Method of Relative Magnetic Helicity Computation II: Boundary Conditions for the Vector Potentials

TL;DR

This paper introduces a boundary condition scheme for computing relative magnetic helicity in finite volumes, removing previous flux balance restrictions, and validates it using a theoretical model.

Contribution

It presents a new boundary condition scheme for vector potentials that enables more flexible magnetic helicity calculations in finite volumes.

Findings

Scheme successfully removes flux balance restriction.

Validated scheme with theoretical model.

Improves accuracy of magnetic helicity computation.

Abstract

We have proposed a method to calculate the relative magnetic helicity in a finite volume as given the magnetic field in the former paper (Yang et al. {\it Solar Physics}, {\bf 283}, 369, 2013). This method requires that the magnetic flux to be balanced on all the side boundaries of the considered volume. In this paper, we propose a scheme to obtain the vector potentials at the boundaries to remove the above restriction. We also used a theoretical model (Low and Lou, {\it Astrophys. J.} {\bf 352}, 343, 1990) to test our scheme.