Turbulent dynamo in a conducting fluid and partially ionized gas

TL;DR

This paper develops a unified theory of turbulent dynamo in conducting and partially ionized gases, revealing new growth regimes and implications for magnetic field generation in early cosmic structures.

Contribution

It introduces a comprehensive model covering both kinematic and nonlinear dynamo stages across all magnetic Prandtl numbers and ionization levels, including new growth regimes.

Findings

Extended kinematic stage with linear growth in weakly ionized media

Universal linear growth rate in nonlinear stage proportional to turbulent energy transfer

Magnetic field amplification insufficient during star formation timescales

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 Pm and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on Pm 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.