Non-linear   -dynamos driven by magnetic buoyancy

It is now widely accepted that the large-scale solar magnetic field is generated by some kind of non-linear av-dynamo.However, these dynamos have the disadvantage that the nonlinearities, and in particular the a -effect, are chosen in an ad hoc fashion and are only vaguely related to the underlying physical processes.Here, on the other hand, an av-dynamo with an a -effect based on magnetic buoyancy instabilities is described.This a -effect has one main advantage over previous descriptions, namely that it is derived from a numerical model of the physical processes that are thought to occur at the base of the convection zone.In this paper we investigate a one-dimensional and a two-dimensional av-dynamo in a cylindrical and a spherical shell, respectively.In both models the v-effect is described by a simple shear flow, while a is proportional to the radial gradient of the magnetic field because, simply speaking, this gradient determines when magnetic buoyancy instabilities occur and hence when the a -effect sets in.