Magnetic field dynamics in presence of Hall conductivity and thermal diffusion

TL;DR

This paper derives equations describing magnetic field dynamics considering Hall currents and thermal diffusion, highlighting their influence on magnetic structures and including a mechanism for seed magnetic field generation.

Contribution

It introduces a new equation incorporating Hall currents and thermal diffusion effects, including a Biermann battery term for seed magnetic field creation.

Findings

Hall currents affect magnetic field structure in thermal diffusion scenarios.

Derived equations include a Biermann battery term for seed magnetic field generation.

Models demonstrate the influence of anisotropic kinetic coefficients on magnetic dynamics.

Abstract

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.