Confined steady states of a Vlasov-Poisson plasma in an infinitely long cylinder

TL;DR

This paper studies the two-dimensional Vlasov-Poisson system modeling a plasma in an infinite cylinder, proving the existence of steady states with nontrivial electric potential, extending previous work on compactly supported states.

Contribution

It demonstrates the existence of compactly supported steady states with non-zero electric potential in a 2D plasma model, adapting methods from 3D analysis.

Findings

Existence of steady states with nontrivial electric potential

Extension of previous compact support results to 2D system

Method adaptation from 3D to 2D plasma models

Abstract

We consider the two-dimensional Vlasov-Poisson system to model a two-component plasma whose distribution function is constant with respect to the third space dimension. First, we show how this two-dimensional Vlasov-Poisson system can be derived from the full three-dimensional system. The existence of compactly supported steady states with vanishing electric potential in a three-dimensional setting has already been investigated by A. L. Skubachevskii [15]. We show that his approach can easily be adapted to the two-dimensional system. However, our main result is to prove the existence of compactly supported steady states even with a nontrivial self-consistent electric potential.