Stability analysis of collisionless plasmas with specularly reflecting boundary

TL;DR

This paper establishes precise criteria for the linear stability or instability of collisionless plasma equilibria within bounded domains, focusing on the relativistic Vlasov-Maxwell system with reflective and conducting boundary conditions in symmetric geometries.

Contribution

It introduces sharp stability criteria for the relativistic Vlasov-Maxwell system with boundary conditions, advancing understanding of plasma behavior in confined geometries.

Findings

Derived sharp stability and instability criteria

Analyzed the relativistic Vlasov-Maxwell system with boundary conditions

Focused on symmetric geometries for initial investigation

Abstract

In this paper we provide sharp criteria for linear stability or instability of equilibria of collisionless plasmas in the presence of boundaries. Specifically, we consider the relativistic Vlasov-Maxwell system with specular reflection at the boundary for the particles and with the perfectly conducting boundary condition for the electromagnetic field. Here we initiate our investigation in the simple geometry of radial and longitudinal symmetry.