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). ow 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 B0 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 -> infinity.