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Fluctuating αΩ dynamos by iterated matrices




Recent publications have suggested various scaling laws for dynamo growth rates when dynamo action is made possible or enhanced by shear. In order to understand the relation between the different scalings, we study a simple model mean field dynamo, in which the α-effect is piecewise constant in time, allowing a simple derivation of the growth rates in terms of iterated matrices. It is found that all the different scaling laws that appear in earlier work can be seen in different parameter regimes.