Jhgm. Vangeffen, DISTRIBUTION OF MAGNETIC ENERGY IN ALPHA-OMEGA-DYNAMOS, .2. A SOLAR CONVECTION ZONE DYNAMO, Geophysical and astrophysical fluid dynamics, 71(1-4), 1993, pp. 223-241
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.