Influence of the Hall effect on the Rayleigh-Taylor instability of a plasma slab accelerated by a magnetic field

The Rayleigh-Taylor instability of a slab of a low-density plasma accelerated by a magnetic field is studied with allowance for the Hall effect. When dissipation is neglected, the equations describing perturbations with k·B=0 (where B is the magnetic field and k is the perturbation wave vector) in a frame moving with the plasma slab can be exactly integrated in the case of a constant acceleration with allowance for the finite plasma pressure. The main result of the study is that these equations can be exactly integrated in the case of an arbitrary density profile n(x) in the slab and an arbitrary density dependent p=p(n) of the plasma pressure. Taking into account the pressure balance at the slab boundaries makes it possible to determine the evolutionary condition for the perturbed solutions. The perturbations of both the global mode of the Rayleigh-Taylor instability (Ω2=-κ, where Ω and κ are the dimensionless frequency and dimensionless wave vector of the perturbation, respectively) and the higher modes are considered