Linear and Non linear stability for the kinetic plasma sheath on a bounded interval

TL;DR

This paper proves the linear and nonlinear stability of a kinetic plasma sheath model on a bounded interval, showing exponential decay of fluctuations under certain conditions, advancing understanding of plasma-wall interactions.

Contribution

It establishes the first rigorous stability results for kinetic plasma sheaths in a bounded domain, including exponential decay rates for small perturbations.

Findings

Linear stability with exponential decay when injection rate is less than absorption rate.

Nonlinear stability for small equilibrium and localized perturbations.

Provides mathematical foundation for plasma sheath stability analysis.

Abstract

Plasma sheaths are inhomogeneous stationary states that form when a plasma is in contact with an absorbing wall. We prove linear and non linear stability of a kinetic sheath stationary state for a Vlasov-Poisson type system in a bounded interval. Notably, in the linear setting, we obtain exponential decay of the fluctuation provided the rate of injection of particles at equilibrium is smaller than the rate of absorption at the wall. In the non linear setting, we prove a similar result for small enough equilibrium and small localized perturbation of the equilibrium.