Nonlinear Rayleigh-Taylor stability of a fluid layer between homogeneous magnetic fields

The stability of a plane-parallel slab between two homogeneous magnetic fields is studied. Both the parallel and anti-parallel deformations of the interface are considered. In the linear theory a general dispersion relation is obtained, from which some familiar dispersion relations (interchange modes) are recovered. The general dispersion relation is discussed both numerically and analytically. In the nonlinear theory, the method of Callebaut has been used. In the second order the coefficients are obtained and studied. Some of the coefficients turned out to be identically zero because the dissipative effects were neglected for the problem under consideration. Hence, no phase shift can be generated. No singularities occurred in the second order coefficients, as expected in this problem, but contrast to some other configurations. The domain of validity of the linear theory has been studied. (author). 4 figs