Observational evidence of accelerating electron holes and their effects on passing ions

As a universal structure in space plasma, electron holes represent an obvious signature of nonlinear process. Although the theory has a 60-year history, whether electron hole can finally accelerate ambient electrons (or ions) is quite controversial. Previous theory for one-dimensional holes predicts that net velocity change of passing electrons (or ions) occurs only if the holes have non-zero acceleration. However, the prediction has not yet been demonstrated in observations. Here, we report four electron holes whose acceleration/deceleration is obtained by fitting the spatial separations and detection time delays between different Magnetospheric Multiscale spacecraft. We find that electron hole acceleration/deceleration is related to the ion velocity distribution gradient at the hole's velocity. We observe net velocity changes of ions passing through the accelerating/decelerating holes, in accordance with theoretical predictions. Therefore, we show that electron holes with non-zero acceleration can cause the velocity of passing ions to increase in the acceleration direction.

Direct observations of energy transfer from resonant electrons to whistler-mode waves in magnetosheath of Earth

Electromagnetic whistler-mode waves in space plasmas play critical roles in collisionless energy transfer between the electrons and the electromagnetic field. Although resonant interactions have been considered as the likely generation process of the waves, observational identification has been extremely difficult due to the short time scale of resonant electron dynamics. Here we show strong nongyrotropy, which rotate with the wave, of cyclotron resonant electrons as direct evidence for the locally ongoing secular energy transfer from the resonant electrons to the whistler-mode waves using ultra-high temporal resolution data obtained by NASA’s Magnetospheric Multiscale (MMS) mission in the magnetosheath. The nongyrotropic electrons carry a resonant current, which is the energy source of the wave as predicted by the nonlinear wave growth theory. This result proves the nonlinear wave growth theory, and furthermore demonstrates that the degree of nongyrotropy, which cannot be predicted even by that nonlinear theory, can be studied by observations.

Excitation of whistler-mode waves by cyclotron instability is considered as the likely generation process of the waves. Here, the authors show direct observational evidence for locally ongoing secular energy transfer from the resonant electrons to the whistler-mode waves in Earth’s magnetosheath.

Energy Flux Densities near the Electron Dissipation Region in Asymmetric Magnetopause Reconnection

Magnetic reconnection is of fundamental importance to plasmas because of its role in releasing and repartitioning stored magnetic energy. Previous results suggest that this energy is predominantly released as ion enthalpy flux along the reconnection outflow. Using Magnetospheric Multiscale data we find the existence of very significant electron energy flux densities in the vicinity of the magnetopause electron dissipation region, orthogonal to the ion energy outflow. These may significantly impact models of electron transport, wave generation, and particle acceleration.

MMS SITL Ground Loop: Automating the Burst Data Selection Process

Global-scale energy flow throughout Earth's magnetosphere is catalyzed by processes that occur at Earth's magnetopause (MP). Magnetic reconnection is one process responsible for solar wind entry into and global convection within the magnetosphere, and the MP location, orientation, and motion have an impact on the dynamics. Statistical studies that focus on these and other MP phenomena and characteristics inherently require MP identification in their event search criteria, a task that can be automated using machine learning so that more man hours can be spent on research and analysis. We introduce a Long-Short Term Memory (LSTM) Recurrent Neural Network model to detect MP crossings and assist studies of energy transfer into the magnetosphere. As its first application, the LSTM has been implemented into the operational data stream of the Magnetospheric Multiscale (MMS) mission. MMS focuses on the electron diffusion region of reconnection, where electron dynamics break magnetic field lines and plasma is energized. MMS employs automated burst triggers onboard the spacecraft and a Scientist-in-the-Loop (SITL) on the ground to select intervals likely to contain diffusion regions. Only low-resolution survey data is available to the SITL, which is insufficient to resolve electron dynamics. A strategy for the SITL, then, is to select all MP crossings. Of all 219 SITL selections classified as MP crossings during the first five months of model operations, the model predicted 166 (76%) of them, and of all 360 model predictions, 257 (71%) were selected by the SITL. Most predictions that were not classified as MP crossings by the SITL were still MP-like, in that the intervals contained mixed magnetosheath and magnetospheric plasmas. The LSTM model and its predictions are public to ease the burden of arduous event searches involving the MP, including those for EDRs. For MMS, this helps free up mission operation costs by consolidating manual classification processes into automated routines.

