Hydromagnetic stability of a compressible plasma with hall-currents

The hydromagnetic stability of an electrically conducting compressible plasma having variable density in the vertical direction has been investigated taking into account the effects of Hallcurrents. The solution is shown to be characterized by a variational principle. Based on the existence of variational principle, the dispersion relation has been obtained for the case of a plasma having exponentially varying density with special reference to stellar atmosphere. It is found that both compressibility of the medium and Hall-currents destabilize the configuration for the disturbances, for which it was stable otherwise. The Hall-currents even suppress the mode of maximum instability for large magnitudes.