A simplified nonlinear dynamo model is constructed that allows the transition from the kinematic to the dynamic regime to be studied in detail. We apply this construction to a chaotic flow recently studied in the context of fast dynamo action. It is found that the structure of the magnetic field in the two regimes is markedly different. Furthermore, the saturation of the exponential growth of the magnetic field is achieved by a drastic suppression of the chaotic properties of the flow.
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Cattaneo et al. (1996) studied this question.
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