Galactic dynamo equations with random coefficients

A problem connected with magnetic fields of galaxies is considered. Their evolution is described by the dynamo mechanism existing due to the alpha-effect and the differential rotation. These phenomena are characterized by dimensionless coefficients of the dynamo equations. Usually, it is assumed that these parameters are deterministic. We assume that one of them is described by a random process and is renewed on some small time interval. We also assume that this parameter can take one of two values with some dispersion and probability. Each of these values characterizes a component of the interstellar medium. The growth rates of statistical moments of the magnetic field are evaluated. It is shown that there exists the intermittency phenomenon in this problem (the higher moments grow faster). The problem that has only a time dependence and the problem that has a spatial dependence are also considered. It is shown that the spatial dependence lowers the magnetic field growth rate, which can be explained by some extra dissipation of the magnetic field energy. A nonlinear modification of the problem is discussed.