The stability of gravitational compressible surface modes of a plasma-vacuum interface is investigated. Stratified equilibrium profiles of density and magnetic field in the plasma are considered. The corresponding boundary conditions for magnetohydrodynamic linear perturbations are deduced. Three types of surface normal modes (slow, intermediate and fast) may appear. The slow mode is unstable below a critical wavenumber. The stability criterion is affected in general by the compressibility. The growth rate of the unstable modes is increased by compressibility. It is shown that for 'flute' or pure interchange modes with respect to the vacuum magnetic field (but not with respect to the equilibrium magnetic field in the plasma) the compressibility enlarges the instability domain of surface modes. The interval of existence of unstable surface perturbations, as well as their growth rates, are larger than those of the internal unstable modes. Intervals of non-existence of surface modes appear for the flute perturbations with respect to the plasma magnetic field. The critical values of the wavenumber below which the modes are unstable, are discussed in general.
Nonlinear Magnetohydrodynamics