A turbulent dynamo threshold in the shell-model approximation.

Turbulent magnetic dynamo models were created about fifty years ago to describe the growth of the average magnetic energy in random convective plasma flows. A typical feature of such models is the generation threshold, when the exponential growth of magnetic energy begins only at sufficiently large magnetic Reynolds numbers Rm. In particular, one of the first models, proposed in the 70th by Kazantsev and Kraichnan, predicts a generation threshold in the region of Reynolds numbers of the order of 100. This threshold is difficult to achieve even for modern laboratory experiments, and therefore many studies in recent years have been devoted to clarifying this critical value. However, there is a sufficient disadvantage of usually used turbulent dynamo model – the assumption about delta-correlated in time random velocity field. This nonphysical assumption makes one unconfident in the correctness of the estimate of the dynamo threshold. In this work, using shell MHD models, we are trying to find out how accurate Kazantsev’s estimate of the generation threshold is, and how this threshold depends on the flow velocity, diffusion coefficients, and hydrodynamic helicity. This work was supported by the BASIS Foundation grant no. 21-1-3-63-1.