Extending the FOTE Method to Three-dimensional Plasma Flow Fields

In this study, we examine whether the First-Order Taylor Expansion (FOTE) method can be applied to steady-state plasma flow fields in space. We particularly examine whether this method (termed FOTE-V) can be used to identify the flow critical points (including both stagnation point and vortex center) and reconstruct the flow patterns around these points. Quantitatively, we test the accuracy of this method using 3D kinetic simulation data, and find the FOTE-V method can give accurate reconstruction results within an area about 2 times the size of the spacecraft tetrahedron, particularly when there are no clear nonlinear flow structures in the simulation box. With simulation data, we also reveal the ability of the FOTE-V method on reconstructing 3D flow field topology of both radial-type null and spiral-type nulls. We further test the accuracy of this method using measurements from NASA's Magnetospheric Multi-scale (MMS) mission. In a current sheet crossing event, the FOTE-V method successfully identifies the spiral-type nulls in the reconnection exhaust region. In an EDR crossing event, the FOTE-V method detects the stagnation point near the reconnection center. We find these 3D flow structures are quasi-linear at the MMS separation scale. Utilizing the continuity equation of the steady flow, we define a parameter, α = ∇·(nV)/∇ × (nV), to quantify the error of this method - the smaller this parameter the better the results. This study demonstrates that the plasma flows at small scale are indeed linear, and thus the FOTE-V method can be applied to such flow fields. In particular, this method will be useful to study stagnation points and electron vortices in space plasmas.