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Abstract
We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finiteB 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 worklike 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 wellorganized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.
Original language  English 

Article number  032106 
Number of pages  10 
Journal  Physics of Plasmas 
Volume  22 
Issue number  3 
DOIs  
Publication status  Published  Mar 2015 
ASJC Scopus subject areas
 Condensed Matter Physics
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 1 Finished

Complex Magnetic Fields: An Enigma of Solar Plasmas (joint with Durham University)
Hornig, G., Pontin, D. & WilmotSmith, A.
Science and Technology Facilities Council
1/04/13 → 30/06/16
Project: Research