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

Abstract

This article completes and extends a recent study of the Grad-Shafranov (GS) reconstruction in toroidal geometry, as applied to a 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 \textit{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. We also compare the results with the original straight-cylinder GS reconstruction and discuss our findings.