Cylindrical anisotropic alpha² dynamos

We explore the influence of geometrical variations on the structure and the time-dependence of the magnetic field that is induced by kinematic alpha² dynamos in a finite cylinder. The dynamo action is due to an anisotropic alpha tensor which can be derived from an underlying columnar flow. The investigated geometry variations concern, in particular, the aspect ratio of height to radius of the cylinder, and the thickness of the annular space to which the columnar flow is restricted. Motivated by the quest for laboratory dynamos which exhibit Earth-like features, we start with modifications of the Karlsruhe dynamo experiment. Its dynamo action is reasonably described by an alpha² mechanism with anisotropic alpha tensor. We find a critical aspect ratio below which the dominant magnetic field changes from an equatorial dipole to an axial dipole. Similar results are found for alpha² dynamos working in an annular space when a radial dependence of alpha is assumed. Finally, we study the effect of varying aspect ratios of dynamos with an alpha tensor depending both on r and z. In this case only dominant equatorial fields are found and most of the solutions are oscillatory, contrary to all previous cases where the resulting
fields are steady.