Fluctuation Dynamo and Turbulent Induction at Small Prandtl Number

TL;DR

This paper investigates the fluctuation dynamo mechanism at zero Prandtl number using the Kazantsev-Kraichnan model, revealing the importance of stochastic flux-freezing, anti-dynamo effects, and magnetic induction in turbulent flows.

Contribution

It introduces a Lagrangian perspective on the fluctuation dynamo at small Prandtl numbers, highlighting the role of stochastic flux-freezing and magnetic induction in turbulent magnetic field growth.

Findings

Flux-freezing holds only stochastically in turbulent flows.

Initial separation of field lines influences dynamo behavior.

Magnetic induction and fluctuation dynamo produce similar growth rates.

Abstract

We study the Lagrangian mechanism of the fluctuation dynamo at zero Prandtl number and infinite magnetic Reynolds number, in the Kazantsev-Kraichnan model of white-noise advection. With a rough velocity field corresponding to a turbulent inertial-range, flux-freezing holds only in a stochastic sense. We show that field-lines arriving to the same point which were initially separated by many resistive lengths are important to the dynamo. Magnetic vectors of the seed field that point parallel to the initial separation vector arrive anti-correlated and produce an "anti-dynamo" effect. We also study the problem of "magnetic induction" of a spatially uniform seed field. We find no essential distinction between this process and fluctuation dynamo, both producing the same growth-rates and small-scale magnetic correlations. In the regime of very rough velocity fields where fluctuation dynamo fails, we obtain the induced magnetic energy spectra. We use these results to evaluate theories proposed for magnetic spectra in laboratory experiments of turbulent induction