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The Grad–Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: First Applications

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Abstract

This article completes and extends a recent study of the Grad–Shafranov (GS) reconstruction in toroidal geometry, as applied to two and a half dimensional configurations in space plasmas with rotational symmetry. A further application to the benchmark study of an analytic solution to the toroidal GS equation with added noise shows deviations in the reconstructed geometry of the flux rope configuration, characterized by the orientation of the rotation axis, the major radius, and the impact parameter. On the other hand, the physical properties of the flux rope, including the axial field strength, and the toroidal and poloidal magnetic flux, agree between the numerical and exact GS solutions. We also present a real-event study of a magnetic cloud flux rope from in situ spacecraft measurements. The devised procedures for toroidal GS reconstruction are successfully executed. Various geometrical and physical parameters are obtained with associated uncertainty estimates. The overall configuration of the flux rope from the GS reconstruction is compared with the corresponding morphological reconstruction based on white-light images. The results show overall consistency, but also discrepancy in that the inclination angle of the flux rope central axis with respect to the ecliptic plane differs by about 20 – 30 degrees in the plane of the sky. The results, in terms of the magnetic flux content, are also consistent with the original straight-cylinder GS reconstruction when using exactly the same reconstruction interval in this case.

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Acknowledgements

QH acknowledges partial support from NASA grants NNX14AF41G and NNX12AH50G and NRL contract N00173-14-1-G006. All authors were supported as part of an FST team on flux ropes led by Mark Linton and funded by NASA LWS award NNH14AX61I under ROSES NNH13ZDA001N. We thank the reviewer for knowledgeable comments that helped to improve the presentation.

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Authors and Affiliations

  1. Department of Space Science and CSPAR, The University of Alabama in Huntsville, Huntsville, AL, 35805, USA

    Qiang Hu

  2. Space Science Division, Naval Research Laboratory, Washington, DC, 20375, USA

    Mark G. Linton, Brian E. Wood & Teresa Nieves-Chinchilla

  3. PSI, San Diego, CA, USA

    Pete Riley

  4. Catholic University of America, Washington, DC, USA

    Teresa Nieves-Chinchilla

Authors
  1. Qiang Hu
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  2. Mark G. Linton
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  3. Brian E. Wood
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  4. Pete Riley
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  5. Teresa Nieves-Chinchilla
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Correspondence to Qiang Hu.

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Hu, Q., Linton, M.G., Wood, B.E. et al. The Grad–Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: First Applications. Sol Phys 292, 171 (2017). https://doi.org/10.1007/s11207-017-1195-z

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