On inverse cascades in alpha effect dynamos

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Abstract
The nonlinear evolution of alpha effect dynamo instabilities is considered. It is assumed that the small-scale flow is driven by a body force and that MHD equilibrium holds at large scales, which is the case when the large-scale fields depend on a unique Cartesian coordinate. It is shown that when magnetic modes over an extended range of scales are linearly unstable, an inverse cascade develops, mediated by the small-scale velocity and magnetic fields. Beginning with a weak magnetic field, there is a short transient during which the growth is dominated by the linearly most unstable modes: then the magnetic excitation is transferred to larger and larger scales. Eventually the magnetic field saturates in a stationary configuration dominated by the largest available scale.

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