Lower-Hybrid Drift Waves Driving Electron Nongyrotropic Heating and Vortical Flows in a Magnetic Reconnection Layer

We report measurements of lower-hybrid drift waves driving electron heating and vortical flows in an electron-scale reconnection layer under a guide field. Electrons accelerated by the electrostatic potential of the waves exhibit perpendicular and nongyrotropic heating. The vortical flows generate magnetic field perturbations comparable to the guide field magnitude. The measurements reveal a new regime of electron-wave interaction and how this interaction modifies the electron dynamics in the reconnection layer.

Statistics of Kinetic Dissipation in the Earth's Magnetosheath: MMS Observations

A familiar problem in space and astrophysical plasmas is to understand how dissipation and heating occurs. These effects are often attributed to the cascade of broadband turbulence which transports energy from large scale reservoirs to small scale kinetic degrees of freedom. When collisions are infrequent, local thermodynamic equilibrium is not established. In this case the final stage of energy conversion becomes more complex than in the fluid case, and both pressure-dilatation and pressure strain interactions (Pi-D≡-Π_{ij}D_{ij}) become relevant and potentially important. Pi-D in plasma turbulence has been studied so far primarily using simulations. The present study provides a statistical analysis of Pi-D in the Earth's magnetosheath using the unique measurement capabilities of the Magnetospheric Multiscale (MMS) mission. We find that the statistics of Pi-D in this naturally occurring plasma environment exhibit strong resemblance to previously established fully kinetic simulations results. The conversion of energy is concentrated in space and occurs near intense current sheets, but not within them. This supports recent suggestions that the chain of energy transfer channels involves regional, rather than pointwise, correlations.

In Situ Observation of Hall Magnetohydrodynamic Cascade in Space Plasma

We present estimates of the turbulent energy-cascade rate derived from a Hall-magnetohydrodynamic (MHD) third-order law. We compute the contribution from the Hall term and the MHD term to the energy flux. Magnetospheric Multiscale (MMS) data accumulated in the magnetosheath and the solar wind are compared with previously established simulation results. Consistent with the simulations, we find that at large (MHD) scales, the MMS observations exhibit a clear inertial range dominated by the MHD flux. In the subion range, the cascade continues at a diminished level via the Hall term, and the change becomes more pronounced as the plasma beta increases. Additionally, the MHD contribution to interscale energy transfer remains important at smaller scales than previously thought. Possible reasons are offered for this unanticipated result.

Electron Heating by Debye-Scale Turbulence in Guide-Field Reconnection

We report electrostatic Debye-scale turbulence developing within the diffusion region of asymmetric magnetopause reconnection with a moderate guide field using observations by the Magnetospheric Multiscale mission. We show that Buneman waves and beam modes cause efficient and fast thermalization of the reconnection electron jet by irreversible phase mixing, during which the jet kinetic energy is transferred into thermal energy. Our results show that the reconnection diffusion region in the presence of a moderate guide field is highly turbulent, and that electrostatic turbulence plays an important role in electron heating.

In situ spacecraft observations of a structured electron diffusion region during magnetopause reconnection

The electron diffusion region (EDR) is the region where magnetic reconnection is initiated and electrons are energized. Because of experimental difficulties, the structure of the EDR is still poorly understood. A key question is whether the EDR has a homogeneous or patchy structure. Here we report Magnetospheric Multiscale (MMS) spacecraft observations providing evidence of inhomogeneous current densities and energy conversion over a few electron inertial lengths within an EDR at the terrestrial magnetopause, suggesting that the EDR can be rather structured. These inhomogenenities are revealed through multipoint measurements because the spacecraft separation is comparable to a few electron inertial lengths, allowing the entire MMS tetrahedron to be within the EDR most of the time. These observations are consistent with recent high-resolution and low-noise kinetic simulations.

Publisher Correction: Electron magnetic reconnection without ion coupling in Earth's turbulent magnetosheath

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.

