The Mathematical Institute, University of Oxford, Eprints Archive

On the shape of force–free field lines in the solar corona

Prior, C. and Berger, M. A. (2011) On the shape of force–free field lines in the solar corona. Solar Physics . (Submitted)

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Abstract

This paper studies the shape parameters of looped field lines in a linear force-free magnetic field. Loop structures with a sufficient amount of kinking are generally seen to form S or inverse S (Z) shapes in the corona (as viewed in projection). For a single field line, we can ask how much the field line is kinked (as measured by the writhe), and how much neighbouring flux twists about the line (as measured by the twist number). The magnetic helicity of a flux element surrounding the field line can be decomposed into these two quantities. We find that the twist helicity contribution dominates the writhe helicity contribution, for field lines of significant aspect ratio, even when their structure is highly kinked.

These calculations shed light on some popular assumptions of the field. First, we show that the writhe of field lines of significant aspect ratio (the apex height divided by the foot point width) can sometimes be of opposite sign to the helicity. Secondly, we demonstrate the possibility of field line structures which could be interpreted as Z-shaped, but which have a helicity value sign expected of an S-shaped structure. These results suggest that caution should be exercised in using two dimensional images to draw conclusions on the helicity value of field lines and flux tubes.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1468
Deposited By:Peter Hudston
Deposited On:22 Feb 2012 07:55
Last Modified:22 Feb 2012 07:55

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