Nonlinear Stability and Instability of Plasma Boundary Layers

TL;DR

This paper analyzes the nonlinear stability and instability of plasma boundary layers modeled by the Vlasov--Poisson system, focusing on the behavior of stationary solutions under perturbations.

Contribution

It provides a rigorous analysis of the nonlinear stability and instability of plasma sheath solutions within the Vlasov--Poisson framework.

Findings

Identification of conditions for stability and instability

Characterization of boundary layer behavior

Extension of previous stationary solution results

Abstract

We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov--Poisson system on a half-line with the completely absorbing boundary condition. In an earlier paper by the first two authors, the solvability of the stationary problem is studied. In this paper, we study the nonlinear stability and instability of these stationary solutions of the Vlasov--Poisson system.