Magnetic fields with random initial conditions in discs with Kepler rotation curve

Abstract Magnetic fields of various astrophysical objects are described using the dynamo mechanism. Corresponding equations in the three-dimensional case are quite difficult to be solved. So, the two-dimensional models can be useful for such problems. For galactic and accretion discs, it is convenient to use the no- z z approximation. The initial conditions for the magnetic field have a special interest. It seems that the seed field is generated by the Biermann mechanism, and after that they are transformed by the small-scale dynamo which gives a random structure of the field. Previously it has been shown that random initial conditions can lead to generation of large-scale magnetic field structures which correspond to the galaxies at the moment. In this work, we have studied generation of the magnetic field for the case of Kepler rotation curve, which is mostly suitable to the accretion discs. Here, we have studied the field generation in the thin disc for rapidly changing angular velocity in the case of simple model assumptions.