Inverse cascade from helical and nonhelical decaying columnar magnetic fields

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.