Non-Gaussian Generalization of the Kazantsev–Kraichnan Model for a Turbulent Dynamo

Abstract We consider a natural generalization of the Kazantsev–Kraichnan model for small-scale turbulent dynamo. This takes into account statistical time asymmetry flow and thus allows one to describe velocity fields with energy cascade. For three-dimensional fields, generalized Kazantsev equation is derived, evolution second-order magnetic field correlator investigated large but finite Prandtl numbers. It shown that as Pr m ? ?, growth increment tends limit known from T-exponential (Lagrangian deformation) method. Magnetic generation be weaker than in Gaussian any direction cascade essentially depends on number.