Wave Phenomena and Beam-Plasma Interactions at the Magnetopause Reconnection Region.

This paper reports on Magnetospheric Multiscale observations of whistler mode chorus and higher-frequency electrostatic waves near and within a reconnection diffusion region on 23 November 2016. The diffusion region is bounded by crescent-shaped electron distributions and associated dissipation just upstream of the X-line and by magnetic field-aligned currents and electric fields leading to dissipation near the electron stagnation point. Measurements were made southward of the X-line as determined by southward directed ion and electron jets. We show that electrostatic wave generation is due to magnetosheath electron beams formed by the electron jets as they interact with a cold background plasma and more energetic population of magnetospheric electrons. On the magnetosphere side of the X-line the electron beams are accompanied by a strong perpendicular electron temperature anisotropy, which is shown to be the source of an observed rising-tone whistler mode chorus event. We show that the apex of the chorus event and the onset of electrostatic waves coincide with the opening of magnetic field lines at the electron stagnation point.

Introduction

Background and Previous Studies

The NASA Magnetospheric Multiscale (MMS) mission extends the investigation of magnetic reconnection in the boundary regions of the Earth's magnetosphere to the electron scale (Burch et al., 2016). In doing so, it extends the comprehensive studies of reconnection at the magnetohydrodynamic (MHD) and ion scales by previous missions to the smallest plasma scales at which the reconnection process operates. With its unprecedentedly high data rate and the smallest ever separations among four spacecraft, MMS is uniquely capable of evaluating the occurrence of various wave modes and wave‐particle interactions and their importance for magnetic reconnection.

Previous observations have shown the importance of lower hybrid, Langmuir, and whistler mode waves in the vicinity of magnetopause reconnection sites (e.g., Cao et al., 2017; Fujimoto et al., 2011; Graham, Khotyaintsev, et al., 2016; Vaivads et al., 2004, 2007), and some important new insights made available by MMS have been discussed by Graham, Khotyaintsev, Norgren, et al. (2017), Graham, Khotyaintsev, Vaivads, et al. (2017), and Khotyaintsev et al. (2016). The crescent‐shaped electron distributions identified by Burch et al. (2016) are shown by Graham, Khotyaintsev, Vaivads, et al. (2017) to generate upper hybrid waves in the electron diffusion region (EDR) via the beam mode. Whistler mode waves have been observed by Graham, Vaivads, et al. (2016) and Wilder et al. (2017) near the reconnection separatrix with the generation mechanism being a Tperp/Tpar anisotropy although Wilder et al. showed evidence that the beam mode can also produce whistler mode waves in certain parameter regimes. Lower hybrid waves have been shown to be present in the EDR because of the lower hybrid drift instability (Graham, Khotyaintsev, Norgren, et al., 2017).

Summary of Observations

The current study was motivated by the occurrence of a magnetopause crossing on 23 November 2016 with the four MMS spacecraft moving from the magnetosheath to the magnetosphere south of the X‐line as indicated by the ion jets. During this event there was a unique observation of rising‐tone whistler mode chorus emissions with peak frequency at the location of the transition from closed to open magnetic field lines at the electron stagnation point. As a result, the entire chorus band was located on open magnetic field lines on the magnetosphere side of the reconnection X‐line. As noted by Stenberg et al. (2007), chorus waves are generally observed in closed field line regions and particularly in the equatorial dawnside magnetosphere or in magnetic minima at high latitudes (Tsurutani & Smith, 1977). As is shown in this report, MMS observed rising‐tone chorus waves in a region of open field lines, as determined by the mixture of magnetosheath and magnetospheric electrons in the region of the EDR between the X‐line and the electron stagnation point.

Throughout the chorus band a southward directed field‐aligned beam of magnetosheath energy electrons was observed as expected for the reconnection electron jet. We show that these beams are likely the source of electron plasma oscillations that are observed at frequencies extending from above the electron cyclotron frequency (Fce) to near the electron plasma frequency (Fpe). Also observed throughout the chorus band was a perpendicular electron temperature gradient with Tperp/Tpar ~ 1.6, and it is this temperature gradient that is the most likely source of the whistler mode chorus waves.

On the magnetosheath side of the X‐line there was another southward electron beam, which also was associated with a reconnection electron jet. These electron beams were accompanied by broadband waves that were electromagnetic at frequencies below Fce and electrostatic up to 20 kHz as expected for beam‐generated waves (Graham, Khotyaintsev, Vaivads, et al., 2017). The coexistence of whistler mode chorus and higher‐frequency electrostatic waves in the dayside outer magnetosphere was noted by Reinleitner et al. (1983) and attributed to electron trapping and Landau acceleration of keV electrons by the whistler waves.

