Linear Stability Analysis of the Relativistic Vlasov-Maxwell System in an Axisymmetric Domain

TL;DR

This paper establishes a precise spectral stability criterion for axisymmetric plasma equilibria in a bounded domain, providing explicit examples of stable and unstable configurations.

Contribution

It introduces a sharp stability criterion for the relativistic Vlasov-Maxwell system in axisymmetric domains, including explicit stable and unstable equilibrium families.

Findings

Derived a spectral stability criterion for the system.

Identified explicit stable and unstable equilibrium families.

Provided conditions for stability in axisymmetric plasma confinement.

Abstract

We consider the plasma confined in a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, and look at a certain class of equilibria, assuming axisymmetry in the problem. We prove a sharp criterion of spectral stability under these settings. Moreover, we provide several explicit families of stable/unstable equilibria using this criterion.