Plasma Physics Approximations in Ares
Abstract
Lee & More derived analytic forms for the transport properties of a plasma. Many hydrocodes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of FermiDirac integrals, F _{n}( μ/θ ), the chemical potential, μ or ζ = ln(1+e ^{ μ/θ} ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A ^{α} (ζ ),A ^{β} (ζ ), ζ, f(ζ ) = (1 + e ^{μ/θ})F _{1/2}(μ/θ), F _{1/2}'/F _{1/2}, F _{c} ^{α}, and F _{c} ^{β}. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the nondegenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.
 Authors:
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1179438
 Report Number(s):
 LLNLPROC666110
TRN: US1600149
 DOE Contract Number:
 AC5207NA27344
 Resource Type:
 Conference
 Resource Relation:
 Conference: NECDC, Los Alamos, NM (United States), 2024 Oct 2014
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION; APPROXIMATIONS; THERMAL CONDUCTIVITY; ELECTRONS; FUNCTIONS; PLASMA; COMPARATIVE EVALUATIONS; POTENTIALS; LIMITING VALUES; ERRORS; INTEGRALS; TRANSPORT THEORY; ANALYTICAL SOLUTION; ELECTRIC CONDUCTIVITY
Citation Formats
Managan, R. A. Plasma Physics Approximations in Ares. United States: N. p., 2015.
Web.
Managan, R. A. Plasma Physics Approximations in Ares. United States.
Managan, R. A. 2015.
"Plasma Physics Approximations in Ares". United States.
doi:. https://www.osti.gov/servlets/purl/1179438.
@article{osti_1179438,
title = {Plasma Physics Approximations in Ares},
author = {Managan, R. A.},
abstractNote = {Lee & More derived analytic forms for the transport properties of a plasma. Many hydrocodes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of FermiDirac integrals, Fn( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for Aα (ζ ),Aβ (ζ ), ζ, f(ζ ) = (1 + eμ/θ)F1/2(μ/θ), F1/2'/F1/2, Fcα, and Fcβ. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the nondegenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2015,
month = 1
}

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