Skip to main content

Research Repository

Advanced Search

On the helicity of open magnetic fields

Prior, C.B.; Yeates, A.R.

On the helicity of open magnetic fields Thumbnail



We reconsider the topological interpretation of magnetic helicity for magnetic fields in open domains, and relate this to the relative helicity. Specifically, our domains stretch between two parallel planes, and each of these ends may be magnetically open. It is demonstrated that, while the magnetic helicity is gauge-dependent, its value in any gauge may be physically interpreted as the average winding number among all pairs of field lines with respect to some orthonormal frame field. In fact, the choice of gauge is equivalent to the choice of reference field in the relative helicity, meaning that the magnetic helicity is no less physically meaningful. We prove that a particular gauge always measures the winding with respect to a fixed frame, and propose that this is normally the best choice. For periodic fields, this choice is equivalent to measuring relative helicity with respect to a potential reference field. However, for aperiodic fields, we show that the potential field can be twisted. We prove by construction that there always exists a possible untwisted reference field.


Prior, C., & Yeates, A. (2014). On the helicity of open magnetic fields. Astrophysical Journal, 787(2), Article 100.

Journal Article Type Article
Acceptance Date Apr 10, 2014
Online Publication Date May 7, 2014
Publication Date Jun 1, 2014
Deposit Date May 12, 2014
Publicly Available Date May 13, 2014
Journal Astrophysical Journal
Print ISSN 0004-637X
Electronic ISSN 1538-4357
Publisher American Astronomical Society
Peer Reviewed Peer Reviewed
Volume 787
Issue 2
Article Number 100
Keywords Magnetohydrodynamics (MHD), Methods: analytical, Methods: numerical, Sun: magnetic fields.


Published Journal Article (1.8 Mb)

Copyright Statement
© 2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

You might also like

Downloadable Citations