Kinetic theory of nonlinear transport processes in dilute ionized gases subject to an electromagnetic field

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Abstract
The modified moment method is applied to study transport processes in a plasma subject to a homogeneous electromagnetic field. Various balance and evolution equations are derived for macroscopic variables chosen, by starting from a kinetic equation. Extended Gibbs relations are also derived as extensions of the extended Gibbs relation for neutral gases. The evolution equations are solved under the adiabatic approximation in the case of the steady state by using an iterative solution method. The first iterative solution yields various linear transport coefficients which reproduce the Chapman–Enskog formulas for the transport coefficients as the magnetic field vanishes, and the second iterative solution gives rise to a set of transport coefficients which depend on the thermodynamic forces as well as the magnetic field. In the sense that they depend on thermodynamic forces they are nonlinear. As the density tends to zero (the rarefied gas limit), the second order transport coefficients vanish as expected for the transport coefficients for rarefied gases.