Stochastic dynamo in critical situations

Based on the functional method of consecutive approximations, we consider the problem of magnetic field excitation (stochastic dynamo) by a random velocity field with a finite temporal correlation radius. In critical situations, in the first (diffusion) approximation, the Lyapunov characteristic parameter of the magnetic field energy vanishes. This implies the absence of structure formation (clustering) in realizations of the magnetic field in that approximation. Critical situations occur in problems of magnetic field diffusion in an equilibrium thermal and random pseudoequilibrium and acoustic (in the absence of dissipation) velocity fields. The sign of the Lyapunov characteristic parameter in the second-order approximation determines the possibility of clustering of the magnetic field energy. We show that energy clustering does not occur in a thermal velocity field. In the cases of pseudoequilibrium and acoustic velocity fields, clustering occurs with probability one, i.e., in almost every realization. We evaluate the characteristic time for clustering to be established.