The Vlasov-Poisson-Boltzmann system for a disparate mass binary mixture

TL;DR

This paper investigates the long-term behavior of a plasma model with electrons and ions of different masses, focusing on how their properties influence the system's evolution toward equilibrium, especially in the presence of self-consistent potentials.

Contribution

It extends macro-micro decomposition techniques to two-component Boltzmann equations with disparate masses, analyzing asymptotic stability toward non-constant equilibrium states.

Findings

Demonstrates convergence to quasineutral nonisentropic Euler system

Analyzes the influence of mass and charge disparities on system dynamics

Develops new analytical tools for two-component Boltzmann equations

Abstract

The Vlasov-Poisson-Boltzmann system is often used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are described by the two-component Boltzmann collision operator. The perturbation theory of the system around global Maxwellians recently has been well established in [42]. It should be more interesting to further study the existence and stability of nontrivial large time asymptotic profiles for the system even with slab symmetry in space, particularly understanding the effect of the self-consistent potential on the non-trivial long-term dynamics of the binary system. In the paper, we consider the problem in the setting of rarefaction waves. The analytical tool is based on the macro-micro decomposition introduced in [59] that we can be able to develop into the case for the two-component Boltzmann equations around local bi-Maxwellians. Our focus is to explore how the disparate masses and charges of particles play a role in the analysis of the approach of the complex coupling system time-asymptotically toward a non-constant equilibrium state whose macroscopic quantities satisfy the quasineutral nonisentropic Euler system.