A 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, $\text{emfb}$. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of $\text{emfb}$ 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.