Understanding magnetic field growth in astrophysical objects is a persistent challenge. In stars and galaxies, turbulent flows with net kinetic helicity are believed to be responsible for driving large-scale magnetic fields. However, numerical simulations have demonstrated that such helical dynamos in closed volumes saturate at lower magnetic field strengths when increasing the magnetic Reynolds number $\text{Rm}$. This would imply that helical large-scale dynamos cannot be efficient in astrophysical bodies without the help of helicity outflows such as stellar winds. But do these implications actually apply for very large $\text{Rm}$? Here we tackle the long-standing question of how much helical large-scale dynamo growth occurs independent of $\text{Rm}$ in a closed volume. We analyze data from numerical simulations with a new method that tracks resistive versus nonresistive drivers of helical field growth. We identify a presaturation regime when the large-scale field grows at a rate independent of $\text{Rm}$, but to an $\text{Rm}$-dependent magnitude. The latter $\text{Rm}$ dependence is due to a dominant resistive contribution, but whose fractional contribution to the large-scale magnetic energy decreases with increasing $\text{Rm}$. We argue that the resistive contribution would become negligible at large $\text{Rm}$ and an $\text{Rm}$-independent dynamical contribution would dominate if the current helicity spectrum in the inertial range is steeper than $k^0$. As such helicity spectra are plausible, this renews optimism for the relevance of closed dynamos. Our work pinpoints how modest $\text{Rm}$ simulations can cause misapprehension of the $\text{Rm}\to \infty$ behavior.

• Received 12 February 2023
• Revised 18 July 2023
• Accepted 21 December 2023

DOI:https://doi.org/10.1103/PhysRevE.109.015206

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Published by the American Physical Society