Convective Instability Induced by Gravity in a Plasma with a Frozen-In Magnetic Field

Abstract

The convective instability induced by gravity in a compressible fluid layer is investigated in the special case of a plasma with a frozen‐in magnetic field B. The necessary and sufficient condition for stability, which is here derived from the hydromagnetic energy principle, is that the density gradient should exceed a certain critical value that is independent of B. Thus the rigidity given to the plasma by the frozen‐in field does not suffice to remove the instability but only to slow it down. The growth rates of the unstable displacements are calculated by means of a normal mode analysis and are shown to be inversely proportional to B when B is sufficiently large.