Structure of the Current Sheet in the 11 July 2017 Electron Diffusion Region Event

The structure of the current sheet along the Magnetospheric Multiscale (MMS) orbit is examined during the 11 July 2017 Electron Diffusion Region (EDR) event. The location of MMS relative to the X-line is deduced and used to obtain the spatial changes in the electron parameters. The electron velocity gradient values are used to estimate the reconnection electric field sustained by nongyrotropic pressure. It is shown that the observations are consistent with theoretical expectations for an inner EDR in 2-D reconnection. That is, the magnetic field gradient scale, where the electric field due to electron nongyrotropic pressure dominates, is comparable to the gyroscale of the thermal electrons at the edge of the inner EDR. Our approximation of the MMS observations using a steady state, quasi-2-D, tailward retreating X-line was valid only for about 1.4 s. This suggests that the inner EDR is localized; that is, electron outflow jet braking takes place within an ion inertia scale from the X-line. The existence of multiple events or current sheet processes outside the EDR may play an important role in the geometry of reconnection in the near-Earth magnetotail.

Turbulence-Driven Ion Beams in the Magnetospheric Kelvin-Helmholtz Instability

The description of the local turbulent energy transfer and the high-resolution ion distributions measured by the Magnetospheric Multiscale mission together provide a formidable tool to explore the cross-scale connection between the fluid-scale energy cascade and plasma processes at subion scales. When the small-scale energy transfer is dominated by Alfvénic, correlated velocity, and magnetic field fluctuations, beams of accelerated particles are more likely observed. Here, for the first time, we report observations suggesting the nonlinear wave-particle interaction as one possible mechanism for the energy dissipation in space plasmas.

Kinetic Range Spectral Features of Cross Helicity Using the Magnetospheric Multiscale Spacecraft

We study spectral features of ion velocity and magnetic field correlations in the magnetosheath and in the solar wind using data from the Magnetospheric Multiscale (MMS) spacecraft. High-resolution MMS observations enable the study of the transition of these correlations between their magnetofluid character at larger scales into the subproton kinetic range, previously unstudied in spacecraft data. Cross-helicity, angular alignment, and energy partitioning is examined over a suitable range of scales, employing measurements based on the Taylor frozen-in approximation as well as direct two-spacecraft correlation measurements. The results demonstrate signatures of alignment at large scales. As kinetic scales are approached, the alignment between v and b is destroyed by demagnetization of protons.

Electron-scale dynamics of the diffusion region during symmetric magnetic reconnection in space

Magnetic reconnection is an energy conversion process that occurs in many astrophysical contexts including Earth's magnetosphere, where the process can be investigated in situ by spacecraft. On 11 July 2017, the four Magnetospheric Multiscale spacecraft encountered a reconnection site in Earth's magnetotail, where reconnection involves symmetric inflow conditions. The electron-scale plasma measurements revealed (i) super-Alfvénic electron jets reaching 15,000 kilometers per second; (ii) electron meandering motion and acceleration by the electric field, producing multiple crescent-shaped structures in the velocity distributions; and (iii) the spatial dimensions of the electron diffusion region with an aspect ratio of 0.1 to 0.2, consistent with fast reconnection. The well-structured multiple layers of electron populations indicate that the dominant electron dynamics are mostly laminar, despite the presence of turbulence near the reconnection site.

Autogenous and efficient acceleration of energetic ions upstream of Earth's bow shock

Earth and its magnetosphere are immersed in the supersonic flow of the solar-wind plasma that fills interplanetary space. As the solar wind slows and deflects to flow around Earth, or any other obstacle, a 'bow shock' forms within the flow. Under almost all solar-wind conditions, planetary bow shocks such as Earth's are collisionless, supercritical shocks, meaning that they reflect and accelerate a fraction of the incident solar-wind ions as an energy dissipation mechanism^1,2, which results in the formation of a region called the ion foreshock³. In the foreshock, large-scale, transient phenomena can develop, such as 'hot flow anomalies'^4-9, which are concentrations of shock-reflected, suprathermal ions that are channelled and accumulated along certain structures in the upstream magnetic field. Hot flow anomalies evolve explosively, often resulting in the formation of new shocks along their upstream edges^5,10, and potentially contribute to particle acceleration^11-13, but there have hitherto been no observations to constrain this acceleration or to confirm the underlying mechanism. Here we report observations of a hot flow anomaly accelerating solar-wind ions from roughly 1-10 kiloelectronvolts up to almost 1,000 kiloelectronvolts. The acceleration mechanism depends on the mass and charge state of the ions and is consistent with first-order Fermi acceleration^14,15. The acceleration that we observe results from only the interaction of Earth's bow shock with the solar wind, but produces a much, much larger number of energetic particles compared to what would typically be produced in the foreshock from acceleration at the bow shock. Such autogenous and efficient acceleration at quasi-parallel bow shocks (the normal direction of which are within about 45 degrees of the interplanetary magnetic field direction) provides a potential solution to Fermi's 'injection problem', which requires an as-yet-unexplained seed population of energetic particles, and implies that foreshock transients may be important in the generation of cosmic rays at astrophysical shocks throughout the cosmos.

