On relaxation phenomena in a two-component plasma

TL;DR

This paper investigates the relaxation of temperatures and velocities in a two-component plasma using a generalized Chapman-Enskog method, revealing positive relaxation rates and corrections to classical Landau results, with implications for hydrodynamic modeling.

Contribution

It introduces a generalized kinetic approach accounting for kinetic modes and provides perturbative solutions for relaxation processes in a two-component plasma.

Findings

Relaxation rates are positive, confirming the existence of relaxation.

Corrections to Landau distribution functions and relaxation rates are derived.

Perturbation theory in the square root of the electron-to-ion mass ratio is developed.

Abstract

The relaxation of temperatures and velocities of the components of a quasi-equilibrium two-component homogeneous completely ionized plasma is investigated on the basis of a generalization of the Chapman-Enskog method applied to the Landau kinetic equation. The generalization is based on the functional hypothesis in order to account for the presence of kinetic modes of the system. In the approximation of a small difference of the component temperatures and velocities, it is shown that relaxation really exists (the relaxation rates are positive). The proof is based on the arguments that are valid for an arbitrary two-component system. The equations describing the temperature and velocity kinetic modes of the system are investigated in a perturbation theory in the square root of the small electron-to-ion mass ratio. The equations of each order of this perturbation theory are solved with the help of the Sonine polynomial expansion. Corrections to the known Landau results related to the distribution functions of the plasma and relaxation rates are obtained. The hydrodynamic theory based on these results should take into account a violation of local equilibrium in the presence of relaxation processes.