Convective instability of internal modes in accelerated compressible plasmas

A compact second order differential equation for small amplitude magnetohydrodynamic modes of a plasma stratification in a uniform effective gravity field is derived. The steady state includes non-uniform density, mass motion, magnetic shear and non-isotropic pressure, given by arbitrary profiles. The perturbation treatment is of the magnetohydrodynamic class, with two closure equations for the time evolution of the pressure, in order to encompass ideal MHD, the Chew et al. (1956) and other non-isotropic models. As an application a detailed study of the compressible, convective-gravity modes in the ideal isotropic MHD case is presented. Local criteria for the convective instability are first obtained by means of physically intuitive arguments for unidirectional and for sheared magnetic field. In both instances a rigorous variational energy treatment is then provided. In the second case, a criterion analogous to that of B.R. Suydam (1958) for the pinch is shown to hold for plasma atmospheres. Global internal modes for an isothermal equilibrium with unidirectional magnetic field are then analysed. Stability criteria and growth rates of the unstable modes are studied. Areas of application of the reported results are indicated.