Electron Bulk Acceleration and Thermalization at Earth's Quasiperpendicular Bow Shock

Electron heating at Earth's quasiperpendicular bow shock has been surmised to be due to the combined effects of a quasistatic electric potential and scattering through wave-particle interaction. Here we report the observation of electron distribution functions indicating a new electron heating process occurring at the leading edge of the shock front. Incident solar wind electrons are accelerated parallel to the magnetic field toward downstream, reaching an electron-ion relative drift speed exceeding the electron thermal speed. The bulk acceleration is associated with an electric field pulse embedded in a whistler-mode wave. The high electron-ion relative drift is relaxed primarily through a nonlinear current-driven instability. The relaxed distributions contain a beam traveling toward the shock as a remnant of the accelerated electrons. Similar distribution functions prevail throughout the shock transition layer, suggesting that the observed acceleration and thermalization is essential to the cross-shock electron heating.

Energy partitioning constraints at kinetic scales in low-β turbulence

Turbulence is a fundamental physical process through which energy injected into a system at large scales cascades to smaller scales. In collisionless plasmas, turbulence provides a critical mechanism for dissipating electromagnetic energy. Here we present observations of plasma fluctuations in low-β turbulence using data from NASA's Magnetospheric Multiscale mission in Earth's magnetosheath. We provide constraints on the partitioning of turbulent energy density in the fluid, ion-kinetic, and electron-kinetic ranges. Magnetic field fluctuations dominated the energy density spectrum throughout the fluid and ion-kinetic ranges, consistent with previous observations of turbulence in similar plasma regimes. However, at scales shorter than the electron inertial length, fluctuation power in electron kinetic energy significantly exceeded that of the magnetic field, resulting in an electron-motion-regulated cascade at small scales. This dominance should be highly relevant for the study of turbulence in highly magnetized laboratory and astrophysical plasmas.

Multiscale Currents Observed by MMS in the Flow Braking Region

We present characteristics of current layers in the off-equatorial near-Earth plasma sheet boundary observed with high time-resolution measurements from the Magnetospheric Multiscale mission during an intense substorm associated with multiple dipolarizations. The four Magnetospheric Multiscale spacecraft, separated by distances of about 50 km, were located in the southern hemisphere in the dusk portion of a substorm current wedge. They observed fast flow disturbances (up to about 500 km/s), most intense in the dawn-dusk direction. Field-aligned currents were observed initially within the expanding plasma sheet, where the flow and field disturbances showed the distinct pattern expected in the braking region of localized flows. Subsequently, intense thin field-aligned current layers were detected at the inner boundary of equatorward moving flux tubes together with Earthward streaming hot ions. Intense Hall current layers were found adjacent to the field-aligned currents. In particular, we found a Hall current structure in the vicinity of the Earthward streaming ion jet that consisted of mixed ion components, that is, hot unmagnetized ions, cold E × B drifting ions, and magnetized electrons. Our observations show that both the near-Earth plasma jet diversion and the thin Hall current layers formed around the reconnection jet boundary are the sites where diversion of the perpendicular currents take place that contribute to the observed field-aligned current pattern as predicted by simulations of reconnection jets. Hence, multiscale structure of flow braking is preserved in the field-aligned currents in the off-equatorial plasma sheet and is also translated to ionosphere to become a part of the substorm field-aligned current system.

