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arXiv · 0901.3734

Dynamo Action in the Presence of an Imposed Magnetic Field

D. W. Hughes·M. R. E. Proctor
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Abstract

We consider the linear stability to three-dimensional perturbations of two-dimensional nonlinear magnetohydrodynamic basic states obtained from a specified forcing function in the presence of an imposed initially uniform magnetic field of strength $B_0$. The forcing is chosen such that it drives the CP flow of Galloway & Proctor (1992) when $B_0=0$. We first examine the properties of these basic states and their dependence on $B_0$ and on the magnetic Reynolds number $Rm$. The linear stability of these states is then investigated. It is found that at a given $Rm$ the presence of a background field is stabilising. The results also allow us to speculate that at a fixed value of $B_0$ the growth of the unstable perturbations is `fast', in the sense that the growth rate becomes independent of $Rm$ as $Rm \to \infty$.

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D. W. Hughes, M. R. E. Proctor. 2009-01-23. Dynamo Action in the Presence of an Imposed Magnetic Field. https://doi.org/10.1098/rspa.2008.0493

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