Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge

TL;DR

This paper rigorously proves the emergence of the Debye screening length in a nonlinear Vlasov-Poisson plasma interacting with a point charge, extending understanding beyond linearized models.

Contribution

It provides the first rigorous proof of Debye screening in the nonlinear Vlasov-Poisson equation with a point charge, confirming linear theory predictions.

Findings

Debye length emerges in nonlinear plasma models

Screened stationary states are characterized rigorously

Results align with linearized theory predictions

Abstract

We prove that the Debye screening length emerges in a spatially homogeneous plasma described by the nonlinear Vlasov-Poisson equation interacting with a point charge. While screened stationary states as well as the time-dependent problem are well-studied for the linearized equation, there are few rigorous results on screening in the nonlinear setting. As such, the results presented here cover the stationary case under the assumptions predicted by the linearized theory.