Homopolar oscillating-disc dynamo driven by parametric resonance |
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Authors: | Jānis Priede Franck Plunian |
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Affiliation: | a Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, United Kingdom b Universidad Autónoma de San Luis Potosí, Dr. Manuel Nava 8, CP. 78290, San Luis Potosí, SLP, Mexico c Université Joseph Fourier, LGIT (CNRS), B.P. 53, 38041 Grenoble Cedex 9, Grenoble, France |
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Abstract: | We use a simple model of Bullard-type disc dynamo, in which the disc rotation rate is subject to harmonic oscillations, to analyze the generation of magnetic field by the parametric resonance mechanism. The problem is governed by a damped Mathieu equation. The Floquet exponents, which define the magnetic field growth rates, are calculated depending on the amplitude and frequency of the oscillations. Firstly, we show that the dynamo can be excited at significantly subcritical disc rotation rate when the latter is subject to harmonic oscillations with a certain frequency. Secondly, at supercritical mean rotation rates, the dynamo can also be suppressed but only in narrow frequency bands and at sufficiently large oscillation amplitudes. |
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Keywords: | Magnetohydrodynamics Dynamo effect Instability Parametric resonance Mathieu equation |
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