Recent Developments in Magnetic Dynamo Theory
  Some recent results and open issues in magnetic dynamo theory are addressed. The distinction between small-scale and mean-field dynamo (MFD) action in forced turbulent flows is emphasized. Though useful, the MFD has been controversial. This is partly due to concerns about its need for helically forced turbulence, but mainly because simple "textbook" treatments are kinematic and linear. The non-linear backreaction of the growing magnetic field has been suspected to prematurely quench MFD action. To resolve the controversy, we must first understand those non-linear MFDs which can be numerically simulated. Recently, there has been progress on this front. For simple MFDs in closed systems, dynamical quenching models that incorporate a transfer of magnetic helicity between small and large scales agree reasonably well with fully 3-D numerical periodic box simulations. Unresolved issues such as the quenching of turbulent diffusion and the additional physics needed to apply these results to real systems are also discussed herein. The following summarizes conceptual progress in describing mean-field magnetic energy growth in the simplest MFDs:   For a closed turbulent flow, the non-linear mean-field dynamo, is first fast and kinematic, then slow and dynamic, and magnetic helicity transfer makes it so. 
Eric G. Blackman (Univ. of Rochester)