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Instability of the homopolar disk-dynamo in presence of white noise

Abstract : We study a modified Bullard dynamo and show that this system is equivalent to a non-linear oscillator subject to a multiplicative noise. The stability analysis of this oscillator is performed. Two bifurcations are identified, first, towards an łqłq intermittent\rq\rq state, where the absorbing (non-dynamo) state is no more stable but the most probable value of the amplitude of the oscillator is still zero, and, secondly, towards a łqłq turbulent\rq\rq (dynamo) state, where it is possible to define unambiguously a (non-zero) most probable value, around which the amplitude of the oscillator fluctuates. The bifurcation diagram of this system exhibits three regions, which are analytically characterized.
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Nicolas Leprovost, Bérengère Dubrulle, Franck Plunian. Instability of the homopolar disk-dynamo in presence of white noise. Magnetohydrodynamics c/c of Magnitnaia Gidrodinamika, Institute of Physics, University of Latvia, 2006, 42 (2-3), pp.131 à 142. ⟨insu-00354244⟩

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