Large-Scale Convection of Rotating Partially Ionized Space and Astrophysical Plasmas in the Hall-Magnetohydrodynamics Approximation

The theory of Hall magnetohydrodynamics of rotating partially ionized plasma taking into account the effects of viscosity and thermal conduction is developed. The key supposition of the developed theory consists in the assumption that the temperature of each component of the partially ionized plasma is determined by the temperature of the neutral component. In fact, the neutral component plays the role of a heat bath for the charged components. Equations governing the motion of the center of mass of the partially ionized plasma that take into account the effects of viscosity and thermal conduction are derived. The developed theory describes convection processes in rotating partially ionized plasma. The obtained equations of the Hall magnetohydrodynamics are expressed in the Boussinesq approximation. The Bénart problem of the layer of rotating partially ionized plasma heated from below is formulated. The linear problem of hydrodynamic instability is solved, and the threshold and growth rate of the convective instability are found. The obtained threshold of the onset of instability of the layer of partially ionized plasma heated from below depends on the Taylor number, the Chandrasekhar number, along with the ratios of the Hall and ambipolar diffusion coefficients to the ohmic diffusion coefficient.