SOTE: A Nonlinear Method for Magnetic Topology Reconstruction in Space Plasmas

Complex magnetic structures are ubiquitous in turbulent astrophysical plasmas. Such structures can be host to many dynamic processes, such as magnetic reconnection and energy dissipation. Thus, revealing the 3D topologies of these structures is necessary. In this study, we propose a new method to reconstruct complex magnetic topologies in quasi-steady space plasmas, by utilizing eight-point measurements of magnetic fields and particles. Such a method, based on the Second-Order Taylor Expansion (SOTE) of a magnetic field, is nonlinear; it is constrained by ∇ · B = 0 and ∇ X B = μ₀ J, where J = ne(V_i - V_e) is from particle moments. A benchmark test of this method, using the simulation data, shows that the method can give accurate reconstruction results within an area about three times the size of a spacecraft tetrahedron. By comparing to the previous First-Order Taylor Expansion (FOTE) method, this method (SOTE) gives similar results for reconstructing quasilinear structures but exhibits better accuracy in reconstructing nonlinear structures. Such a method will be useful to the multi-scale missions, such as the future European Space Agencyʼs “cross-scale” mission and Chinaʼs “self-adaptive” mission. Also, it can be applied to four-point missions, such as Cluster and the Magnetospheric Multiscale Mission. We demonstrated how to apply this method to the four-point missions. In principle, this method will be useful to study shocks, magnetic holes, dipolarization fronts, and other nonlinear structures in space plasmas