ИСТИНА

The averaging of the magnetic induction equation over a random velocity field forms the basis of the dynamo theory, which describes the formation and evolution of large-scale astrophysical magnetic fields. The standard approach is the asymptotic method, proposed by Krause and Radler in the 1960’s for two-scale plasma turbulence. Two-scale assumption assumes that a random velocity field can be represented as a sum of a large-scale slowly varying component and a small-scale fluctuating one. Exactly by this method the classical systems of the Parker Solar dynamo and the galactic disk dynamo were obtained. In our report we discuss a different method of the averaging, proposed in 1985 by Molchanov, Ruzmaikin, and Sokoloff for working with a shortcorrelated in time random flow. It does not require the assumption of a spatial two-scale velocity field structure and easily allows one to derive the dynamo equations for both the first and the second magnetic field moments in locally anisotropic and inhomogeneous conditions. The advantages of the functional integral approach and possible areas of its application in astrophysical plasma are discussed.