Biermann battery as a source of astrophysical magnetic fields

A large number of galaxies have large-scale magnetic fields which are usually measured by the Faraday rotation of radio waves. Their origin is usually connected with the dynamo mechanism which is based on differential rotation of the interstellar medium and alpha-effect characterizing the helicity of the small-scale motions. However, it is necessary to have initial magnetic field which cannot be generated by the dynamo. One of the possible mechanisms is connected with the Biermann battery which acts because of different masses of protons and electrons passing from the central object. They produce circular currents which induce the vertical magnetic field. As for this field we can obtain the integral equation which can be solved by simulated annealing method which is widely used in different branches of mathematics