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

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.