Dynamo action in the presence of an imposed magnetic field
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 ‘circularly polarized’ (CP) flow of Galloway & Proctor ( Galloway & Proctor 1992 Nature 356 , 691–693) when B 0 =0. We first examine the properties of these basic states and their dependence on B 0 and 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 stabilizing. 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 →∞.