A general way to confined stationary Vlasov-Poisson plasma configurations

TL;DR

This paper establishes a general method for proving the existence of stationary plasma configurations confined by magnetic fields in various domains, advancing understanding of plasma confinement in fusion devices.

Contribution

It introduces a unified approach for constructing stationary solutions of the Vlasov-Poisson system under magnetic confinement, applicable to different geometries and plasma setups.

Findings

Existence of stationary solutions in confined plasma models.

Application to cylindrical and toroidal geometries.

Results relevant for magnetic confinement fusion devices.

Abstract

We address the existence of stationary solutions of the Vlasov-Poisson system on a domain $\Omega\subset\mathbb{R}^3$ describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a subregion of $\Omega$. In a first part we provide such an existence result for a generalized system of Vlasov-Poisson type and investigate the relation between the strength of the external magnetic field, the sharpness of the confinement and the amount of plasma that is confined measured in terms of the total charges. The key tools here are the method of sub-/supersolutions and the use of first integrals in combination with cutoff functions. In a second part we apply these general results to the usual Vlasov-Poisson equation in three different settings: the infinite and finite cylinder, as well as domains with toroidal symmetry. This way we prove the existence of stationary solutions corresponding to a two-component plasma confined in a Mirror trap, as well as a Tokamak.