Braided magnetic fields: equilibria, relaxation and heating

TL;DR

This paper investigates the existence and properties of braided magnetic field equilibria, their role in current sheet formation, and the turbulent relaxation process relevant to solar coronal heating, using mathematical and computational models.

Contribution

It demonstrates the existence of braided force-free equilibria with current sheets in non-periodic domains and explores their relaxation dynamics, advancing understanding of magnetic braiding in plasma physics.

Findings

Braided equilibria exist with current sheets whose thickness scales with braid complexity.

Exact equilibria are absent in periodic domains, but approximate ones contain thin current sheets.

Resistivity triggers reconnection and turbulent relaxation, influencing final magnetic states.

Abstract

We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling, in the context of testable predictions for the laboratory and their significance for solar coronal heating. We investigate the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity - as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We finish by discussing the properties of the turbulent relaxation and the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor's hypothesis.