Gravitational Resistive Instability of an Incompressible Plasma in a Sheared Magnetic Field

The gravitational resistive instability analysed by Furth, Killeen, and Rosenbluth and subsequent authors is examined from a new point of view, which brings out the connection with ordinary Rayleigh-Taylor instability and thermal convection. In contrast to the modes found by earlier authors, which are either sharply localized in the vertical direction or require a boundary layer, it is shown that coherent motions of arbitrary vertical extent can occur. These alternative modes are derived by first considering a simpler but related model in which resistivity is concentrated at the ends of a system of finite length. This analysis shows that such systems may be unstable even if they satisfy the Newcomb criterion. The new resistive modes do not have the usual periodic dependence along the horizontal direction of the main field, but have finite length and represent convective rolls which are twisted to conform to the field lines. The relation of these new modes to the original periodic localized modes is examined.