Effects of neutral gas friction and ion viscosity on the Rayleigh-Taylor instability of a stratified plasma in the presence of Hall currents

The effects of neutral gas friction, on the Rayleigh–Taylor instability of an infinitely conducting plasma of variable density, with ion viscosity and Hall currents, are investigated. For an ambient horizontal magnetic field, it is shown that the solution is characterized by a variational principle. Making use of the existence of this, proper solutions are obtained for a semi-infinite plasma, in which the density is stratified exponentially along the vertical, confined between two planes. In the simultaneous presence of the effects of ion viscosity and Hall currents, it is found that the potentially unstable stratification is unstable for all wavenumber perturbations, irrespective of whether or not the effects of neutral gas friction are included. Further, it is found that the growth rate increases with both Hall currents and neutral gas friction, and decreases with ion viscosity. The influence of the Hall currents and the neutral gas friction, therefore, is destabilizing, while that of ion viscosity is stabilizing. In the absence of Hall currents, it is found that the viscous plasma is stable, even for a potentially unstable stratification, for perturbations confined to a cone about the magnetic field vector. The angle of the cone of stable propagation of an inviscid plasma,. however, decreases with both Hall currents and effects of neutral gas friction.