Parametric Instabilities of the Ponomarenko dynamo

Abstract : We have studied the influence of large scale fluctuations on the dynamo threshold. For that purpose, we have solved the kinematic problem for a helical flow, to the stationary part of which, we have added a periodic and also helical time modulation. For a helical stationary flow, previous studies have shown that for high magnetic Reynolds numbers, the magnetic field is generated on a resonance surface characterised by a resonant condition on the velocity flow. For a modulated flow, we have shown that, for low amplitude of modulation, it is the resonant condition of the stationary part, that controls the generation of the magnetic field. For large amplitude of the fluctuations, it is the resonant condition of the fluctuating part of the flow that governs the dynamo efficiency as well as the dynamo threshold. In most cases and if the resonant condition is satisfied for both parts of the flow, we find that the threshold increases with the intensity of the fluctuations, and then decreases, while remaining higher than the threshold corresponding to the stationary threshold of the same geometry. If the resonant condition is not verified for the modulation, then the threshold increases drastically with its intensity.
These results show that the optimization of the dynamo experiments may not only depend on the stationary part of the flow but also on its non stationary large scale part. If the fluctuations are not optimized, then the threshold may increase drastically, even if the amplitude of these fluctuations is low.
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Marine Peyrot. Parametric Instabilities of the Ponomarenko dynamo. Planète et Univers [physics]. Université Joseph-Fourier - Grenoble I, 2008. Français. ⟨tel-00325286⟩

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