First, I will tell readers about memories of my graduate student days at Cornell. I will highlight some of my experiences there, and what I learned, and didn't learn from them. Then I will then discuss a few of the research topics I have been working on over the years, including data interpretation and the tools for it, with special emphasis on the magnetopause. Aspects of MHD shocks and other structures, including boundary layers, are among those topics. I will mention a few people with whom I have worked closely and a few famous individuals, who influenced me in a significant way. The presentation contains material of potential interest to new, as well as more seasoned workers in the field. It will not always be in time order.

Observations by the Magnetospheric Multiscale spacecraft (MMS) of an unusual layer, located between the dayside magnetosheath and the magnetosphere, alternating with encounters with the magnetosheath during an extended time period between December 31, 2015 and January 01, 2016, when the interplanetary magnetic field was strongly southward and the Earth's dipole tilt large and negative, are presented. It appears to have been magnetically connected to both magnetosphere and magnetosheath. The layer appears to be located mostly on closed field lines and was bounded by a rotational discontinuity (RD) at its magnetosheath edge and by the magnetosphere on its earthward side. A separatrix layer, with heated magnetosheath electrons streaming unidirectionally along the field lines, was present sunward of the RD. We infer that the layer was started by a dominant reconnection site well north of the spacecraft and that it may have gained additional width, from a large drop in solar wind density and ram pressure, which preceded the beginning of the event by more than an hour. Relative to the magnetosheath, in which the magnetic field was strongly southward, this unusual layer was characterized by a less southward, more dawnward magnetic field of lower magnitude. The plasma density and flow speed in the region were lower than in the magnetosheath, albeit with Alfvénic jetting occurring at the magnetosheath edge as well as at the magnetospheric edge of the layer. The closing of the magnetic field lines requires the existence of another reconnection site, located southward/tailward of MMS.

The standard method for identifying magnetohydrodynamic rotational discontinuities in spacecraft data has been to examine how well the Walén relation is satisfied. In this paper, we apply two different versions of the Walén test to a database of nearly 1,000 dayside magnetopause crossings by the Magnetospheric Multi‐Scale spacecraft, with the objective of comparing their performance. The first approach is to evaluate the Walén relation as a jump condition, by determining the level of agreement between the change in plasma velocity across a discontinuity with the corresponding change in the Alfvén velocity. For this purpose, we use a recently developed quality index, Q, for which Q=±1 indicates perfect agreement. As was the case for a previously used quality index, ΔV∗, this new index employs data from two carefully chosen measurement times, located on opposite sides of the discontinuity. The second approach is to check the level of Alfvénicity of the flow for all measurements between those two points. Here, the quality index used is Wsl, the slope of the regression line in a scatter plot of plasma velocity components (after transformation into the deHoffmann‐Teller frame) versus the corresponding Alfvén velocity components, with Wsl=±1 indicating perfect agreement. For the two indices to give comparable numbers of rotational discontinuity candidates, a substantially higher threshold value is needed for |Q| than for |Wsl|. Even so, the events selected by the two methods are not identical. We also identify statistical relationships between Wsl and its associated correlation coefficient, Wcc, as well as between Wsl and Q and between Wsl and ΔV∗.

Change history: In this Letter, the y -axis values in Fig. 3f should go from 4 to −8 (rather than from 4 to −4), the y -axis values in Fig. 3h should appear next to the major tick marks (rather than the minor ticks), and in Fig. 1b, the arrows at the top and bottom of the electron-scale current sheet were going in the wrong direction; these errors have been corrected online.

