Theory of the solar cycle

The properties of kinematic αω-dynamos are briefly reviewed. The mean field concept, including turbulent diffusivity, is defended against recent criticism. It is pointed out that although the Maunder minimum cannot be explained by kinematic dynamo theory alone, this does not invalidate dynamo theory in general. A special discussion is devoted to attempts to evaluate the coefficients of the mean field induction equation in the case of very large conductivity. The field then behaves intermittent, in the form of locally concentrated flux tubes, and the α-effect and the turbulent diffusivity may be determined by assymptotic techniques or with the help of an exact solution of the non-dissipative induction equation in Lagrangian co-ordinated. Magnetic cycles of main sequence stars other than the Sun are briefly discussed. Besides rotation, the depth of the convection zone is probably the most influencial parameter for period and amplitude of the stellar cycle. Observational programmes to advance the theory of the solar cycle must include the solar magnetic and velocity fields, over the entire Sun and on all scales. In particular the angular velocity as a function of depth should be studied further with the help of the p-eigenmodes. The knowledge of luminosity, radius and (or) temperature variations with the solar cycle would also stimulate the theoretical approach. (orig.)