Advances in mean-field dynamo theories

Pipin Valery, valery.pipin@gmail.com, Institute for Solar-Terrestrial Physics


Abstract
The mean-field magnetohydrodynamic presents one of the most powerful tools for exploring the nature of the large-scale magnetic activity in cosmic bodies. The purpose of the dynamo theory is to describe mechanisms which transform the kinetic energy of hydrodynamic motions into the magnetic energy, taking into account the nonlinear feedback of the large-scale magnetic field on the motions. The key problems of the solar dynamo models are related to the solar cycle period, the phase relation between activity of the poloidal and toroidal components of the large-scale magnetic field, and their spatial-temporal activity pattern. We review advances in the basic ingredients of the theory which could help to resolve these issues. The discussion includes the recent analytical and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We review the results for the statistical effects of fluctuations in the turbulent sources dynamo and show how it could highlight the most important nonlinearities in the solar mean field dynamo.