This paper describes the generation and initial utilization of a database containing 80 vector and scalar quantities, for a total of 8,670 magnetopause and magnetosheath current sheet crossings by MMS1, using plasma and magnetic field data from the Fast Plasma Investigation, Fluxgate Magnetometer, and Hot Plasma Composition Analyzer instruments, augmented by solar wind and interplanetary magnetic field data from CDAWeb. Based on a determination of the current sheet width, measured and calculated vector and scalar quantities are stored for the two sides of the current sheet and for selected times within the current sheet. The only manual operations were the classification of the current sheets according to the type of boundary, the character of the magnetic field transition, and the quality of the current sheet fit. To characterize the database, histograms of selected key quantities are presented. We then give the statistics for the duration, motion, and thicknesses of the magnetopause current sheet, using single-spacecraft techniques for the determination of the normal velocities, obtaining median results of 12.9 s, 38.5 km/s, and 705.4 km, respectively. When scaled to the ion inertial length, the median thickness became 12.6; there were no thicknesses less than one. Next, we apply the Walen relation to find crossings that are rotational discontinuities and thus may indicate ongoing magnetic reconnection. For crossings where the velocities in the outflow region exceed the velocity on the magnetosheath side by at least 250 km/s, 47% meet our rotational discontinuity criteria. If we require the outflow to exceed 250 km/s along the L direction, then the percentage rises to 68%.

We discuss methods to determine L‐M‐N coordinate systems for current sheet crossings observed by the Magnetospheric Multiscale (MMS) spacecraft mission during ongoing reconnection, where eL is the direction of the reconnecting component of the magnetic field, B, and eN is normal to the magnetopause. We present and test a new hybrid method, with eL estimated as the maximum variance direction of B (MVAB) and eN as the direction of maximum directional derivative of B, and then adjust these directions to be perpendicular. In the best case, only small adjustment is needed. Results from this method, applied to an MMS crossing of the dayside magnetopause at 1305:45 UT on 16 October 2015, are discussed and compared with those from other methods for which eN is obtained by other means. Each of the other evaluations can be combined with eL from MVAB in a generalized hybrid approach to provide an L‐M‐N system. The quality of the results is judged by eigenvalue ratios, constancy of directions using different data segments and methods, and expected sign and magnitude of the normal component of B. For this event, the hybrid method appears to produce eN accurate to within less than 10°. We discuss variance analysis using the electric current density, J, or the J × B force, which yield promising results, and minimum Faraday residue analysis and MVAB alone, which can be useful for other events. We also briefly discuss results from our hybrid method and MVAB alone for a few other MMS reconnection events.

A new quality index is proposed for quantitatively assessing the level of Alfvenicity of the flow in the magnetopause and other quasi one-dimensional plasma/field structures. Perfect Alfvenicity is expressed by the so-called Walen relation, which describes the agreement of the observed jump in velocity across a suitable portion of the magnetopause and the corresponding jump in Alfven velocity. In the past, approximate agreement with this relation has been used as an important indicator of ongoing magnetic reconnection. The new index incorporates the effects of deviations in direction as well as in magnitude of the two vectors. Its properties and utility are illustrated by application to a large set of dayside magnetopause crossings by the Magnetospheric Multiscale spacecraft MMS 1. Time series for two of these events are also presented and discussed.

We present first results of the reconstruction of the electron diffusion region (EDR) based on a two‐dimensional, incompressible, and inertialess version of the electron magnetohydrodynamics equations. The method is applied to 30 ms resolution magnetic field, and electron moments data taken when the Magnetospheric Multiscale (MMS) spacecraft observed an EDR of near‐antiparallel magnetopause reconnection on 16 October 2015. An X‐type magnetic field configuration and quadrupolar Hall fields, consistent with the electron inflow and outflow, are successfully recovered. While MMS encountered a region of significant energy dissipation on the magnetospheric side of the sub‐ion‐scale current sheet, the reconstructions show that the MMS tetrahedron missed the X line by a distance of a few kilometers (~2 electron inertial lengths). The estimated reconnection electric field is 0.42–0.98 mV/m, equivalent to the dimensionless reconnection rate of 0.11–0.25. Signatures of three‐dimensional structures and/or time‐dependent processes are also identified.

AbstractWe report Magnetospheric Multiscale observations of a series of five small‐scale magnetic flux ropes (FR1–5) embedded in the southward reconnection outflow during a magnetopause reconnection event with a small guide field (~2.2 nT). These small‐scale flux ropes (diameter ~3–11 ion inertial lengths) are found inside or near the ion diffusion region on the magnetosheath side of the magnetopause boundary layer. A consistent result for determining the axis orientation of the flux ropes is achieved using two different methods, namely, minimum variance analysis of the axial electric field and constrained minimum variance analysis of the magnetic field. Our results show that the axes of these flux ropes (FR1–4) form a large angle (53°−66°) to the guide‐field orientation and are tilted toward the direction of the reconnecting field. These observations provide evidence for the presence of oblique ion‐scale flux ropes near the ion diffusion region during reconnection with a weak guide field. Our findings are similar to those obtained from a 3‐D kinetic simulation of turbulent reconnection.

