of the solar convection zone of [@stix:02]. In particular, it uses the mixing length $\ell=\alpha_{{\rm MLT}}\left|\Lambda^{(p)}\right|^{-1}$, where $\Lambda{}^{(p)}={\nabla}\log\overline{p}$, is the reverse scale of the thermodynamic pressure and $\alpha_{{\rm MLT}}=2$.]{} The profile of the turbulent diffusivity is given in form $\eta_{T}=C_{\eta}{\displaystyle \frac{u'^{2}\tau_{c}}{3f_{ov}\left(r\right)}}$, where $f_{ov}(r)=1+\exp\left(50\left(r_{ov}-r\right)\right)$, $r_{ov}=0.725R_{\odot}$ controls quenching of the turbulent effects near the bottom of the convection zone. The parameter $C_{\eta}$, (with the range $0<C_{\eta}<1$) is a free parameter to control the efficiency of the mixing of the large-scale magnetic field by the turbulence. It is used to adjust the period of the dynamo cycle. We use the same model of the convection zone for all the rotational periods.

At the bottom of the convection zone we apply the superconductor boundary condition both in the case of the D- and B-types dynamos. At the top of the convection zone the poloidal field is smoothly matched to the external potential field and the toroidal field is allowed to penetrated to the surface: $$\begin{aligned}
\left(\delta+\frac{B}{B_{esq}}\right)\frac{\eta_{T}}{r_{e}}B+\left(1-\delta\right)\mathcal{E}_{\theta} & = & 0,\label{eq:tor-vac}\end{aligned}$$ where $\delta=0.99$, $B_{esq}=10$G. For the $B\gg B_{esq}$ the condition (\[eq:tor-vac\]) is close to the vacuum boundary conditions . The given boundary conditions provide the non-zero Poynting magnetic energy flux $S=-{\displaystyle \frac{1}{4\pi}\left.\mathcal{E}_{\theta}B\right|_{r_{e}}}$ through the top. 