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

We study the free boundary problem for the plasma-vacuum interface in ideal com- pressible 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 plasma-vacuum interface, we prove the well-posedness of the linearized problem in anisotropic weighted Sobolev spaces.

Keywords

ideal compressible magnetohydrodynamics, vacuum Maxwell equations, plasma-vacuum interface

2010 Mathematics Subject Classification

35L50, 35Q35, 35R35, 76E17, 76E25, 76W05

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Published 20 March 2014