# Plasma Physics Approximations in Ares

## Abstract

Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac 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 non-degenerate 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):
- LLNL-PROC-666110

TRN: US1600149

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Conference

- Resource Relation:
- Conference: NECDC, Los Alamos, NM (United States), 20-24 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. Thu .
"Plasma Physics Approximations in Ares". United States. 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 hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac 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 + e-μ/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 non-degenerate 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 = {Thu Jan 08 00:00:00 EST 2015},

month = {Thu Jan 08 00:00:00 EST 2015}

}