Grad-Shafranov Reconstruction of Magnetic Flux Ropes in the Near-Earth Space

Electric currents permeate space plasmas and often have a significant component along the magnetic field to form magnetic flux ropes. A larger spatial perspective of these structures than from the direct observation along the satellite path is crucial in visualizing their role in plasma dynamics. For magnetic flux ropes that are approximately two-dimensional equilibrium structures on a certain plane, Grad-Shafranov reconstruction technique, developed by Bengt Sonnerup and his colleagues (see Sonnerup et al. in J. Geophys. Res. 111:A09204, 2006), can be used to reveal two-dimensional maps of associated plasma and field parameters. This review gives a brief account of the technique and its application to magnetic flux ropes near the Earth’s magnetopause, in the solar wind, and in the magnetotail. From this brief survey, the ranges of the total field-aligned current and the total magnetic flux content for these magnetic flux ropes are assessed. The total field-aligned current is found to range from ∼0.14 to ∼9.7×10⁴ MA, a range of nearly six orders of magnitude. The total magnetic flux content is found to range from ∼0.25 to ∼2.3×10⁶ MWb, a range of nearly seven orders of magnitude. To the best of our knowledge, this review reports the largest range of both the total field-aligned current and the total magnetic flux content for magnetic flux ropes in space plasmas.