DISTRIBUTION OF MAGNETIC ENERGY IN ALPHA-OMEGA-DYNAMOS, .1. THE METHOD

In this paper a method for solving the equation for the mean magnetic energy [BB] of a solar type dynamo with an axisymmetric convection zon e geometry is developed and the main features of the method are descri bed. This method is referred to as the finite magnetic energy method s ince it is based on the idea that the real magnetic field B of the dyn amo remains finite only if [BB] remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, sm all-scale as well as large-scale fields. The method yields an energy b alance for the mean energy density epsilon = [B2]/8pi of the dynamo, f rom which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the sur face with the observed values. We neglect resistive effects and presen t arguments indicating that this is a fair assumption for the solar co nvection zone. The model considerations and examples presented indicat e that (1) the energy loss at the solar surface is almost instantaneou s; (2) the convection in the convection zone takes place in the form o f giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 10(14) cm2 s-1, which is an order of magnitude larger than usually ad opted in solar mean field models.