Coalescence of Macroscopic Flux Ropes at the Subsolar Magnetopause: Magnetospheric Multiscale Observations

We report unambiguous in situ observation of the coalescence of macroscopic flux ropes by the magnetospheric multiscale (MMS) mission. Two coalescing flux ropes with sizes of ∼1  R_{E} were identified at the subsolar magnetopause by the occurrence of an asymmetric quadrupolar signature in the normal component of the magnetic field measured by the MMS spacecraft. An electron diffusion region (EDR) with a width of four local electron inertial lengths was embedded within the merging current sheet. The EDR was characterized by an intense parallel electric field, significant energy dissipation, and suprathermal electrons. Although the electrons were organized by a large guide field, the small observed electron pressure nongyrotropy may be sufficient to support a significant fraction of the parallel electric field within the EDR. Since the flux ropes are observed in the exhaust region, we suggest that secondary EDRs are formed further downstream of the primary reconnection line between the magnetosheath and magnetospheric fields.

Instability of Agyrotropic Electron Beams near the Electron Diffusion Region

During a magnetopause crossing the Magnetospheric Multiscale spacecraft encountered an electron diffusion region (EDR) of asymmetric reconnection. The EDR is characterized by agyrotropic beam and crescent electron distributions perpendicular to the magnetic field. Intense upper-hybrid (UH) waves are found at the boundary between the EDR and magnetosheath inflow region. The UH waves are generated by the agyrotropic electron beams. The UH waves are sufficiently large to contribute to electron diffusion and scattering, and are a potential source of radio emission near the EDR. These results provide observational evidence of wave-particle interactions at an EDR, and suggest that waves play an important role in determining the electron dynamics.

Multipoint Measurements of the Electron Jet of Symmetric Magnetic Reconnection with a Moderate Guide Field

We report observations from the Magnetospheric Multiscale (MMS) satellites of the electron jet in a symmetric magnetic reconnection event with moderate guide field. All four spacecraft sampled the ion diffusion region and observed the electron exhaust. The observations suggest that the presence of the guide field leads to an asymmetric Hall field, which results in an electron jet skewed towards the separatrix with a nonzero component along the magnetic field. The jet appears in conjunction with a spatially and temporally persistent parallel electric field ranging from -3 to -5  mV/m, which led to dissipation on the order of 8  nW/m^{3}. The parallel electric field heats electrons that drift through it, and is associated with a streaming instability and electron phase space holes.

Structure, force balance, and topology of Earth's magnetopause

The magnetopause deflects the solar wind plasma and confines Earth's magnetic field. We combine measurements made by the four spacecraft of the Magnetospheric Multiscale mission to demonstrate how the plasma and magnetic forces at the boundary affect the interaction between the shocked solar wind and Earth's magnetosphere. We compare these forces with the plasma pressure and examine the electron distribution function. We find that the magnetopause has sublayers with thickness comparable to the ion scale. Small pockets of low magnetic field strength, small radius of curvature, and high electric current mark the electron diffusion region. The flow of electrons, parallel and antiparallel to the magnetic field, reveals a complex topology with the creation of magnetic ropes at the boundary.

Wave-particle energy exchange directly observed in a kinetic Alfvén-branch wave

Alfvén waves are fundamental plasma wave modes that permeate the universe. At small kinetic scales, they provide a critical mechanism for the transfer of energy between electromagnetic fields and charged particles. These waves are important not only in planetary magnetospheres, heliospheres and astrophysical systems but also in laboratory plasma experiments and fusion reactors. Through measurement of charged particles and electromagnetic fields with NASA's Magnetospheric Multiscale (MMS) mission, we utilize Earth's magnetosphere as a plasma physics laboratory. Here we confirm the conservative energy exchange between the electromagnetic field fluctuations and the charged particles that comprise an undamped kinetic Alfvén wave. Electrons confined between adjacent wave peaks may have contributed to saturation of damping effects via nonlinear particle trapping. The investigation of these detailed wave dynamics has been unexplored territory in experimental plasma physics and is only recently enabled by high-resolution MMS observations.

Alfvén waves are fundamental plasma modes that provide a mechanism for the transfer of energy between particles and fields. Here the authors confirm experimentally the conservative energy exchange between Alfvén wave fields and plasma particles via high-resolution MMS observations of Earth's magnetosphere.

