The theory of Hall magnetohydrodynamics is developed to describe convection in partially ionized plasma. The key assumption of the developed theory is that the temperature of each component of partially ionized plasma is determined by the temperature of the neutral component. In fact, the neutral component acts as a thermostat for the charged components. The equations of the partially ionized plasma's center of mass are obtained including the effects of viscosity and thermal conductivity. The obtained equations of Hall magnetohydrodynamics are written in Boussinesq approximation. The Bénard problem of a rotating partially ionized plasma layer heated from below is formulated. The linear hydrodynamic instability problem is solved, and the threshold and the increment of convective instability are found. The obtained threshold of instability generation of the partially ionized plasma layer depends on the Chandrasekhar number and the ratios of Hall and ambipolar diffusion coefficients to the Ohmic diffusion coefficient.
Galstyan et al. (Sun,) studied this question.