An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations for marginally unstable systems

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations is obtained. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field is incorporated into the model. To single out the effect of the Lorentz force on the omega-effect, the effect of the Lorentz force on the alpha-effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo number N. The amplitude is proportional to N - 1, while the period is almost exactly the same as the dissipation time of the unstable mode (proportional to N).