Recent Developments in Magnetic Dynamo Theory

Two spectral regimes of magnetic field amplification in magnetohydrodynamic (MHD) flows can be distinguished by the scale on which fields are amplified relative to the primary forcing scale of the turbulence. For field amplification at or below the forcing scale, the amplification can be called a “small-scale dynamo.” For amplification at and above the forcing scale the process can be called a “large-scale dynamo.” Non - local (in wave number) effects play a key role in both the growth of the small-scale field in non-helical turbulence and the growth of large and smallscale fields in helical turbulence. Mean field dynamo (MFD) theory represents a simple semi-analytic way to get a handle on large-scale field amplification in MHD turbulence. Helicity has long been known to be important for large scale, flux generating, externally forced MFDs. The extent to which such MFDs operate “slow” or “fast” (dependent or independent on magnetic Reynolds number) has been controversial, but there has been recent progress. Simulations of α2 dynamos in a periodic box dynamo and their quenching can now be largely understood within a simplified dynamical non-linear paradigm in which the MFD growth equation is supplemented by the total magnetic helicity evolution equation. For α2 dynamos, the large-scale field growth is directly related to the large-scale magnetic helicity growth. Magnetic helicity conservation then implies that growth of the large-scale magnetic helicity induces growth of small-scale magnetic (and current) helicity of the opposite sign, which eventually suppresses the α effect driving the MFD growth. Although the α2 MFD then becomes slow in the long time limit, substantial large-scale field growth proceeds in a kinematic, “fast” phase before non-linear asymptotic quenching of the “slow” phase applies. Ultimately, the MFD emerges as a process that transfers magnetic helicity between small and large scales. How these concepts apply to more general dynamos with shear, and open boundary dynamos is a topic of ongoing research. Some unresolved issues are identified. Overall, the following summarizes the most recent progress in mean-field dynamo theory: 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.