number(s):
 LAUR1823684
Journal ID: ISSN 1070664X
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 25; Journal Issue: 8; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; electrical conductivity; stochastic processes; plasma dynamics; viscosity; thermal conductivity; electron gas
Citation Formats
Daligault, Jérôme. Collisional transport coefficients of dense hightemperature plasmas within the quantum LandauFokkerPlanck framework. United States: N. p., 2018.
Web. doi:10.1063/1.5045330.
Daligault, Jérôme. Collisional transport coefficients of dense hightemperature plasmas within the quantum LandauFokkerPlanck framework. United States. doi:https://doi.org/10.1063/1.5045330
Daligault, Jérôme. Wed .
"Collisional transport coefficients of dense hightemperature plasmas within the quantum LandauFokkerPlanck framework". United States. doi:https://doi.org/10.1063/1.5045330. https://www.osti.gov/servlets/purl/1467341.
@article{osti_1467341,
title = {Collisional transport coefficients of dense hightemperature plasmas within the quantum LandauFokkerPlanck framework},
author = {Daligault, Jérôme},
abstractNote = {In this paper, we extend the longestablished formulas for the transport coefficients of classical plasmas inside the dense plasma regime for temperatures and densities where the classical Landau equation breaks down but its quantum extension that includes quantum degeneracy effects is valid. To this end, the quantum Landau kinetic equation is solved by the ChapmanEnskog method. The mathematical derivation is done in full generality, i.e., for multicomponent systems and to all orders of the polynomials expansion used to approximate the distribution functions. We apply the general results to two important examples, the electron gas model and an electronion plasma model consisting of one type of ions of any charge. We discuss the combined effects of the Pauli exclusion principle, of the electronelectron, and of the electronion collisions on the transport coefficients and on the convergence of the ChapmanEnskog method. For the electron gas model, the effect of the Pauli exclusion principle on the transport coefficients rapidly becomes nonnegligible outside the domain of validity of the classical Landau equation. For the electronion plasmas, the effect of the Pauli exclusion principle depends sensitively on the ion charge Z and varies nonmonotonically with Θ. For instance, for ion charge Z = 1, the electrical conductivity is increased by up to ~30% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~9%, and the shear viscosity coefficient is increased by up to ~13%. Finally, in the Lorentz gas (Z→∞) limit, the electrical conductivity is reduced by up to ~14% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~39%, and the shear viscosity coefficient is not affected.},
doi = {10.1063/1.5045330},
journal = {Physics of Plasmas},
number = 8,
volume = 25,
place = {United States},
year = {2018},
month = {8}
}
Web of Science
Works referenced in this record:
On the quantum Landau collision operator and electron collisions in dense plasmas
journal, March 2016
 Daligault, Jérôme
 Physics of Plasmas, Vol. 23, Issue 3
Crossover from Classical to Fermi Liquid Behavior in Dense Plasmas
journal, July 2017
 Daligault, Jérôme
 Physical Review Letters, Vol. 119, Issue 4
Nonrelativistic and relativistic Landau/FokkerPlanck equation for arbitrary statistics
journal, January 1980
 Danielewicz, P.
 Physica A: Statistical Mechanics and its Applications, Vol. 100, Issue 1
Convergence of the ChapmanEnskog Method for a Completely Ionized Gas
journal, May 1951
 Landshoff, Rolf
 Physical Review, Vol. 82, Issue 3
Transport Phenomena in a Completely Ionized Gas
journal, March 1953
 Spitzer, Lyman; Härm, Richard
 Physical Review, Vol. 89, Issue 5
Transport Coefficients of Plasmas in a Magnetic Field
journal, September 1960
 Kaneko, Shobu
 Journal of the Physical Society of Japan, Vol. 15, Issue 9
Transport Properties of Ionized Monatomic Gases
journal, January 1966
 Devoto, R. S.
 Physics of Fluids, Vol. 9, Issue 6
Electron transport in a collisional plasma with multiple ion species
journal, February 2014
 Simakov, Andrei N.; Molvig, Kim
 Physics of Plasmas, Vol. 21, Issue 2
Transport Theory of a Partially Degenerate Plasma
journal, October 1968
 Lampe, Martin
 Physical Review, Vol. 174, Issue 1
Thermal Conduction by Electrons in Stellar Matter
journal, June 1969
 Hubbard, W. B.; Lampe, Martin
 The Astrophysical Journal Supplement Series, Vol. 18
Thermal conduction in laser fusion
journal, June 1975
 Brysk, H.; Campbell, P. M.; Hammerling, P.
 Plasma Physics, Vol. 17, Issue 6
Algorithm 745; computation of the complete and incomplete FermiDirac integral
journal, September 1995
 Goano, Michele
 ACM Transactions on Mathematical Software, Vol. 21, Issue 3
Rational Function Approximations for FermiDirac Integrals
journal, January 1993
 Antia, H. M.
 The Astrophysical Journal Supplement Series, Vol. 84
The theory of a fermi liquid (the properties of liquid 3He at low temperatures)
journal, January 1959
 Abrikosov, A. A.; Khalatnikov, I. M.
 Reports on Progress in Physics, Vol. 22, Issue 1