Singularities in the Rayleigh-Taylor instability of a thin plasma slab

A theoretical study of the interchangelike (Rayleigh-Taylor) instability of a thin slab of weakly ionized plasma is presented. We have found an analytical solution for the stationary motion of a plasma slab under the effect of the magnetic field pressure. This solution describes a shock-wave-like structure of the magnetic field and is unstable against the interchange mode. Using an approach developed earlier [E. Ott, Phys. Rev. Lett. 29, 1429 (1972); S.V. Bulanov, and P.V. Sasorov, Sov. J. Plasma Phys. 4, 418 (1978)] we have obtained exact solutions, in terms of analytical functions of a complex variable, of the Cauchy problem for the evolution of nonlinear perturbations. We have investigated the formation of the typical singularities that correspond to different wave breaking regimes in an unstable medium. We discuss Ott's problem of the Rayleigh-Taylor instability of initially nonplanar shells. [S1063-651X(99)10602-0].