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. O. 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.