ИСТИНА

The mean-field model is one of the most used models of mhd-dynamo theory, which describes the magnetic field generation in a turbulent astrophysical plasma. It was firstly obtained by Steenbeck, Krause and Rädler for two-scale turbulence under local isotropy and uniformity assumptions. In this work, we develop the multiplicative integral approach, obtaining similar equations for a short-correlated random velocity field in anisotropic streams. This approach was proposed by Molchanov, Ruzmaikin and Sokoloff in 1985 and it is very close to the functional integrals method used in quantum mechanics. It does not require the assumption of a spatial two-scale velocity field and allows deriving dynamo equations for both: the first and the second moments of the magnetic field. The approach is based on two assumptions: first, the velocity field with short time correlations is considered, which makes it possible to do the averaging over the magnetic and the velocity field independently to each other. Second, the trajectories of liquid particles are replaced by Winner beams trajectories, averaging over which allows one to take into account dissipative effects. Note that this approach traditionally uses the magnetic induction equation written for the magnetic field, while in our report we use the equation for the vector potential. The goal here is not to prove the applicability of the multiplicative approach for the potential, but rather to demonstrate the advantages of this modification of the method for an anisotropic and non-uniform setting. To obtain a system for the Parker solar dynamo, we use a spherical coordinate system and divide the magnetic field into the sum of the poloidal and toroidal components. Using anisotropic equations, we analyse the classical system of the Parker's solar dynamo: the emphasis is on the anisotropy associated with azimuthal rotation that means turbulent media is considered with different average characteristics along and perpendicular to the axis of rotation. We demonstrate the influence of local velocity field anisotropy on the generation properties in this approach. A number of interesting anisotropic effects were analyzed, one of which, for example, is the possibility of generating a magnetic field at zero helicity. This work was supported by the BASIS Foundation grant no. 21-1-3-63-1.