Inverse cascade from helical and nonhelical decaying columnar magnetic fields

TL;DR

This study uses simulations to demonstrate that turbulent decay of magnetic fields, whether initially helical or nonhelical, leads to isotropization and reveals the role of magnetic helicity fluctuations governed by the Hosking integral, with implications for cosmological magnetic fields.

Contribution

The paper shows that anisotropic magnetic fields spontaneously become isotropic during decay and introduces the Hosking integral as a key quantity for nonhelical magnetic helicity fluctuations.

Findings

Magnetic fields undergo spontaneous isotropization during decay.

Nonhelical magnetic fields develop helicity fluctuations quantified by the Hosking integral.

The decay time to Alfvén time ratio is around 50, reaching up to 100 at intermediate times.

Abstract

Powerful lasers may in future produce magnetic fields that would allow us to study turbulent magnetohydrodynamic inverse cascade behavior. This has so far only been seen in numerical simulations. In the laboratory, however, the produced fields may be highly anisotropic. Here, we present corresponding simulations to show that, during the turbulent decay, such a magnetic field undergoes spontaneous isotropization. As a consequence, we find the decay dynamics to be similar to that in isotropic turbulence. We also find that an initially pointwise nonhelical magnetic field is unstable and develops magnetic helicity fluctuations that can be quantified by the Hosking integral. It is a conserved quantity that characterizes magnetic helicity fluctuations and governs the turbulent decay when the mean magnetic helicity vanishes. As in earlier work, the ratio of the magnetic decay time to the Alfv\'en time is found to be around $50$ in the helical and nonhelical cases. At intermediate times, the ratio can even reach a hundred. This ratio determines the endpoints of cosmological magnetic field evolution.