On the oscillatory behaviour of kinematic mean-field dynamos

The paper considers the question after the circumstances in which kinematic mean-field dynamos can have oscillatory magnetic field modes. The conducting fluid body is allowed to be of almost arbitrary shape; its surroundings are vacuum. A general relation for the frequency of oscillation is derived. This relation is discussed more closely for models with pure α2-mechanism. Proof is given that no oscillations can occur for constant α. The investigations published so far on spherical models with pure α2-mechanism call up the question whether there is a chance for axisymmetric modes to be oscillatory. For both spherical models and disk models the possibility of oscillatory axisymmetric modes is demonstrated by examples. (author)