First-order Taylor Expansion Method Research Articles

The Effect of Current on Magnetic Null Topology during Turbulent Reconnection

Abstract Using data from the Cluster mission and the First-Order Taylor Expansion method, we investigate the spiral magnetic nulls nested in the diffusion region of turbulent reconnection in the magnetotail. We particularly focus on the relation between the magnetic null topologies and currents, which can be decomposed into a component perpendicular to spine (j ⊥) and a component parallel to spine (j ∥). We find that (1) the currents surrounding the spiral nulls are mainly contributed by j ∥; (2) the null with large (j ⊥) and small spine-fan angle (θ), which are predicted by traditional linear theory, does not exist in the turbulent diffusion region; (3) the background current j b plays an important role in determining the direction of the currents around spiral nulls and consequently the orientation of the magnetic null structures; and (4) the spiral nulls with strong current (large magnitude j ) tend to degenerate into 2D configurations, whereas the nulls with weak currents retain the 3D features. Since the spiral magnetic nulls are crucial for the energy dissipation during the turbulent reconnection process, all of these results can provide important information for better understanding 3D turbulent reconnection.

Electron Distribution Functions Around a Reconnection X‐Line Resolved by the FOTE Method

AbstractUsing data from the MMS mission and the First‐Order Taylor Expansion (FOTE) method, here we reveal electron distribution functions around a reconnection X‐line at the Earth's magnetopause. We find cigar distribution of electrons in both the magnetosphere‐side and magnetosheath‐side inflow regions, isotropic distribution of electrons at the separatrix, and loss of high‐energy electrons in the antiparallel direction in the magnetosheath‐side inflow region. We interpret the formation of cigar distribution in the inflow regions using the Fermi mechanism—as suggested in previous simulations, the loss of high‐energy electrons in the magnetosheath side using the parallel electric fields—which evacuate electrons to escape the diffusion region along the antiparallel direction, and the isotropic distribution at the separatrix using the pitch angle scattering by whistler waves—which exist frequently at the separatrix. We also find that the electron distribution functions can change rapidly (within 60 ms) from isotropic to cigar as the spacecraft moves slightly away from the separatrix.

Detection of Magnetic Nulls around Reconnection Fronts

Abstract Magnetic nulls, where magnetic-field strength becomes zero, play a crucial role in energy conversion and particle acceleration during magnetic reconnection. Recent simulations have suggested that reconnection fronts (RFs) inside the reconnection jet can host magnetic nulls. However, observational evidence for the RF-associated magnetic nulls remains absent so far. In this study, we present such evidence by using the first-order Taylor expansion method and Cluster measurements. We confirm for the first time the existence of magnetic nulls around RFs, and find that the dip region ahead of RFs and the nearby magnetic flux ropes around RFs can be host to magnetic nulls. The observed magnetic nulls are all spiral types, and the reconstructed topologies are consistent with theoretical models. Our results verify the existence of magnetic nulls around RFs, and may shed new light on the study of magnetic reconnection and RF dynamics.

Identifying magnetic reconnection events using the FOTE method

AbstractA magnetic reconnection event detected by Cluster is analyzed using three methods: Single‐spacecraft Inference based on Flow‐reversal Sequence (SIFS), Multispacecraft Inference based on Timing a Structure (MITS), and the First‐Order Taylor Expansion (FOTE). Using the SIFS method, we find that the reconnection structure is an X line; while using the MITS and FOTE methods, we find it is a magnetic island (O line). We compare the efficiency and accuracy of these three methods and find that the most efficient and accurate approach to identify a reconnection event is FOTE. In both the guide and nonguide field reconnection regimes, the FOTE method is equally applicable. This study for the first time demonstrates the capability of FOTE in identifying magnetic reconnection events; it would be useful to the forthcoming Magnetospheric Multiscale (MMS) mission.

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

AbstractIn 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.

Solving the Schrödinger equation without integration

The Waller-Hartree spin-free method is used to compute local energy HY/Y at some configurational points. Wavefunctions are optimized using a first-order Taylor expansion method. Results for H2 are reported and discussed. The advantages of the present method over the method of Frost and his co-workers are discussed.

A Simulation Study Comparison of Bayesian Estimation With Conventional Methods for Estimating Unknown Change Points

The main purpose of this research is to evaluate the performance of a Bayesian approach for estimating unknown change points using Monte Carlo simulations. The univariate and bivariate unknown change point mixed models were presented and the basic idea of the Bayesian approach for estimating the models was discussed. The performance of Bayesian estimation was evaluated using simulation studies of longitudinal data with different sample sizes, varying change point values, different levels of Level-1 variances, and univariate versus bivariate outcomes. The numerical results compared the performance of the Bayesian methods with the first-order Taylor expansion method and the adaptive Gaussian quadrature method implemented in SAS PROC NLMIXED. These simulation results showed that the first-order Taylor expansion method and the adaptive Gaussian quadrature method were sensitive to the initial values, making the results somewhat unreliable. In contrast, these simulation results showed that Bayesian estimation was not sensitive to the initial values and the fixed-effects and Level-1 variance parameters can be accurately estimated in all of the conditions. One concern was that the estimates of the Level-2 covariance parameters were found to be biased when the Level-1 variance was large in the bivariate model. However, and in general, the new Bayesian approach to the estimation of turning points in longitudinal data proved to be quite robust and practically useful.