Nonlinear theory of a “shear-current” effect and mean-field magnetic dynamos

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Abstract
The nonlinear theory of a "shear-current" effect in a nonrotating and nonhelical homogeneous turbulence with an imposed mean velocity shear is developed. The shear-current effect is associated with the W x J term in the mean electromotive force and causes the generation of the mean magnetic field even in a nonrotating and nonhelical homogeneous turbulence (where W is the mean vorticity and J is the mean electric current). It is found that there is no quenching of the nonlinear shear-current effect contrary to the quenching of the nonlinear alpha effect, the nonlinear turbulent magnetic diffusion, etc. During the nonlinear growth of the mean magnetic field, the shear-current effect only changes its sign at some value B (*) of the mean magnetic field. The magnitude B (*) determines the level of the saturated mean magnetic field which is less than the equipartition field. It is shown that the background magnetic fluctuations due to the small-scale dynamo enhance the shear-current effect and reduce the magnitude B (*) . When the level of the background magnetic fluctuations is larger than 1/3 of the kinetic energy of the turbulence, the mean magnetic field can be generated due to the shear-current effect for an arbitrary exponent of the energy spectrum of the velocity fluctuations.

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