Based on estimates of the characteristic values of the terms in the hydromagnetic dynamo equations, it is shown that for both planetary-type dynamo and solar dynamo, the stabilizing nonlinearity inversely proportional to the electric current value is significant. Using the average value obtained for it, the simplest hydromagnetic model for magnetic energy is constructed, consisting of one non-homogeneous linear ordinary differential equation.
Starchenko et al. (Wed,) studied this question.