Dynamo models with magnetic diffusivity-quenching

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Abstract
The magnetic influence on a turbulent plasma also produces a complicated structure of the eddy diffusivity tensor rather than a simple and traditional quenching of the eddy diffusivity. Dynamo models in plane (galaxy) and spherical (star) geometries with differential relation are developed here to answer the question whether the dynamo mechanism is still yielding stable configurations. Magnetic saturation of the dynamos is always found—at magnetic energies exceeding the energy-equipartition value. We find that the effect of magnetic back-reaction on the turbulent diffusivity depends highly on whether the dynamo is oscillatory or not. The steady modes are extremely influenced. They saturate at field strengths strongly exceeding its turbulence-equipartition value. Subcritical excitation is even found for strong seed fields. The oscillating dynamos, however, only provide a small effect. Hence, the strong over-equipartition of the internal solar magnetic fields revealed by studies of flux-tube dynamics cannot be explained with the theory presented. Also the run of the cycle frequency with the dynamo number is too smooth in order to explain observations of stellar chromospheric activity.