Small-Scale Turbulent Dynamo

Part of the Springer Theses book series (Springer Theses)


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]).


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.University of Wisconsin-MadisonMadisonUSA

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