Rayleigh-Taylor instability of a viscous compressible plasma of variable density

A study has been made of the problem of the Rayleigh-Taylor instability of a hydromagnetic plasma of varying density to investigate the influence of the simultaneous presence of the effects of compressibility and viscosity. The solution is shown to be characterized by a variational principle. Based on the variational principle proper solutions have been obtained for a semi-infinite plasma, in which the density has a one-dimensional gradient along the direction of a uniform vertical magnetic field, confined between two planes. Both the viscosity and magnetic field are found to have a stabilizing influence. The effect of compressibility is found to be destabilizing.