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A physical description of magnetic helicity evolution in the presence of reconnection lines

Published online by Cambridge University Press:  13 March 2009

Andrew N. Wright  and
Mitchell A. Berger
Andrew N. Wright
Affiliation:
Astronomy Unit, School of Mathematical Sciences, Queen Mary and Westfield College, London El 4NS, England
Mitchell A. Berger
Affiliation:
Department of Mathematics, University College London, 25 Gordon Street, London WC1E 6BT, England
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Abstract

The dissipation of relative magnetic helicity due to the presence of a resistive reconnection region is considered. We show that when the reconnection region has a vanishing cross-section, helicity is conserved, in agreement with previous studies. It is also shown that in two-dimensional systems reconnection can produce highly twisted reconnected flux tubes. Reconnection at a high magnetic Reynolds number generally conserves helicity to a good approximation. However, reconnection with a small Reynolds number can produce significant dissipation of helicity. We prove that helicity dissipation in two-dimensional configurations is associated with the retention of some of the inflowing magnetic flux by the reconnection region, vr. When the reconnection site is a simple Ohmic conductor, all of the magnetic field parallel to the reconnection line that is swept into vr is retained. (In contrast, the inflowing magnetic field perpendicular to the line is annihilated.) We are able to relate the amount of helicity dissipation to the retained flux. A physical interpretation of helicity dissipation is developed by considering the diffusion of magnetic field lines through vr. When compared with helicity-conserving reconnection, the two halves of a reconnected flux sheet appear to have slipped relative to each other parallel to the reconnection line. This provides a useful method by which the reconnected field geometry can be constructed: the incoming flux sheets are ‘cut’ where they encounter vr, allowed to slip relative to each other, and then ‘pasted’ together to form the reconnected flux sheets. This simple model yields estimates for helicity dissipation and the flux retained by vr in terms of the amount of slippage. These estimates are in agreement with those expected from the governing laws.

Type
Research Article
Information
Journal of Plasma Physics , Volume 46 , Issue 1 , August 1991 , pp. 179 - 199
Copyright
Copyright © Cambridge University Press 1991

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References

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