Helicity invariants of force-free field for a rectangular box

TL;DR

This paper presents an algorithm to compute three gauge-invariant magnetic helicities within a rectangular box, tested on a known force-free model, enhancing the accuracy of magnetic field analysis in confined geometries.

Contribution

The paper introduces a novel algorithm for calculating gauge-invariant helicities in a rectangular box, applicable to force-free magnetic fields.

Findings

Algorithm successfully computes three types of helicities.

Tested on Low and Lou's force-free model with positive results.

Provides a reliable method for magnetic helicity analysis.

Abstract

An algorithm for calculating three gauge-invariant helicities (self-, mutual- and Berger relative helicity) for a magnetic field specified in a rectangular box is described. The algorithm is tested on a well-known force-free model (Low and Lou, 1990) presented in vector-potential form.