Distribution of magnetic energy in αΩ-dynamos, II: A solar convection zone dynamo

An αomega-dynamo operating in the solar convection zone is considered as a possible explanation for the 22-year magnetic cycle of the Sun. The finite magnetic energy method of Van Geffen and Hoyng (1993) is used to find the stationary distribution of the mean magnetic energy BB, where <·> is an ensemble average. This method is based on the idea that the magnetic field B remains finite only if BB remains finite. To ensure the latter, a fairly large value for the turbulent diffusion coefficient inside the convection zone is needed: β = 1014cm2s−1. Stationarity of BB determines a combination of parameters, which is then used in the dynamo equation for the mean field B. For various profiles for the solar differential rotation we find that B is very quickly damped: in about 14 days, a minute fraction of the solar cycle. It follows that the dynamo field in the convection zone is rapidly fluctuating and very unstable, that it has no clear period and no well-defined large-scale field: it is a small-scale field dynamo.