Two Types of Nonlinearities in Magnetic Dynamo

Abstract

Two types of nonlinearities (algebraic and dynamic) are discussed. The algebraic nonlinearity implies a nonlinear dependence of the mean electromotive force on the mean magnetic field. The dynamic nonlinearity is determined by a differential equation for the magnetic part of the α-effect. It is shown that the algebraic nonlinearity alone (which includes the nonlinear α-effect, the nonlinear turbulent diffusion, etc) cannot saturate the dynamo generated mean magnetic field while both, the algebraic and dynamic nonlinearities limit the mean magnetic field growth.

The nonlinear mean electromotive force is calculated for an anisotropic background turbulence (i.e., the turbulence with zero mean magnetic field) with one preferential direction. It is shown that the toroidal and poloidal magnetic fields have different nonlinear turbulent diffusion coefficients. It is demonstrated that even for homogeneous turbulence there is an effective nonlinear velocity which exhibits diamagnetic or paramagnetic properties depending on anisotropy of turbulence and level of magnetic fluctuations in the background turbulence. The diamagnetic velocity results in the field is pushed out from the regions with stronger mean magnetic field, while the paramagnetic velocity causes the magnetic field tends to be concentrated in the regions with stronger field. Analysis shows that anisotropy of turbulence strongly affects the nonlinear turbulent diffusion coefficients and the nonlinear effective velocity.