Rayleigh Taylor instability of a viscous Hall plasma with magnetic field

The influence of finite Larmor frequency on the stability of a viscous, finitely conducting liquid in a downward gravitational field under the influence of a uniform magnetic field directed along or normal to gravity, is investigated. The solution in each case is shown to be characterized by a variational principle Based on the variational principle, an approximate solution is obtained for the stability of a layer of fluid of constant kinematic viscosity and an exponentia density distribution. It has been found that finite resistivity and finite Larmor frequency do not introduce any instabifity in a potentially stable configuration. However, for a potentially unstable configuration we find that, for an ideal Hal plasma, the results depend on the orientation of the magnetic field, though the instability persists for all wave-numbers in the presence of non-ideal (finite resistivity and viscosity) effects. For the field aligned with gravity, it is found that a potentially unstable field-free configuration is stabilized if the buoyancy number B ( = gβ/1² V²) is less than unity. For B > 1, the instability arises for wave-numbers exceeding a critical value, which decreases on allowing for Hall terms in the generalized Ohm's law, suggesting a destabilizing influence of finite Larmor frequency. For an ambient horizontal magnetic field, it is found that an ideal plasma is stable, even for B > 0, for perturbations confined to a cone about the magnetic field vector. The angle of the cone of stable propagation, however, decreases on account of finite Larmor frequency.