Spherical dynamos with anisotropic α-effect

Abstract

The mean field induction equation of Steenbeck, Krause and Rädler (1966) is solved for anisotropic α _ik -tensors of varying anisotropy. The attention is restricted to α²-dynamos in spheres with steady axisymmetric magnetic fields. The ratio of the electrical conductivity outside and inside the sphere is varied, but in all cases it is found that a steady dynamo does not exist when the anisotropy of the α _ik -tensor exceeds a critical value. Such a critical value does not exist in the exceptional case of the Fermi boundary condition. The results emphasize the important effect of boundaries on the existence of solutions of the dynamo problem.