Magnetic field decay of three interlocked flux rings with zero linking number

TL;DR

This paper investigates how the decay rate of magnetic flux rings depends on their linking number and magnetic helicity, showing that the decay behavior is primarily influenced by these topological invariants rather than the complexity of the field.

Contribution

It demonstrates that the decay rate of interlocked magnetic flux rings is governed by their linking number and magnetic helicity, challenging the need for higher-order invariants.

Findings

Decay rate varies with the relative orientation of flux rings.

Late-time decay can be fast or slow depending on linking number.

Magnetic helicity is the key invariant influencing decay behavior.

Abstract

The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.