Small-Scale Turbulent Dynamo

Abstract

By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of turbulent dynamo and study the dynamo process for a full range of magnetic Prandtl number \(P_m\) and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on \(P_m\) in a conducting fluid and \(\mathcal {R}\) (a function of ionization fraction) in partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regime of dynamo characterized by linear-in-time growth of magnetic field strength, and the resulting magnetic energy is much higher than the kinetic energy carried by viscous-scale eddies. Unlike the kinematic stage, the subsequent nonlinear stage is unaffected by microscopic diffusion processes and has a universal linear-in-time growth of magnetic energy with the growth rate as a constant fraction 3 / 38 of the turbulent energy transfer rate, showing a good agreement with earlier numerical results. Applying the analysis to the first stars and galaxies, we find that the kinematic stage is able to generate a field strength only an order of magnitude smaller than the final saturation value. But the generation of large-scale magnetic fields can only be accounted for by the relatively inefficient nonlinear stage and requires longer time than the free-fall time. It suggests that magnetic fields may not have played a dynamically important role during the formation of the first stars. This chapter is based on Xu and Lazarian (ApJ 833:215, 2016, [1]), Xu and Lazarian (New J Phys 19:065005, 2017, [2]).