Turbulent Dynamo in a Conducting Fluid and a Partially Ionized Gas

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 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 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.

Discovery of Kolmogorov-like magnetic energy spectrum in Tycho’s supernova remnant by two-point correlations of synchrotron intensity

“…turbulent dynamo in super-Alfvénic turbulence), magnetic field disturbances on the scales larger than l A , at which the turbulent velocity is equal to the Alfvén velocity, grow with time (e.g. Cho & Vishniac 2000a;Brandenburg & Subramanian 2005;Xu & Lazarian 2016). It indicates that the l A evolves toward a larger scale with increasing a distance from the shock front.…”

“…Goldreich & Sridhar 1995;Cho & Vishniac 2000b), a broken power-law (e.g. Lazarian & Vishniac 1999;Cho & Vishniac 2000a;Cho & Lazarian 2003;Brandenburg & Subramanian 2005;Lazarian 2006;Beresnyak et al 2009;Inoue et al 2012;Xu & Lazarian 2016, 2017) and a spectrum containing several discrete peaks (Vladimirov et al 2009). The uncertainty of the spectrum prevents us from determining the maximum energy based on the standard scenario.…”

Ambipolar diffusion in large Prandtl number turbulence

“…They used a two-fluid description, which can have the advantage that no severe (diffusive) time-step constraint occurs when the magnetic field reaches saturation. In their numerical work, Xu et al (2019) focused on verifying the linear growth during the damping stage of the dynamo near saturation, which Xu & Lazarian (2016) found in their earlier work. However, ionization and recombination reactions are here neglected.…”

Synchrotron spectra of GRB prompt emission and pulsar wind nebulae

“…Recent theoretical [7,8] and numerical [9,10,11] studies reveal a critical balance between the turbulent motions in the direction perpendicular to the local magnetic field and magnetic wave-like motions parallel to the local magnetic field in MHD turbulence. Accordingly, the turbulent dynamo with magnetic field lines stretched by turbulent motions [12] and the turbulent reconnection of stochastic magnetic fields [8] are also in dynamical balance in MHD turbulence. As a new acceleration mechanism proposed by [13], particles entrained on turbulent magnetic field lines undergo cycles of deceleration in turbulent dynamo regions and acceleration in turbulent reconnection regions, leading to a globally diffusive acceleration process, which we term as "adiabatic stochastic acceleration (ASA)".…”