Magnetic field dynamics in presence of Hall conductivity and thermal diffusion

Anisotropy of kinetic coefficients in presence of a magnetic field is represented by Hall currents, which appear in a collisional medium due to action of the Lorentz force on the charged particles between collisions. We derive equations, describing dynamics of the magnetic field in presence of thermal diffusion with Hall currents, using a standard electrodynamic consideration. The influence of the Hall currents, at presence of thermal diffusion, on the magnetic field structure is considered in simple models. The equation is derived, which includes additional term for a seed magnetic field creation by the mechanism known as "Biermann battery" in the unmagnetized plasma.