Influence of vacuum electric field on the stability of a plasma-vacuum interface

Abstract

We study the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics. Unlike the classical statement, when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not neglect the displacement current in the vacuum region and 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. We find and analyze a sufficient condition on the vacuum electric field that precludes violent instabilities. Under the assumption that this condition is satisfied at each point of the unperturbed nonplanar plasmavacuum interface, we prove the well-posedness of the linearized problem in anisotropic weighted Sobolev spaces.