The influence of geometry and topology on axisymmetric mean-field dynamos

We study the changes in the dynamical behaviour of axisymmetric spherical m ean-field dynamo models produced by changes in their geometry and topology, by considering a two parameter family of models, ranging from a full spher e to spherical shell, tents and disc-like configurations, within a unified framework. We find that the two parameter space of the family of models con sidered here separates into at least three different regions with distinct characteristics for the onset of dynamo action. In two of these regions, th e most easily excited fields are oscillatory, in one case with dipolar symm etry, and in the other with quadrupolar, whereas in the third region the mo st easily excited field is steady and quadrupolar. In the nonlinear regime, we find that topological changes can alter significantly the dynamical beh aviour, whilst modest changes in geometry can produce qualitative changes, particularly for thin disc-like configurations. This is of potential import ance, since the exact shapes of astrophysical bodies, especially accretion discs and galaxies, are usually not precisely known.