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Evolution of field line helicity during magnetic reconnection

Russell, A.J.B.; Yeates, A.R.; Hornig, G.; Wilmot-Smith, A.L.

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A.J.B. Russell

G. Hornig

A.L. Wilmot-Smith


We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total (relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a work-like term that is evaluated at the field line endpoints, namely, the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a well-organized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.


Russell, A., Yeates, A., Hornig, G., & Wilmot-Smith, A. (2015). Evolution of field line helicity during magnetic reconnection. Physics of Plasmas, 22(3), Article 032106.

Journal Article Type Article
Acceptance Date Feb 12, 2015
Publication Date Mar 1, 2015
Deposit Date Mar 11, 2015
Publicly Available Date Apr 21, 2015
Journal Physics of Plasmas
Print ISSN 1070-664X
Electronic ISSN 1089-7674
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 22
Issue 3
Article Number 032106
Related Public URLs


Published Journal Article (1.6 Mb)

Copyright Statement
© 2015 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Russell, A.J.B. and Yeates, A.R. and Hornig, G. and Wilmot-Smith, A.L. (2015) 'Evolution of field line helicity during magnetic reconnection.', Physics of plasmas., 22 (3). 032106 and may be found at

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