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 Kolmogorov–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.