Topological Constraints on Magnetic Relaxation

TL;DR

This paper explores how topological invariants, specifically the topological degree of the field line mapping, influence magnetic relaxation, explaining deviations from the Taylor state in certain simulations.

Contribution

It introduces the topological degree of the field line mapping as a new invariant constraining magnetic relaxation beyond helicity.

Findings

The topological degree constrains relaxation in flux tubes.

Simulations show some fields do not reach the Taylor state.

Topological invariants explain deviations from classical relaxation theory.

Abstract

The final state of turbulent magnetic relaxation in a reversed field pinch is well explained by Taylor's hypothesis. However, recent resistive-magnetohydrodynamic simulations of the relaxation of braided solar coronal loops have led to relaxed fields far from the Taylor state, despite the conservation of helicity. We point out the existence of an additional topological invariant in any flux tube with non-zero field: the topological degree of the field line mapping. We conjecture that this constrains the relaxation, explaining why only one of three example simulations reaches the Taylor state.