We estimate the guide field near the X point, BM0, for a magnetopause crossing by the Magnetospheric Multiscale (MMS) spacecraft at 1307 UT on 16 October 2015 that showed features of electron‐scale reconnection. This component of the magnetic field is normal to the reconnection plane L‐N containing the reconnection magnetic field, BL, and the direction eN normal to the current sheet. The BM field component appears to approximately have quadrupolar structure close to the X point. Using several different methods to estimate values of the guide field near the X point, some of which use an assumed quadrupolar symmetry, we find values ranging between −3.1 nT and −1.2 nT, with a nominal value of about −2.5 nT. The rough consistency of these values is evidence that the quadrupolar structure exists.

We discuss mathematical tools for the reconstruction of two‐dimensional, time‐independent magnetic field and flow in the electron diffusion region, at a site of antiparallel magnetic reconnection. The basic assumptions are that the ions are stationary and have constant density. The width of the reconnection layer is of the order of the electron gyroradius or the electron inertial length. Our model includes the axial electron pressure term in Ohm's law developed by M. Hesse and coworkers. We demonstrate the feasibility of doing reconstruction of electron magnetohydrodynamic (EMHD) structures for a simplified system with zero electron inertia. The code is benchmarked using an exact solution that has antiparallel unidirectional magnetic fields, plus out‐of‐plane quadrupolar Hall fields, as well as the expected slow electron inflow and rapid exit jets. The inertialess reconstruction is then applied to synthetic data from a 2‐D, particle‐in‐cell, simulation of antiparallel reconnection. We find that the inertialess reconstruction of its electron diffusion region works reasonably well only when the spacecraft path passes close to the center of the reconnection site where the magnetic field is zero and the electron flow has a stagnation point. When the path is located farther away, the effects of electron inertia, and probably also deviations from the Hesse formula, cause the quality of the reconstruction to deteriorate. Electron inertia is included in the theoretical development presented here but requires a more complicated numerical reconstruction code. The development and testing of such a code is underway and will be presented separately.

We discuss observations of reconnection, obtained by Time History of Events and Macroscale Interactions during Substorms (THEMIS) D during an outward bound traversal of the low‐latitude dayside magnetopause. The reconnection signatures include high magnetic shear, a southward directed Alfvénic jet, bounded by slow‐mode shocks near the switch‐off limit (as in the symmetric Petschek geometry), a small, sunward directed normal magnetic field and plasma inflow into the jet from both sides. We conclude that cold, unmeasured ionospheric ions helped establish the symmetry. The effective ion mass, estimated from the switch‐off condition, was 2.39 amu on the magnetospheric side, where the number density was inferred from the spacecraft potential, and 1.09 amu on the magnetosheath side. After a modest pressure correction in the magnetospheric shock, the MHD jump conditions for density, pressure, temperature, and entropy were well satisfied. The shock jumps were much larger on the magnetosphere side than on the magnetosheath side; we show this to be a plasma β effect. The main dissipation mechanism appears to be irreversible transfer between thermal motion parallel and perpendicular to the field, such that both shocks bring about approximate downstream temperature isotropy. Hall currents and electric fields were present, albeit in a strongly asymmetric configuration. The magnetospheric shock had longer duration than the magnetosheath one, possibly as a result of a nonconstant magnetopause speed. We infer an average earthward magnetopause speed (14 km/s), corresponding nominal shock thicknesses (12 and 6 λ i ), dimensionless reconnection rates (0.061–0.085), and reconnection wedge angles (5° between shocks; 13° between separatrices).

