On the proof of Taylor's conjecture in multiply connected domains

TL;DR

This paper extends the proof of Taylor's conjecture to more general magnetic fields in multiply connected domains, removing previous restrictions and addressing a long-standing open problem in plasma physics.

Contribution

It generalizes the proof of Taylor's conjecture to arbitrary vector potentials and removes gauge invariance restrictions in multiply connected domains.

Findings

Extended proof applies to general magnetic fields in closed domains.

Removed conditions on magnetic fields previously required.

Addresses a problem open for nearly 50 years.

Abstract

In this Letter we extend the proof, by Faraco and Lindberg, of Taylor's conjecture in multiply connected domains to cover arbitrary vector potentials and remove the need to impose conditions on the magnetic field due to gauge invariance. This extension allows us to treat general magnetic fields in closed domains that are important in laboratory plasmas and brings closure to a problem that has been open for almost 50 years.