Self-gravitational instability of a stratified plasma in the presence of Hall currents

The hydromagnetic stability of a self-gravitating, incompressible, inviscid, infinitely conducting plasma of variable density has been studied in the presence of Hall currents. The prevailing magnetic field is assumed to be uniform and acting along the vertical. It is first shown that a variational principle characterizes the problem. Proper solutions have then been obtained, by the variational methods, for a semi-infinite plasma having a one-dimensional (exponential) density gradient along the vertical direction. The dispersion relation has been solved numerically and it is found that the growth rate increases with Hall currents, exhibiting thereby the destabilizing character of Hall currents on the dynamic stability of a stratified plasma. (author)