pumping effect to the bottom of the convection zone.]{}

The Figures 1,2 illustrate the main difference between the models with the “local” and non-local $\alpha$- effect. The radial propagation of the dynamo wave is outward for the D-type models and it is opposite for the B-type models. The downward propagation of the dynamo wave is a typical feature of the Babcock-Leighton types dynamo models (see, e.g., @dc99). [ The downward propagation of the dynamo waves drives the magnetic field from the high latitudes at the top to the low latitudes at the bottom of the convection zone where the turbulent magnetic diffusivity is small. The amplitude of the turbulent diffusion is the key parameter that determines the period of the dynamo cycle. The increase of the rotation rate amplifies the concentration of the dynamo wave to the bottom of the convection zone. This likely ]{} results to increase of the dynamo period. [Also, in the given examples of the B-type models, the maxims of the polar magnetic field corresponds to the maxims of the toroidal field at the low latitudes (cf, with the D-type models).]{}

![image](Fig3){width="90.00000%"}

The nonlinear effects due to magnetic buoyancy, magnetic helicity conservation results to saturation both 