The Grad-Shafranov reconstruction in twenty years: 1996–2016

Abstract

We review and summarize the applications of the Grad-Shafranov (GS) reconstruction technique to space plasma structures in the Earth’s magnetosphere and in the interplanetary space. We organize our presentations following the branches of the “academic family tree” rooted on Prof. Bengt U. Ö. Sonnerup, the inventor of the GS method. Special attentions are paid to validations of the GS reconstruction results via (1) the direct validation by co-spatial in-situ measurements among multiple spacecraft, and (2) indirect validation by implications and interpretations of the physical connection between the structures reconstructed and other related processes. For the latter, the inter-comparison and interconnection between the large-scale magnetic flux ropes (i.e., Magnetic Clouds) in the solar wind and their solar source properties are presented. In addition, we also summarize various GS-type (or -like) reconstruction and an extension of the GS technique to toroidal geometry. In particular, we point to a possible advancement with added complexity of “helical symmetry” and mixed helicity, in the hope of stimulating interest in future development. We close by offering some thoughts on appreciating the scientific merit of GS reconstruction in general.

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Acknowledgements

We acknowledge the invitation by Drs. Feng XueShang and Wan WeiXing for this review. The author’s first scientific publication appeared in this journal nearly twenty years ago. As a point of reflection on the author’s own professional career, I am grateful for the mentorship, friendship, and companionship, offered by numerous mentors, colleagues, and families. In particular, the towering figures of Prof. Wei FengSi, Prof. Bengt Sonnerup, Drs. Charles Smith and Norman Ness, Prof. Gary Zank, and Prof. Wu Shi-Tsan, have provided invaluable guidance along the way during my past years as a graduate student, a postdoc, and a professional researcher, up to the present time. I am most indebted to Prof. Sonnerup and Prof. Hau Lin-Ni who laid down the foundation for and led me down the path of the GS reconstruction. I thank numerous colleagues and co-authors in shaping and enriching my professional development and growth. In particular, I benefited tremendously from the collaboration with Prof. Qiu Jiong, which has spanned one decade, and two sub-disciplines in space physics, i.e., solar physics and interplanetary physics. In addition, I have benefited greatly from collaborations with many other Chinese colleagues who have been so prolific that all their works could not possibly be included. I have been inspired by their work ethics and formidable spirit. I am particularly grateful to Prof. Chen Yao and colleagues at Shandong University, Weihai, for their hospitality and support. I wish to thank the reviewers for their enthusiastic review and knowledgeable comments that help improve the manuscript. Upon the completion of this manuscript, we were all saddened by the sudden passing of Dr. Shi-Tsan Wu, with whom the author has been working closely in the past decade or so, till the very last day. Together with many colleagues in China and around the world, we mourn the loss of such an inspirational figure in the field of solar-terrestrial physics. We will miss ST’s wisdom, his mentorship, and his passion for science. The best way to carry on ST’s legacy is to continue to encourage and inspire future generations, as ST always did. I hope this piece of writing will contribute to that noble cause. The author’s work summarized herein has been supported by National Aeronautics and Space Administration (NASA) and National Science Foundation (NSF) (Grants Nos. AGS-1062050, NNG04GF47G, NNG06GD41G, NNX12AF97G, NNX12AH50G, NNH13ZDA001N, and NNX14AF41G).

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Hu, Q. The Grad-Shafranov reconstruction in twenty years: 1996–2016. Sci. China Earth Sci. 60, 1466–1494 (2017). https://doi.org/10.1007/s11430-017-9067-2

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Keywords

  • Grad-Shafranov equation
  • Magnetohydrodynamics
  • Magnetic clouds
  • Magnetic flux ropes
  • Magnetopause
  • Current sheets
  • Flux transfer events
  • Plasmoids
  • Solar flare
  • Coronal mass ejections