Is the geodynamo process intrinsically unstable?

Recent palaeomagnetic studies suggest that excursions of the geomagnetic ¢eld, during which the intensity drops suddenly by a factor of 5^10 and the local direction changes dramatically, are more common than previously expected. The `normal ' state of the geomagnetic ¢eld, dominated by an axial dipole, seems to be interrupted every 30^100 kyr; it may not therefore be as stable as we thought. We have investigated a possible mechanism for the instability of the geodynamo by calculating the critical Rayleigh number (Rc) for the onset of convection in a rotating spherical shell permeated by an imposed magnetic ¢eld with both toroidal and poloidal components. We have found Rc to be a very sensitive function of the poloidal ¢eld at the very small Ekman number pertaining to the core. The magnetic Reynolds number, and therefore the dynamo action, is equally sensitive to the applied ¢eld because of its dependence on the di¡erence between the Rayleigh number and its critical value. This explains why numerical dynamo simulations at small Ekman number fail when similar magneto-convection calculations succeed: the £uctuating magnetic ¢eld of the dynamo leads to rapid swings in convection strength that cannot be resolved numerically. The geo