  Using a rotating flat layer heated from below as an example, we consider
effects which lead to stabilizing an exponentially growing magnetic field in
magnetostrophic convection in transition from the kinematic dynamo to the full
non-linear dynamo. We present estimates of the energy redistribution over the
spectrum and helicity quenching by the magnetic field. We also study the
alignment of the velocity and magnetic fields. These regimes are similar to
those in planetary dynamo simulations.
