Freely decaying turbulence in force-free electrodynamics

TL;DR

This study investigates the decay of relativistic force-free turbulence, revealing inverse cascades, energy spectra consistent with Kolmogorov law, and differences between 2D and 3D relaxations, with implications for astrophysical phenomena.

Contribution

First simulation of freely decaying relativistic force-free turbulence in 2D and 3D, highlighting inverse cascade behavior and topological effects unique to 2D.

Findings

3D turbulence exhibits Kolmogorov $5/3$ energy spectrum.

3D relaxations settle into lowest energy states conserving magnetic helicity.

2D relaxations form persistent structures with higher energy due to additional invariants.

Abstract

Freely decaying relativistic force-free turbulence is studied for the first time. We initiate the magnetic field at a short wavelength and simulate its relaxation toward equilibrium on two and three dimensional periodic domains, in both helical and non-helical settings. Force-free turbulent relaxation is found to exhibit an inverse cascade in all settings, and in 3D to have a magnetic energy spectrum consistent with the Kolmogorov $5/3$ power law. 3D relaxations also obey the Taylor hypothesis; they settle promptly into the lowest energy configuration allowed by conservation of the total magnetic helicity. But in 2D, the relaxed state is a force-free equilibrium whose energy greatly exceeds the Taylor minimum, and which contains persistent force-free current layers and isolated flux tubes. We explain this behavior in terms of additional topological invariants that exist only in two dimensions, namely the helicity enclosed within each level surface of the magnetic potential function. The speed and completeness of turbulent magnetic free energy discharge could help account for rapidly variable gamma-ray emission from the Crab Nebula, gamma-ray bursts, blazars, and radio galaxies.