Biermann battery as a source of cosmic magnetic fields

Nowadays it is well-known that some spiral galaxies, accretion discs, stars etc. have large scale magnetic fields. Theirexistence is supported by Faraday rotation measurements and another observational data. As for theoretical models, themagnetic field generation is usually described by the dynamo mechanism. It explains the exponential growth of the field.However, this model does not describe the formation of initial magnetic field, which should be considered using anotherapproaches. One of the most reasonable methods is connected by the Biermann battery mechanism. It uses the fact thatparticles (protons and electrons) have the same charge and significantly different masses. This leads to the emergence ofcircular currents which produce vertical magnetic fields. Their structure is described by the integral equation which can besolved using regularization methods.