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Relative field-line helicity in bounded domains

Yeates, A.R.; Page, M.H.

Relative field-line helicity in bounded domains Thumbnail


M.H. Page


Models for astrophysical plasmas often have magnetic field lines that leave the boundary rather than closing within the computational domain. Thus, the relative magnetic helicity is frequently used in place of the usual magnetic helicity, so as to restore gauge invariance. We show how to decompose the relative helicity into a relative field-line helicity that is an ideal-magnetohydrodynamic invariant for each individual magnetic field line, and vanishes along any field line where the original field matches the reference field. Physically, this relative field-line helicity is a magnetic flux, whose specific definition depends on the gauge of the reference vector potential on the boundary. We propose a particular ‘minimal’ gauge that depends only on the reference field and minimises this boundary contribution, so as to reveal topological information about the original magnetic field. We illustrate the effect of different gauge choices using the Low–Lou and Titov–Démoulin models of solar active regions. Our numerical code to compute appropriate vector potentials and relative field-line helicity in Cartesian domains is open source and freely available.


Yeates, A., & Page, M. (2018). Relative field-line helicity in bounded domains. Journal of Plasma Physics, 84(6), Article 775840602.

Journal Article Type Article
Acceptance Date Nov 1, 2018
Online Publication Date Nov 26, 2018
Publication Date Dec 1, 2018
Deposit Date Nov 7, 2018
Publicly Available Date May 26, 2019
Journal Journal of Plasma Physics
Print ISSN 0022-3778
Electronic ISSN 1469-7807
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 84
Issue 6
Article Number 775840602
Related Public URLs


Accepted Journal Article (976 Kb)

Copyright Statement
This article has been published in a revised form in Journal of plasma physics This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2018.

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