ИСТИНА

The classical theory of turbulent dynamo, proposed in the 1970s by Kazantsev and Kreichnan (KK) for a short-correlated random flow, predicts the possibility of exponential growth of magnetic energy at sufficiently large magnetic Reynolds numbers. This theory has a number of shortcomings, the main of which is precisely related to the assumption of short- (or even delta-) time correlations in random velocity field [1]. In the framework of KK’s idea, such assumption implies independence of the correlation time from the scales of turbulent vortices, which can hardly be considered true for a typical Kolmogorov turbulence. Despite the recent appearance of the first experimental evidence of such small-scale generation existence, a clear verification of the threshold presence, from which the generation begins, has not yet been found or proved [2]. One of the possible explanations for this failure can follow exactly from the used modeling assumption of short-correlations. Of course, it is impossible to recheck that in the framework of the KK model, but one can suggest that it is possible to simulate the phenomenon of small-scale energy generation in the framework of another, so-called, shell MHD approach [3]. In our work, we use the shell model for three-dimensional isotropic MHD turbulence, which simulates turbulent cascade, describing the interaction of neighboring spectral scales under three motion integrals: total energy, cross- and magnetic helicity (modeling details can be found in [4]). Adding magnetic energy in the balanced hydrodynamic spectrum we observe its exponential growth – in other words, we see the efficient pumping of hydrodynamic energy into magnetic energy due to the property of magnetic field embeddedness in the medium. By calculating the magnetic energy growth rates for different Reynolds numbers and different hydrodynamic helicities, we demonstrate the existence of a threshold boundary analogous to the KK’s threshold and compare the dependence of such regime on the input data. We demonstrate the conditions under which both models can be used simultaneously and discuss possible reasons of failures at experimental verification of the threshold regime of turbulent small-scale dynamo. The investigation was supported by the Theoretical Physics and Mathematics Advancement Foundation ’BASIS’ grant number 21-1-3-63-1.