The force‐free configuration of flux ropes in geomagnetotail: Cluster observations

Abstract Unambiguous knowledge of magnetic field structure and the electric current distribution is critical for understanding the origin, evolution, and related dynamic properties of magnetic flux ropes (MFRs). In this paper, a survey of 13 MFRs in the Earth's magnetotail are conducted by Cluster multipoint analysis, so that their force‐free feature, i.e., the kind of magnetic field structure satisfying J × B = 0, can be probed directly. It is showed that the selected flux ropes with the bipolar signature of the south‐north magnetic field component generally lie near the equatorial plane, as expected, and that the magnetic field gradient is rather weak near the axis center, where the curvature radius is large. The current density (up to several tens of nA/m 2 ) reaches their maximum values as the center is approached. It is found that the stronger the current density, the smaller the angles between the magnetic field and current in MFRs. The direct observations show that only quasi force‐free structure is observed, and it tends to appear in the low plasma beta regime (in agreement with the theoretic results). The quasi force‐free region is generally found to be embedded in the central portion of the MFRs, where the current is approximately field aligned and proportional to the strength of core field. It is shown that ~60% of surveyed MFRs can be globally approximated as force free. The force‐free factor α is found to be nonconstantly varied through the quasi force‐free MFR, suggesting that the force‐free structure is nonlinear.