Simple models and time scales in the dynamo effect

The dynamo effect has been studied for 50 years, starting from the simple homopolar dynamo of Bullard. Numerical calculations on simple models, such as the crossed dynamos of Rikitake, display large oscillations and brutal reversals. The present Note puts emphasis on time scales. One scale tau(1), purely electromagnetic, describes inductive decay (the frequency at which the skin depth is the size of the system), the other tau(2) is magnetohydrodynamic, controlling the exchanges of kinetic and magnetic energies. Usually tau(2) << tau(1): a clear separation of time scales makes the physics much more transparent. We show why sharp reversals must be expected, starting either from the slow or from the fast time scale. Such a comparison clarifies the issue.