Intermittency in the homopolar disc-dynamo

N. Leprovost¹ - B. Dubrulle² - F. Plunian³

¹ LPS/ENS, 24 rue Lhomond, F-75231 Paris cedex 05, France
² DRECAM/SPEC/CEA Saclay, and CNRS (URA2464), F-91190 Gif sur Yvette Cedex, France
³ LEGI, B.P. 53, 38041 Grenoble Cedex 9, France

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. Figs 7, Refs 27.