Introduction

Large-scale magnetic fields could play an important role in the dynamics of astrophysical discs. Here we report some results showing how the structure of non-axisymmetric magnetic fields is affected by differential rotation. A turbulent disc is likely to be surrounded by a gaseous corona. We shall study in particular how the field structure in the disc is affected by surrounding gas.

We are interested in the question of the origin of galactic magnetic fields. It appears that an appreciable fraction of galactic fields are bisymmetric, i.e. the field in alternate spiral arms is in opposite directions (Sofue et al. 1988). This poses a problem, since on general grounds one expects that non-axisymmetric fields should be destroyed by differential rotation on a fairly short timescale. This difficulty would be avoided if it could be shown that a non-spherically symmetric distribution of turbulent diffusivity could actually lead to dynamo generation of non-axisymmetric fields, as was suggested by Rädler (1983) and Skaley (1985). For this reason, and also in order to avoid the uncertainties involved in assuming some specific model, we have not included an α-effect in these computations. Unfortunately, we have not found any growing field modes yet, but the decaying modes are of some interest in their own right.

Method and results

The evolution of the magnetic field is governed by the induction equation. We solve for the eigenmodes in a system consisting of a high-conductivity disc embedded in a low-conductivity corona using the so-called Bullard-Gellman formalism. For details of the model and numerical methods, see Donner & Brandenburg (1989) and references therein.