Nonlinear dynamo in a simplified statistical model

A fully self-consistent nonlinear dynamo is studied in the limit of the low kinetic Reynolds number by adopting a simplified statistical model. Governing equations for the evolution of a mean magnetic field and correlation functions of fluctuating magnetic fields are derived for arbitrary values of the magnetic Reynolds number. Within this model, the alpha-effect is shown to be modified by the back reaction of the Lorentz force whilst the turbulent diffusivity remains the same as in the kinematic case. We also show that the nonlinear saturation of small-scale fields can come about via the suppression of the stretching property of the flow.