On local existence and violent instabilities of a plasma-vacuum interface

We discuss the influence of electric and magnetic fields on the well-posedness in Sobolev spaces of the plasma-vacuum interface problem. For the classical statement of the problem [1], the plasma flow is governed by the equations of ideal compressible or incompressible magnetohydrodynamics while the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics. We show that the Rayleigh–Taylor sign condition is not necessary for well-posedness because the plasma and vacuum magnetic fields play a stabilizing role if they are not collinear at each point of the interface [2, 3]. At the same time, the simultaneous failure of the non-collinearity condition and the Rayleigh–Taylor sign condition leads to Rayleigh–Taylor instability [4]. For the non-classical statement of the problem [5], when 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 makes the interface violently unstable. Moreover, for the technically simpler case of incompressible plasma [6] one can show that as soon as the plasma and vacuum magnetic fields are collinear on the interface, the interface is always violently unstable for any nonzero and even very small vacuum electric field.
REFERENCES
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[6] Trakhinin Y. On violent instability of a plasma-vacuum interface for an incompressible plasma flow and a nonzero displacement current in vacuum. arXiv:1812.08675.