Continuous Family of Equilibria of the 3D Axisymmetric Relativistic Vlasov-Maxwell System

TL;DR

This paper constructs continuous families of equilibrium solutions for the 3D axisymmetric relativistic Vlasov-Maxwell system, demonstrating the existence of solutions with arbitrarily large electromagnetic fields and analyzing their spectral stability.

Contribution

It introduces a method to generate continuous global solution sets for the relativistic Vlasov-Maxwell system with large fields, extending understanding of equilibrium states in plasma physics.

Findings

Existence of continuous equilibrium solution sets with arbitrarily large electromagnetic fields.

Particle density functions depend on energy and angular momentum variables.

Spectral stability varies as parameters change, indicating stability transitions.

Abstract

We consider the relativistic Vlasov-Maxwell system (RVM) on a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, assuming axisymmetry in the problem. We construct continuous global parametric solution sets for the time-independent RVM. The solutions in these sets have arbitrarily large electromagnetic field and the particle density functions have the form $f^\pm = \mu^\pm (e^\pm (x, v), p^\pm (x, v))$, where $e^\pm$ and $p^\pm$ are the particle energy and angular momentum, respectively. In particular, for a certain class of examples, we show that the spectral stability changes as the parameter varies from $0$ to $\infty$.