First Topology of Electron-Scale Magnetic Hole

Electron-scale magnetic holes (ESMHs) have been widely observed in astrophysical and space plasmas, while their generations, evolutions, and three-dimensional topologies are still unclear. Here we report two ESMH events detected by the Magnetospheric Multiscale spacecraft in the solar wind and the magnetosheath, respectively. The divergence analysis for the magnetic field indicates that ESMHs have nonlinear field topologies. Then a recently developed reconstruction method, based on the second-order Taylor expansion, is applied to such ESMHs. Eventually, the first three-dimensional topologies of ESMHs are obtained. The reconstructed results show that the ESMHs may have complex cross-section shapes (e.g., saddle-like shapes) and comparable extension lengths in the parallel and perpendicular directions to the magnetic field, which are inconsistent with the cylinder simplifications for a magnetic hole in previous studies. This work could improve our understandings for the geometric properties and thereby the generations and evolutions of ESMHs.