Effects of harmonic magnetic field boundary conditions in mean-field solar dynamo

Abstract: We consider effects of the harmonic magnetic field boundary conditions at the top of the dynamo domain on the dynamo stability inside the solar convection zone. These boundary conditions allow us to quantify the helical properties of the coronal magnetic field that stems from the dynamo region. In sewing the tangential component of the mean electric field we are able to take into account the effect the diffusive properties of the stellar corona on the dynamo instability. The model shows that effect of the vacuum boundary conditions can be restored if we introduce a few orders of magnitude jump of the coronal magnetic field turbulent diffusion over its typical value at the top of the dynamo domain. The parameters of this jump define the critical instability threshold of the $\alpha$ effect in the $\alpha^{2}\Omega$ dynamo.