Linear Stability Analysis of a Hot Plasma in a Solid Torus

TL;DR

This paper investigates the stability of a collisionless plasma confined within a solid torus using the relativistic Vlasov-Maxwell system, providing criteria for equilibrium stability considering toroidal geometry effects.

Contribution

It introduces the first stability criteria for plasmas in a toroidal geometry based on the relativistic Vlasov-Maxwell system, focusing on cross-sectional dependencies.

Findings

Derived sharp stability criteria for plasma equilibria in a torus

Analyzed the influence of toroidal geometry on plasma stability

Established a foundation for further stability studies in toroidal plasmas

Abstract

This paper is a first step toward understanding the effect of toroidal geometry on the rigorous stability theory of plasmas. We consider a collisionless plasma inside a torus, modeled by the relativistic Vlasov-Maxwell system. The surface of the torus is perfectly conducting and it reflects the particles specularly. We provide sharp criteria for the stability of equilibria under the assumption that the particle distributions and the electromagnetic fields depend only on the cross-sectional variables of the torus.