Electromotive force for an anisotropic turbulence: Intermediate nonlinearity

A nonlinear electromotive force for an anisotropic turbulence in the case o f intermediate nonlinearity is derived. The intermediate nonlinearity impli es that the mean magnetic field is not strong enough to affect the correlat ion time of a turbulent velocity field. The nonlinear mean-field dependenci es of the hydrodynamic and magnetic parts of the rr effect, turbulent diffu sion, and turbulent diamagnetic and paramagnetic velocities for an anisotro pic turbulence are found. It is shown that the nonlinear turbulent diamagne tic and paramagnetic velocities are determined by both an inhomogeneity of the turbulence and an inhomogeneity of the: mean magnetic field B. The latt er implies that there are additional terms in the turbulent diamagnetic and paramagnetic velocities proportional to del B-2 and proportional to(B.del) B. These effects are: caused by a tangling of a nonuniform mean magnetic he ld by hydrodynamic fluctuations. This increases the inhomogeneity of the me an magnetic held. It is also shown that in an isotropic turbulence the mean magnetic field causes an anisotropy of the nonlinear turbulent diffusion. Two types of nonlinearities in magnetic dynamo determined by algebraic and differential equations are discussed. Nonlinear systems of equations for ax isymmetric alpha Ohm dynamos in both spherical and cylindrical coordinates are derived.