Traces of large-scale dynamo action in the kinematic stage

TL;DR

This study uses DNS to analyze the growth and characteristics of large-scale magnetic fields in turbulent helical dynamos during the kinematic stage, revealing how their strength varies with magnetic Reynolds number and helicity.

Contribution

It demonstrates that large-scale dynamo signatures persist in the kinematic regime and clarifies how their strength depends on magnetic Reynolds number and helicity, with improved scale separation.

Findings

Magnetic energy spectrum remains shape-invariant during growth.

Large-scale magnetic field strength decreases with increasing Re_M.

Small-scale dynamo can be excited at Prandtl number 0.1 and moderate Re_M.

Abstract

Using direct numerical simulations (DNS) we verify that in the kinematic regime, a turbulent helical dynamo grows in such a way that the magnetic energy spectrum remains to high precision shape-invariant, i.e., at each wavenumber $k$ the spectrum grows with the same growth rate. Signatures of large-scale dynamo action can be identified through the excess of magnetic energy at small $k$, of one of the two oppositely polarized constituents. Also a suitably defined planar average of the magnetic field can be chosen such that its rms value isolates the strength of the mean field. However, these different means of analysis suggest that the strength of the large-scale field diminishes with increasing magnetic Reynolds number ${\rm Re}_{\rm M}$ like ${\rm Re}_{\rm M}^{-1/2}$ for intermediate values and like ${\rm Re}_{\rm M}^{-3/4}$ for larger ones. Both an analysis from the Kazantsev model including helicity and the DNS show that this arises due to the magnetic energy spectrum still peaking at resistive scales, even when helicity is present. As expected, the amplitude of the large-scale field increases with increasing fractional helicity, enabling us to determine the onset of large scale dynamo action and distinguishing it from that of the small-scale dynamo. Our DNS show that, contrary to earlier results for smaller scale separation (only 1.5 instead of now 4), the small-scale dynamo can still be excited at magnetic Prandtl numbers of 0.1 and only moderate values of the magnetic Reynolds numbers ($\sim 160$).