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Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence

This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action -- the magnetic analogue of the "shear-current" effect. In addition, consideration of $α$ effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of $α$, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.