Synthesis of Small and Large Scale Dynamos

Using a closure model for the evolution of magnetic correlations, we uncover an interesting plausible saturated state of the small-scale fluctuation dynamo (SSD) and a novel anology between quantum mechanical tunneling and the generation of large-scale fields. Large scale fields develop via the $\alpha$-effect, but as magnetic helicity can only change on a resistive timescale, the time it takes to organize the field into large scales increases with magnetic Reynolds number. This is very similar to the results which obtain from simulations using full MHD.