DISTRIBUTION OF MAGNETIC ENERGY IN ALPHA-OMEGA-DYNAMOS, .2. A SOLAR CONVECTION ZONE DYNAMO

An alphaOMEGA-dynamo operating in the solar convection zone is conside red as a possible explanation for the 22-year magnetic cycle of the Su n. 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 id ea that the magnetic field B remains finite only if [BB] remains finit e. To ensure the latter, a fairly large value for the turbulent diffus ion coefficient inside the convection zone is needed: beta = 10(14) cm 2 s-1. Stationarity of [BB] determines a combination of parameters, wh ich is then used in the dynamo equation for the mean field [B]. For va rious 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 rap idly fluctuating and very unstable, that it has no clear period and no well-defined large-scale field: it is a small-scale field dynamo. The finite magnetic energy method also provides the relative rates of pro duction of mean energy by the dynamo processes: differential rotation produces only 2 to 10% of the total; the rest is produced by vorticity (random field line stretching). Helicity does not produce mean energy . Turbulent diffusion transports the energy to the surface where it le aves the dynamo almost instantaneously. Identifying this outgoing ener gy flux with the flux needed to heat the solar corona leads to an esti mate of the r.m.s. field strengths at which the dynamo is operating. A t the base of the convection zone the r.m.s. field strength is about 1 40 G. This is small with respect to what is expected from active-regio n magnetic fields. The r.m.s. values does not exclude the existence of local concentrations of strong fields. Yet, the short time scale of t he small-scale convection zone dynamo indicates that this dynamo canno t be responsible for the solar cycle. This supports the idea that the solar cycle is produced by dynamo processes mainly operating in a boun dary layer at the base of the convection zone. The r.m.s. surface fiel d strength in the present model is about 9 G.