On the diffusion and clustering of a magnetic field in random velocity fields

We have derived an equation for the probability density of the magnetic energy in a random Gaussian, delta-correlated in time, divergent velocity field in the absence of molecular diffusion effects. Basic statistical characteristics of the energy have been calculated using this equation. Based on the ideas of statistical topography, we have studied the processes of magnetic field amplification in space and, in particular, the conditions for the formation of a cluster structure. These phenomena are coherent, occur with a probability equal to unity, and, hence, manifest themselves almost in all individual realizations of the process. The clustering effect is demonstrated with an exact solution for the magnetic field dynamics for the simplest model of a random divergent velocity field.