Topological constraints on magnetic field relaxation

TL;DR

This paper investigates how magnetic field topology, especially magnetic helicity, constrains magnetic relaxation, revealing that helicity is often the dominant factor but other invariants may also impose restrictions.

Contribution

The study demonstrates that magnetic helicity is generally the primary topological constraint on magnetic relaxation and explores potential additional invariants beyond helicity.

Findings

Magnetic helicity is the main determinant of magnetic field relaxation.

Evidence suggests other topological invariants may also restrict relaxation.

Magnetic helicity often provides the strongest constraint on field evolution.

Abstract

Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic helicity and test whether it is a stronger condition than the linking of field lines. Further, we search for evidence of other topological invariants, which give rise to further restrictions in the field's relaxation. We find that magnetic helicity is the sole determinant in most cases. Nevertheless, we see evidence for restrictions not captured through magnetic helicity.