Magnetic field dynamics in presence of Hall conductivity, and thermodiffusion

This anisotropy of kinetic coefficients in presence of a magnetic field is represented by so-called Hall currents, which appear in a collisional medium due to action of the Lorentz force on the charged particles between collisions. In many papers the Hall currents had been considered in different approximate approaches. We derive equations, describing dynamics of the magnetic field in presence of Hall currents, using a standard electrodynamic consideration. We consider collisional media, and take into account a temperature gradients, which create thermodiffusional electric current, in presence of the Hall component. The influence of the Hall currents on the magnetic field structure and damping is considered in simple models. In presence of thermodiffusion the condition for creation of the seed magnetic field in the non-magnetized media is found, which is needed for the action of the mechanism, known as "Biermann battery".