Nonlinear turbulent magnetic diffusion and mean-field dynamo - art. no. 056307

The nonlinear coefficients defining the mean electromotive force (i.e., the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, the nonlinear kappa tensor, etc.) are calculated for an anisotropic turbule nce. A particular case of an anisotropic background turbulence (i.e., the t urbulence with zero-mean magnetic field) with one preferential direction is considered. It is shown that the toroidal and poloidal magnetic fields hav e different nonlinear turbulent magnetic diffusion coefficients. It is demo nstrated that even for a homogeneous turbulence there is a nonlinear effect ive velocity that exhibits diamagnetic or paramagnetic properties depending on the anisotropy of turbulence and the level of magnetic fluctuations in the background turbulence. The diamagnetic velocity results in the field be ing pushed out from the regions with stronger mean magnetic field, while th e paramagnetic velocity causes the magnetic field to be concentrated in the regions with stronger field. Analysis shows that an anisotropy of turbulen ce strongly affects the nonlinear turbulent magnetic diffusion, the nonline ar effective velocity, and the nonlinear a effect. Two types of nonlinearit ies (algebraic and dynamic) are also discussed. The algebraic nonlinearity implies a nonlinear dependence of the mean electromotive force on the mean magnetic field. The dynamic nonlinearity is deter-mined by a differential e quation for the magnetic part of the alpha effect. It is shown that for the alpha Omega axisymmetric dynamo the algebraic nonlinearity alone (which in cludes the nonlinear alpha effect, the nonlinear turbulent magnetic diffusi on, the nonlinear effective velocity, etc.) cannot saturate the dynamo gene rated mean magnetic field while the combined effect of the algebraic and dy namic nonlinearities limits the mean magnetic field growth.