Analysis and Conclusions

The electron distribution function in the region where rising‐band whistler mode chorus and higher‐frequency electrostatic waves were observed together in the region of open field lines between the reconnection X‐line and the electron stagnation region was modeled using four bi‐Maxwellian distributions. A WHAMP (Waves in Homogeneous Anisotropic Multicomponent Plasma) dispersion analysis (Rönnmark, 1982) showed that the whistler mode waves were produced by the observed electron distribution, most likely from the temperature anisotropy (Teperp/Tepar ~ 1.6) while the electrostatic waves resulted from a beam‐plasma interaction.

Using the newly developed 7.5 ms electron moments (Rager et al., 2018), we show that the open‐closed magnetic field boundary occurs just Earthward of the chorus apex in association with an electric field structure with large EL and EM components and J · E > 0, indicating reconnection dissipation at the electron stagnation point.

The whistler mode result agrees with the previous work of Vaivads et al. (2007) and Stenberg et al. (2007), who observed whistlers at the high‐latitude magnetopause with Cluster and associated their generation with an electron temperature anisotropy formed by the escape of magnetospheric electrons from the first open magnetic flux tube. Graham, Vaivads, et al. (2016) drew the same conclusion for Cluster observations at the low‐latitude reconnection separatrix. Thus, we can essentially confirm this explanation while also showing its correlation with the opening of magnetic field lines near the electron stagnation point where they are accompanied by higher‐frequency electrostatic waves generated by reconnection electron jets.

Magnetospheric Multiscale Measurements

Description of MMS Measurements

The measurements made on each of the four MMS spacecraft are listed in Table 1. Especially important for reconnection is the high time resolution of the plasma measurements: 30 ms for electrons and 150 ms for ions, as compared to previous resolutions in the range of a few seconds. This improvement required the use of multiple analyzers rather than one spinning analyzer, resulting in stringent requirements on their absolute calibration and intercalibration. The unprecedented precision and accuracy of the plasma instruments allow MMS to make accurate measurements of currents and electron drift velocities in space for the first time. Another advance is the accurate measurement of three‐axis electric fields with sampling frequencies up to 65,536/s. Data taken at the highest measurement resolution on MMS are referred to as burst mode data, and all instruments operate in burst mode whenever the spacecraft are beyond a geocentric distance of 9 RE on the dayside of Earth. However, even in burst mode the 65,536/s E‐field sampling frequency, which is triggered on board by signal variability, is only available about 1/3 of the time while the remainder of the burst mode data is sampled at 8,192/s. This study takes advantage of an important improvement to the plasma measurement time resolution (Rager et al., 2018), which utilizes the interleaved nature of the coverage of velocity space to yield both electron moments and distribution functions at 7.5 ms time resolution.

Table 1

Measurements Made on Each MMS Spacecraft

	Description
FIELDS	3D electric and magnetic field measurements at <1 ms time resolution (DC) and waves to 6 kHz (B) and 100 kHz (E).
Fast plasma	Full sky viewing of plasma electrons and ions at 32 energies (10 eV to 30 keV): electrons in 30 ms and ions in 150 ms.
Energetic particles	Full sky viewing of ion and electron energetic particles (20–500 keV) with composition.
HPCA	Composition‐resolved 3‐D ion distributions (1 eV–40 keV) for H+, He++, He+, and O+. Full sky at 10 s.
ASPOC	Maintain S/C potential to ≤4 V using ion emitter.

Overview of Observations by MMS on 23 November 2016

Analysis of three separate electron diffusion regions (EDRs) observed by MMS on 23 November 2016 has been presented by Webster et al. (2017). The subject of this report is another EDR, which was situated in time between the first and second of Webster's events. The distinguishing feature of this event is the presence of rising‐tone whistler mode chorus emissions extending into the diffusion region from the magnetosphere‐side separatrix.

During this event the magnetopause was moving Sunward at approximately 44 km/s, which is much faster than the spacecraft velocities of a few km/s. However, there were some oscillations in the direction of magnetopause motion resulting in the multiple encounters reported by Webster et al. (2017). Such an oscillation resulted in a dual encounter with the electron stagnation region for the time period of this study. During this time period the spacecraft were maintained in a tetrahedron configuration with an average interspacecraft separation of ~7 km as shown in Figure 1, which also contains a sketch of the approximate trajectory of the MMS spacecraft through the reconnection diffusion region.

