New dynamical mean-field dynamo theory and closure approach

We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, (epsilon) over bar. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of (epsilon) over bar is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.