Levels of stabilization of velocity and magnetic induction in the convective zone of the Sun

The induction and momentum equations of solar dynamo are simplified to a dynamic system for the convective Root-Mean-Square (rms) velocity and the rms magnetic field in the solar convection zone. The study of stable stationary points of this system gives a minor excess of the critical level of the dynamo and, accordingly, moderate magnetic field typically about 1 T (10 kG). A significantly lower rms magnetic field may be possible at some parameters of the system. The stable rms velocity is about 100 m/sec, and the characteristic magnetic times are about the half-period of solar rotation or about an average lifetime of sunspots. Relative magnetic energy is of order 5 kJ/kg that is about the kinetic energy. The unstable stationary points could be near zero magnetic fields as in periods of very lower solar activity similar to the Maunder minimum.