ИСТИНА

Kazantsev model describes the evolution of the magnetic field energy spectrum in a turbu-lent plasma flow [1]. In particular, this model can be used to describe a small-scale dynamo process in which the magnetic field energy grows exponentially while the average magnetic field not. Traditionally, such generation is considered in locally anisotropic homogeneous turbulence, however, using the method of product integrals, it is possible to extend the ap-plication of this model to the anisotropic or inhomogeneous case. That functional approach, proposed firstly by Molchanov, Ruzmaikin and Sokoloff, bases on two assumptions. First, the velocity field with short time correlations is considered, which makes it possible to do the averaging over the magnetic field and the velocity field independently to each other. Second, the trajectories of liquid particles are replaced by Winner beams trajectories, aver-aging over which allows us to take into account dissipative effects [2]. Writing the solution of the magnetic induction equation in the form of product integrals and calculating the time derivatives of the correlation functions of the magnetic field, we derive the anisotropic Ka-zantsev model and analyze it numerically in the simplest case of axial symmetry. The anal-ysis carried out makes it possible to study the dependence of the threshold value of the magnetic Reynolds number, from which small-scale generation begins, on the measure of the anisotropy of the velocity field. The work was supported by the BASIS Foundation grant no. 21-1-3-63-1. References [1] Kazantsev A., Soviet Physics JETP, Zh. Eksp. Tear. Fiz. (53): 1806-1813. 1967. [2] Molchanov A., Ruzmaĭkin A. , Sokoloff D., Soviet Physics Uspekhi, 28(4), 307, 1985.