Figure 1

(a) MMS tetrahedron at 0750 UT on 23 November 2016 when spacecraft constellation was located at R = 10.27 RE and MLT = 13.24 h. TQF is the tetrahedron quality factor with 1.0 being a regular tetrahedron. (b) Sketch of magnetic field lines for asymmetric reconnection with the magnetosheath to the left and the magnetosphere to the right. Approximate extent of the electron diffusion region is shown by the gray rectangle. Estimated trajectory of MMS through the magnetopause is shown by the gray arrow. This trajectory was caused mainly by the velocity of the magnetopause, which had an average magnitude of ~44 km/s but which oscillated in sign causing multiple magnetopause encounters. X‐line and electron stagnation region are labeled by X and S, respectively. The L, M, and N components in base GSE coordinates are the following: L = [0.31690800, 0.078344800, 0.94521499], M = [0.26392251, −0.96386427, −0.0085962582], and N = [0.91691172, 0.25379226, −0.30580175].

Figure 2 shows an overview of magnetic field and plasma data for a 10 s period on 23 November 2016. Noted in Figure 2a are (X) the approximate location of the closest approach to the reconnection X‐line as indicated by the Bz reversal and local B minimum and (S1 and S2) the approximate locations of the electron stagnation point as indicated by the sharp reduction in energy flux in Figure 2c and the density drop in Figure 2d, which is larger and longer‐lived for S2. We note in Figures 2e and 2g a very large Tepar/Teperp and associated strong plasma currents in mostly the GSE z direction. Figure 2g shows another intense current in mostly the GSE y direction at the second approximate electron stagnation point (S2). In this study we focus on the 3 s time period near the center of Figure 2 (between 33.5 and 36.5 s) and the region of Teperp/Tepar > 0 between 35 and 36 s where rising‐tone whistler mode chorus was observed.

Figure 2

Overview of magnetic field and plasma data for a 10 s period on 23 November 2016. (a) Magnetic field components in GSE coordinates and total B (black trace); (b) ion energy‐time spectrogram; (c) electron energy‐time spectrogram; (d) ion and electron densities; (e) parallel and perpendicular electron temperatures; (f) ion velocity components; and (g) plasma current components. Nearest approaches to the X‐line (based on BZ reversal) and electron stagnation region (based on electron spectrogram) are noted in the top panel by X and S1/S2, respectively. At S1 there was a brief decrease in electron density (Figures 2c and 2d), while at S2 there was a much larger and longer‐lived electron density decrease.

Figure 3 shows overlayed electric and magnetic field data and plasma moments from the four MMS spacecraft for the time period from 07:49:33.5 to 07:49:36.5 UT on 23 November 2016. The electric and magnetic field data are plotted in boundary‐normal coordinates as defined in the caption to Figure 1. We note the close similarity of the magnetic field data from all four spacecraft, particularly in the middle part of the plot. We identify the closest approach to the reconnection X‐line by the polarity reversal of BL at approximately 07:49:34.2 UT and note the strong electric field fluctuations that occurred just upstream of this point and again near 07:49:35.8 UT, which we identify as the electron stagnation region from the rapid transition from Teperp/Tepar > 1 to Teperp/Tepar < 1 (Figures 2g and 2h) as well as from the electron data in Figures 2c and 2d.

Figure 3

Multispacecraft plot of magnetic and electric fields and plasma moments on 23 November 2016 from 07:49:33.5 to 07:49:36.5 UT. Magnetic and electric field quantities are plotted in boundary‐normal coordinates as defined for Figure 1. (a) BL, (b) BM, (c) BN, (d) veL, (e) veM, (f) veN, (g) Tepar, (h) Teperp, (i) EL, (j) EM, and (k) EN.

Figure 4 provides an overview of the MMS1 observations from 07:49:33.5 to 07:49:36.5 UT. The left side of Figure 4, from top to bottom, shows magnetic field components, ion and electron energy‐time spectrograms, ion velocity, electron temperature, electric field, electric field frequency‐time spectrogram, and magnetic field frequency‐time spectrogram. The B, E, and Vi plots are in boundary‐normal (LMN) coordinates with transformation matrices as listed in the caption of Figure 1. MMS was initially in the magnetosheath and moved toward the magnetosphere following the BL reversal (X‐line) occurring at about 07:49:34.2 UT. Throughout the plot ViL is negative, denoting locations below the reconnection midplane in the southward exhaust as sketched in Figure 1b. An electron temperature anisotropy with Teperp > Tepar is evident between 35.1 s and 35.9 s, coinciding with the rising‐tone whistler mode chorus band in Figures 4g and 4h. As noted by Gary and Karimabadi (2006) such a temperature anisotropy leads to whistler mode wave growth, for example, through the whistler anistropy instability.