AbstractWe analyze a magnetopause crossing by the Magnetospheric Multiscale (MMS) spacecraft at 1307 UT on 16 October 2016 that showed features of electron‐scale reconnection. For this event, we find orthonormal LMN coordinates from the magnetic field, with N and L varying respectively along the maximum gradient and maximum variance directions. We find the motion along N from the Spatio‐Temporal Difference analysis and motion along L from measured particle velocities. We locate the position of the magnetic X point, finding that MMS‐4 passed within about 1.4 km from the X point and that MMS‐3 and MMS‐2 passed within about 1.7 km and 2.4 km, respectively, from the position of maximum out of plane current.

The jump conditions are analyzed in detail for two slow shocks bounding a reconnection plasma jet, observed on 3 August 2008 by the spacecraft THEMIS D (Time History of Events and Macroscale Interactions during Substorms) on the dayside, low‐latitude magnetopause. Both shocks are near the switch‐off limit. They have been previously examined by Sonnerup et al. (2016), on the basis of the simplest MHD version of the jump conditions. In the present paper, those conditions now include the pressure anisotropy, normal heat fluxes, and a finite normal magnetic field component, the effects of all of which are found to be small. We also present and discuss the, mostly field‐aligned, measured total heat fluxes, which are found to be substantial and directed away from the reconnection site. We show that the double‐adiabatic (Chew‐Goldberger‐Low) invariants are far from invariant. Their combination indicates a large entropy increase across the shock on the magnetospheric side with a much smaller increase across the shock on the magnetosheath side. The detailed cause of the entropy changes remains unclear but appears to involve irreversible transfer of energy between thermal motion parallel and perpendicular to the magnetic field. The new results confirm the previously found presence of heavy ions and the values of the effective ion mass on both sides of the event. They also confirm the need for an ion pressure correction in the shock on the magnetospheric side.

We present the first results of a data analysis method, developed by Sonnerup and Hasegawa (2011), for reconstructing three-dimensional (3-D), magnetohydrostatic structures from data taken as two closely spaced satellites traverse the structures. The method is applied to a magnetic flux transfer event (FTE), which was encountered on 27 June 2007 by at least three (TH-C, TH-D, and TH-E) of the five THEMIS probes near the subsolar magnetopause. The FTE was sandwiched between two oppositely directed reconnection jets under a southward interplanetary magnetic field condition, consistent with its generation by multiple X-line reconnection. The recovered 3-D field indicates that a magnetic flux rope with a diameter of ~ 3000 km was embedded in the magnetopause. The FTE flux rope had a significant 3-D structure, because the 3-D field reconstructed from the data from TH-C and TH-D (separated by ~ 390 km) better predicts magnetic field variations actually measured along the TH-E path than does the 2-D Grad–Shafranov reconstruction using the data from TH-C (which was closer to TH-E than TH-D and was at ~ 1250 km from TH-E). Such a 3-D nature suggests that the field lines reconnected at the two X-lines on both sides of the flux rope are entangled in a complicated way through their interaction with each other. The generation process of the observed 3-D flux rope is discussed on the basis of the reconstruction results and the pitch-angle distribution of electrons observed in and around the FTE.

This chapter contains sections titled: Introduction Dehoffmann-Teller Analysis Field and Flow Perturbations Field Line Reconstruction Summary and Discussion

We re‐examine the basic premises of a single‐spacecraft data analysis method, developed by Sonnerup and Hasegawa (2005), for determining the axis orientation and proper frame velocity of quasi two‐dimensional, quasi‐steady structures of magnetic field and plasma. The method, which is based on Faraday's law, makes use of magnetic and electric field data measured by a single spacecraft traversing the structure, although in many circumstances the convection electric field, − v × B, can serve as a proxy for E. It has been used with success for flux ropes observed at the magnetopause but has usually failed to provide acceptable results when applied to real space data from reconnection events as well as to virtual data from numerical MHD simulations of such events. In the present paper, the reasons for these shortcomings are identified, analyzed, and discussed in detail. Certain basic properties of the method are presented in the form of five theorems, the last of which makes use of singular value decomposition to treat the special case where the magnetic variance matrix is non‐invertible. These theorems are illustrated using data from analytical models of flux ropes and also from MHD simulations as well as a 2‐D kinetic simulation of reconnection. The results make clear that the method requires the presence of a significant, non‐removable electric field distribution in the plane transverse to the invariant direction and that it is sensitive to deviations from strict two‐dimensionality and strict time stationarity.