Biermann Battery and Magnetic Fields of Accretion Discs

Magnetic fields should be studied to understand different processes in accretion discs, such as transition of angular momentum which is closely connected with them. There are different ways to describe the growth of magnetic fields of cosmic objects. One of them is based on Biermann battery mechanism which previously has been used to study the origin of magnetic fields in galaxies. It is based on different masses and same absolute values of charges of protons and electrons, which move across the disc. They interact with rotating medium, get azimuthal velocity and produce circular currents that are associated with the magnetic fields in the disc. Such magnetic field influences the motion of the charged particles that created it, and we should take into account the feedback. Mathematical description of this mechanism leads us to the Fredholm-type integral equation of the 2nd kind. In the presented work it is solved numerically using Galerkin methods. Here we give the solutions of different cases.