On the helicity of open magnetic fields

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

Abstract

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.

Citation

Prior, C., & Yeates, A. (2014). On the helicity of open magnetic fields. Astrophysical Journal, 787(2), Article 100. https://doi.org/10.1088/0004-637x/787/2/100

• 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
• DOI: https://doi.org/10.1088/0004-637x/787/2/100
• Keywords: Magnetohydrodynamics (MHD), Methods: analytical, Methods: numerical, Sun: magnetic fields.
• Public URL: https://durham-repository.worktribe.com/output/1433846