Stability of relativistic plasma-vacuum interfaces

TL;DR

This paper investigates the stability of relativistic plasma-vacuum interfaces with density jumps, identifying conditions under which large vacuum electric fields cause instability and establishing criteria to prevent such violent disruptions.

Contribution

It introduces a new stability criterion for relativistic plasma-vacuum interfaces considering density jumps and develops an energy estimate using a secondary symmetrization of Maxwell equations.

Findings

Large vacuum electric fields can cause violent interface instabilities.

A sufficient condition is derived to prevent violent instabilities.

An energy a priori estimate is established for the linearized problem.

Abstract

We study the plasma-vacuum interface problem in relativistic magnetohydrodynamics for the case when the plasma density does not go to zero continuously, but jumps. In the vacuum region we consider the Maxwell equations for electric and magnetic fields. We show that a sufficiently large vacuum electric field can make the planar interface violently unstable. By using a suitable secondary symmetrization of the vacuum Maxwell equations, we find a sufficient condition that precludes violent instabilities. Under this condition we derive an energy a priori estimate in the anisotropic weighted Sobolev space $H^1_*$ for the variable coefficients linearized problem for nonplanar plasma-vacuum interfaces.