A consistent kinetic model for a two-component mixture with an application to plasma

TL;DR

This paper introduces a consistent kinetic BGK model for a two-component gas mixture, ensuring conservation laws, positivity, and convergence to equilibrium, with applications to plasma physics and derivation of MHD equations.

Contribution

The paper develops a novel BGK-based kinetic model for multi-species gases that guarantees key physical properties and connects microscopic dynamics to macroscopic plasma equations.

Findings

Model satisfies conservation laws and positivity

Solutions converge to Maxwellian equilibrium

Derivation of ideal MHD equations from the kinetic model

Abstract

We consider a non reactive multi component gas mixture.We propose a class of models, which can be easily generalized to multiple species. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the solutions for the space homogeneous case, positivity of all temperatures, H-theorem and convergence to a global equilibrium in the space homogeneous case in the form of a global Maxwell distribution. Thus, we are able to derive the usual macroscopic conservation laws. In particular, by considering a mixture composed of ions and electrons, we derive the macroscopic equations of ideal MHD from our model.