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The mean electromotive force generated by random Alfvén waves in a collision-less plasma is evaluated taking into account mean magnetic field gradients. It is shown that the mean electromotive force associated with a magnetic shear of the mean field and the helicity spectrum function of the random velocity field exists and has a component parallel to the mean magnetic field when it is generated by random waves propagating along the mean magnetic field and by statistically anisotropic random waves propagating in arbitrary directions. The results are applied to the magnetospheric substorms.