Relativistic Ohm and Fourier laws for binary mixtures of electrons with protons and photons

TL;DR

This paper derives relativistic Ohm and Fourier laws for binary electron-ion and electron-photon mixtures using the Anderson and Witting model, providing explicit transport coefficients for various relativistic regimes.

Contribution

It introduces a comprehensive relativistic framework for electrical and thermal conductivities in ionized gas mixtures, extending classical laws to relativistic conditions.

Findings

Explicit expressions for transport coefficients in different relativistic regimes

General formulas for electrical and thermal conductivities in relativistic mixtures

Application to mixtures with non-degenerate and degenerate electrons

Abstract

Binary mixtures of electrons with protons and of electrons with photons subjected to external electromagnetic fields are analyzed by using the Anderson and Witting model equation. The relativistic laws of Ohm and Fourier are determined as well as general expressions for the electrical and thermal conductivities for relativistic ionized gas mixtures. Explicit expressions for the transport coefficients are given for the particular cases: a non-relativistic mixture of protons and non-degenerate electrons; an ultra-relativistic mixture of photons and non-degenerate electrons; a non-relativistic mixture of protons and completely degenerate electrons; an ultra-relativistic mixture of photons and completely degenerate electrons and a mixture of non-relativistic protons and ultra-relativistic completely degenerate electrons.