A new philosophy is presented for the excitation of non-axisymmetric m
agnetic fields in spherical dynamo models. For the first time the dyna
mo operation is considered with an alpha-tensor whose components altog
ether result from one and the same turbulence model in a density-strat
ified plasma. The related a-tensor is highly anisotropic, its azimutha
l component dominates all the other components. As a consequence, in a
ll models without differential rotation the preferred magnetic modes a
re non-axisymmetric - independently of their rotation rate. The often
discussed traditional alpha2-dynamo with axisymmetric large-scale fiel
d geometry seems not to exist. Differential rotation, however, works i
n favour of the axisymmetric modes. For slow and rapid basic rotation
the critical value of the differential rotation, for which the transit
ion to axisymmetry occurs, is determined. It proves to be so large tha
t the question appears why the Sun's magnetic field is basically axisy
mmetric.