The dynamics of magnetic fields in a highly conducting turbulent medium and the generalized Kolmogorov-Fokker-Planck equations

It is shown that a consideration of the magnetic field in a highly conducting turbulent medium, using Lagrange variables, involves deriving kinetic equations of fluid-particle transition probability densities. A derivation of such equations is performed for joint probability densities of n particles up to n=4. By assuming normality of one particle distribution function it was found that these kinetic equations are the generalized Kilmogorov-Fokker-Planck (KFP) equations. The dynamics of mean and fluctuating magnetic fields is described by means of these equations. The eddy diffusivity of a mean field for processes described by generalized KFP equations coincides with that of a scalar field (depending in general on helicity in implicit form). It is shown that at sufficiently large magnetic Reynolds number, a turbulence with any spectrum generates fluctuating magnetic fields. (author)