Spacecraft Observations and Analytic Theory of Crescent-Shaped Electron Distributions in Asymmetric Magnetic Reconnection

Supported by a kinetic simulation, we derive an exclusion energy parameter E_{X} providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell demon, only high-energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low-density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low-density separatrix.

Rippled Quasiperpendicular Shock Observed by the Magnetospheric Multiscale Spacecraft

Collisionless shock nonstationarity arising from microscale physics influences shock structure and particle acceleration mechanisms. Nonstationarity has been difficult to quantify due to the small spatial and temporal scales. We use the closely spaced (subgyroscale), high-time-resolution measurements from one rapid crossing of Earth's quasiperpendicular bow shock by the Magnetospheric Multiscale (MMS) spacecraft to compare competing nonstationarity processes. Using MMS's high-cadence kinetic plasma measurements, we show that the shock exhibits nonstationarity in the form of ripples.

Magnetospheric Multiscale Observations of the Electron Diffusion Region of Large Guide Field Magnetic Reconnection

We report observations from the Magnetospheric Multiscale (MMS) satellites of a large guide field magnetic reconnection event. The observations suggest that two of the four MMS spacecraft sampled the electron diffusion region, whereas the other two spacecraft detected the exhaust jet from the event. The guide magnetic field amplitude is approximately 4 times that of the reconnecting field. The event is accompanied by a significant parallel electric field (E_{∥}) that is larger than predicted by simulations. The high-speed (∼300  km/s) crossing of the electron diffusion region limited the data set to one complete electron distribution inside of the electron diffusion region, which shows significant parallel heating. The data suggest that E_{∥} is balanced by a combination of electron inertia and a parallel gradient of the gyrotropic electron pressure.

Magnetospheric Multiscale Satellites Observations of Parallel Electric Fields Associated with Magnetic Reconnection

We report observations from the Magnetospheric Multiscale satellites of parallel electric fields (E_{∥}) associated with magnetic reconnection in the subsolar region of the Earth's magnetopause. E_{∥} events near the electron diffusion region have amplitudes on the order of 100  mV/m, which are significantly larger than those predicted for an antiparallel reconnection electric field. This Letter addresses specific types of E_{∥} events, which appear as large-amplitude, near unipolar spikes that are associated with tangled, reconnected magnetic fields. These E_{∥} events are primarily in or near a current layer near the separatrix and are interpreted to be double layers that may be responsible for secondary reconnection in tangled magnetic fields or flux ropes. These results are telling of the three-dimensional nature of magnetopause reconnection and indicate that magnetopause reconnection may be often patchy and/or drive turbulence along the separatrix that results in flux ropes and/or tangled magnetic fields.

Electron-scale measurements of magnetic reconnection in space

Magnetic reconnection is a fundamental physical process in plasmas whereby stored magnetic energy is converted into heat and kinetic energy of charged particles. Reconnection occurs in many astrophysical plasma environments and in laboratory plasmas. Using measurements with very high time resolution, NASA's Magnetospheric Multiscale (MMS) mission has found direct evidence for electron demagnetization and acceleration at sites along the sunward boundary of Earth's magnetosphere where the interplanetary magnetic field reconnects with the terrestrial magnetic field. We have (i) observed the conversion of magnetic energy to particle energy; (ii) measured the electric field and current, which together cause the dissipation of magnetic energy; and (iii) identified the electron population that carries the current as a result of demagnetization and acceleration within the reconnection diffusion/dissipation region.

Magnetospheric Multiscale Satellite Observations of Parallel Electron Acceleration in Magnetic Field Reconnection by Fermi Reflection from Time Domain Structures

The same time domain structures (TDS) have been observed on two Magnetospheric Multiscale Satellites near Earth's dayside magnetopause. These TDS, traveling away from the X line along the magnetic field at 4000  km/s, accelerated field-aligned ∼5  eV electrons to ∼200  eV by a single Fermi reflection of the electrons by these overtaking barriers. Additionally, the TDS contained both positive and negative potentials, so they were a mixture of electron holes and double layers. They evolve in ∼10  km of space or 7 ms of time and their spatial scale size is 10-20 km, which is much larger than the electron gyroradius (<1  km) or the electron inertial length (4 km at the observation point, less nearer the X line).