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 α 2 ‐mechanism. Proof is given that no oscillations can occur for constant α. The investigations published so far on spherical models with pure α 2 ‐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.