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    On the Shape of Force-Free Field Lines in the Solar Corona

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    Type
    Article
    Authors
    Prior, C.
    Berger, M. A.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2012-02-02
    Online Publication Date
    2012-02-02
    Print Publication Date
    2012-06
    Permanent link to this record
    http://hdl.handle.net/10754/599068
    
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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 footpoint 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. © 2012 Springer Science+Business Media B.V.
    Citation
    Prior C, Berger MA (2012) On the Shape of Force-Free Field Lines in the Solar Corona. Sol Phys 278: 323–345. Available: http://dx.doi.org/10.1007/s11207-012-9938-3.
    Sponsors
    C.P. wishes to thanks John Brooke for his comments and observations on the manuscript. C.P. was supported by the EPSRC and Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). M.B. was partially supported by an STFC grant and a Leverhulme grant.
    Publisher
    Springer Nature
    Journal
    Solar Physics
    DOI
    10.1007/s11207-012-9938-3
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11207-012-9938-3
    Scopus Count
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    Publications Acknowledging KAUST Support

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