The flux ejection dynamo with small diffusivity

Abstract

The flux ejection dynamo in an infinitely broad convective layer of finite depth is treated in the limit of large electrical conductivity. The upper surface of the convective layer is open to empty space while the lower surface is closed to the passage of fluid and field. An idealized convective overturning is employed, permitting an exact description of the symmetry and distribution of the magnetic field carried with the fluid. Escape of the reverse field through the free surface restores the initial vertical distribution of mean field and adds a thin sheet of flux in the initial direction across the bottom of the convective layer. The total flux in the mean horizontal field grows linearly with the number of convective cycles. We discuss the boundary conditions to be applied to an astronomical body with the flux ejection dynamo operating at its surface. It is pointed out that if there were a flux ejection dynamo operating in the Sun, the implications of the magnetic bipolar regions emerging through the surface would be the opposite of the usual.