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Title: On the helicity of open magnetic fields

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.

Authors:
Publication Date:
OSTI Identifier:
22356799
Resource Type:
Journal Article
Journal Name:
Astrophysical Journal
Additional Journal Information:
Journal Volume: 787; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CONSTRUCTION; HELICITY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PERIODICITY; SUN

Citation Formats

Prior, C., and Yeates, A. R., E-mail: anthony.yeates@durham.ac.uk. On the helicity of open magnetic fields. United States: N. p., 2014. Web. doi:10.1088/0004-637X/787/2/100.
Prior, C., & Yeates, A. R., E-mail: anthony.yeates@durham.ac.uk. On the helicity of open magnetic fields. United States. https://doi.org/10.1088/0004-637X/787/2/100
Prior, C., and Yeates, A. R., E-mail: anthony.yeates@durham.ac.uk. 2014. "On the helicity of open magnetic fields". United States. https://doi.org/10.1088/0004-637X/787/2/100.
@article{osti_22356799,
title = {On the helicity of open magnetic fields},
author = {Prior, C. and Yeates, A. R., E-mail: anthony.yeates@durham.ac.uk},
abstractNote = {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.},
doi = {10.1088/0004-637X/787/2/100},
url = {https://www.osti.gov/biblio/22356799}, journal = {Astrophysical Journal},
issn = {0004-637X},
number = 2,
volume = 787,
place = {United States},
year = {Sun Jun 01 00:00:00 EDT 2014},
month = {Sun Jun 01 00:00:00 EDT 2014}
}