How to find magnetic nulls and reconstruct field topology with MMS data?

Abstract

In this study, we apply a new method—the first‐order Taylor expansion (FOTE)—to find magnetic nulls and reconstruct magnetic field topology, in order to use it with the data from the forthcoming MMS mission. We compare this method with the previously used Poincare index (PI), and find that they are generally consistent, except that the PI method can only find a null inside the spacecraft (SC) tetrahedron, while the FOTE method can find a null both inside and outside the tetrahedron and also deduce its drift velocity. In addition, the FOTE method can (1) avoid limitations of the PI method such as data resolution, instrument uncertainty (Bz offset), and SC separation; (2) identify 3‐D null types (A, B, As, and Bs) and determine whether these types can degenerate into 2‐D (X and O); (3) reconstruct the magnetic field topology. We quantitatively test the accuracy of FOTE in positioning magnetic nulls and reconstructing field topology by using the data from 3‐D kinetic simulations. The influences of SC separation (0.05~1 di) and null‐SC distance (0~1 di) on the accuracy are both considered. We find that (1) for an isolated null, the method is accurate when the SC separation is smaller than 1 di, and the null‐SC distance is smaller than 0.25~0.5 di; (2) for a null pair, the accuracy is same as in the isolated‐null situation, except at the separator line, where the field is nonlinear. We define a parameter ξ ≡ |( λ1 + λ2 + λ3 )|/|λ|max in terms of the eigenvalues (λi) of the null to quantify the quality of our method—the smaller this parameter the better the results. Comparing to the previously used parameter (η≡|∇ ⋅ B|/|∇ × B|), ξ is more relevant for null identification. Using the new method, we reconstruct the magnetic field topology around a radial‐type null and a spiral‐type null, and find that the topologies are well consistent with those predicted in theory. We therefore suggest using this method to find magnetic nulls and reconstruct field topology with four‐point measurements, particularly from Cluster and the forthcoming MMS mission. For the MMS mission, this null‐finding algorithm can be used to trigger its burst‐mode measurements.

Evidence of Magnetic Nulls in Electron Diffusion Region

“…The recent MMS mission can readily satisfy the first criterion: from September 2015 to electron agyrotropy ( P 2 xy þ P 2 xz þ P 2 Swisdak, 2016) is prominent (Webster et al, 2018), meaning that MMS was located inside the EDRs. This technique is able to accurately resolve the magnetic null position and reconstruct the magnetic topology around the spacecraft tetrahedron and is particularly useful for the spacecraft mission with small separation, like MMS (Fu et al, 2015). This technique is able to accurately resolve the magnetic null position and reconstruct the magnetic topology around the spacecraft tetrahedron and is particularly useful for the spacecraft mission with small separation, like MMS (Fu et al, 2015).…”

MMS observations of ion‐scale magnetic island in the magnetosheath turbulent plasma

“…The reported magnetic islands were observed from shock surface to the vicinity of the magnetopause, had a spatial size of a few tens of ion inertial length in the magnetosheath, and were characterized by a density depletion and magnetic field compression [Karimabadi et al, 2014, Figures 6, 9, and 13]. In spacecraft data, distinguishing between magnetic islands and flux ropes is not obvious (magnetic islands can indeed be seen as the 2-D version of 3-D flux ropes [e.g., Fu et al, 2015Fu et al, , 2016). In spacecraft data, distinguishing between magnetic islands and flux ropes is not obvious (magnetic islands can indeed be seen as the 2-D version of 3-D flux ropes [e.g., Fu et al, 2015Fu et al, , 2016).…”

Magnetic Null Points in Kinetic Simulations of Space Plasmas

“…The topological degree equals the sum of the numbers of positive and negative nulls inside a closed volume of space. Its drawbacks are the inability to detect nulls outside this closed volume of space (e.g., a tetrahedron formed by four spacecraft)and theimpossibility of recovering the exact number and positions of the nulls enclosed (Fu et al 2015).…”

“…The interest to the magnetic nulls is growing in the community. Most recently Fu et al (2015) suggested a new method of null point identification based on the first-order Taylor expansion of themagnetic field (FOTE). In distinction from the widely adopted methods (Greene 1992;Haynes & Parnell 2007), FOTE could locate nulls even outside the region of space enclosed by the spacecraft.…”