Saturation of the magnetic field above the dynamo threshold

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We show that the saturation level of the magnetic field generated by a fluid dynamo just above threshold, can be estimated using simple dimensional arguments when the flow is turbulent. We then discuss other scalings by considering the structure of the weakly nonlinear problem above the dynamo threshold. Finally, we compare these predictions with recent experimental results.

Received 23 April 2001 and Received in final form 21 June 2001