Figure 4

Overview of magnetopause crossing on 23 November 2016. (a) Magnetic field components in boundary‐normal coordinates; (b) ion energy‐time spectrogram; (c) electron energy‐time spectrogram; (d) ion velocity; (e) electron temperature; (f) DC electric field; and (g) AC electric field frequency‐time spectrogram with black, red, and blue curves denoting Fce, Fpi, and Flh; (h) AC magnetic field frequency‐time spectrogram, (i) (left) polar plot centered at 07:49:33.906 UT (noted by left vertical line in left panel) of electron velocity space distribution with v⊥1 in the (b × v) × b direction, which is a proxy for E × B, and v⊥2 in the E direction. (right) Line plots in red and black showing average velocity space distributions within the red and black sectors in each polar plot. (j) Same as Figure 4i except in the plane containing the magnetic field and v⊥1, (k and l) same as Figures 4i and 4j except for 07:49:35.736 UT (noted by right vertical line in left panel).

In Figures 4a–h two times of interest are noted by the vertical dashed lines (at 07:49:33.900 UT and 07:49:35.735 UT), and electron distribution functions (DFs) from MMS1 for these two times are shown in the right side of the figure. In Figures 4i–4l polar plots of the electron distribution functions in planes perpendicular and parallel to B are accompanied by line plots in two directions noted by black and red angular sectors. Each line plot is composed of the average DF within the corresponding sector. Figures 4i and 4j show that just upstream of the BL reversal the electrons show moderate agyrotropy in the plane perpendicular to B, indicating the possibility of a weak crescent distribution. In the plane parallel to B there is an intense beam along B, forming a southward electron jet. Such beams are expected to produce electron plasma oscillations via a beam‐plasma instability (e. g., Fuselier et al., 1985). Figure 4g shows waves at this time that are consistent with electrostatic waves extending above Fce with the electromagnetic waves at lower frequencies mainly populating the lower hybrid frequency range.

Figures 4k and 4l are taken from near the crest of the rising‐tone whistler mode chorus emissions and are typical of the distribution functions throughout the chorus ramp. While the distribution perpendicular to B in (k) is highly gyrotropic, the v par, v perp plot in Figure 4l shows a reduction in Tpar caused by the escape of magnetospheric electrons as suggested by Vaivads et al. (2007), Stenberg et al. (2007), and Graham, Vaivads, et al. (2016) and by the formation of a beam along −v par resulting from the incursion and subsequent field‐aligned acceleration of magnetosheath electrons. We note that the line plots in Figures 4i–4l extend to 2 × 104 km/s (1,137 eV), while the polar plots only extend to 1 × 104 km/s. The black curve (at 180° average pitch angle) shows a significant decrease from the red curve (0° pitch angle) at all velocities above 0.5 × 104 km/s. This plot is very similar to Figure 4g of Graham, Vaivads, et al. (2016), which extends to higher energies. As in Graham, Vaivads, et al. (2016) we identify the higher energy particles as magnetospheric electrons, it is clear from their relatively low energies that they are most likely from the closed field line region of the low‐latitude boundary layer.

While the electron temperature anisotropy (Teperp/Tepar > 1) is the most likely cause of the whistler mode chorus, the low‐energy beam (or electron jet) should generate electrostatic waves above Fce via the electrostatic beam mode (Fuselier et al., 1985). Such waves are seen throughout the region occupied by the whistler mode chorus emissions, and these will be seen to extend to near the electron plasma frequency (Fpe) in a subsequent plot.

Evaluation of Ohm's Law Terms and Dissipation

The dissipative processes that occur in the reconnection diffusion region can be expressed by the electron momentum equation or generalized Ohm's law: where E and B are the vector electric and magnetic field, respectively; J is the vector current; ν is the electron velocity; η is anomalous resistivity; P is the electron pressure tensor; m is electron mass; n is the plasma density; and e is the electron charge. Ideal MHD physics will occur if the right‐hand side (RHS) of equation (1) is zero. If any of the terms are nonzero then MHD will be violated and reconnection might occur.

Measurements by the tetrahedron of MMS spacecraft can be used to gain insight into the sources of electric fields associated with reconnection to a greater or lesser extent depending on whether or not all four spacecraft are in the reconnection diffusion region simultaneously. The average 7 km separation among the spacecraft during the second magnetopause exploration of MMS (September 2016–March 2017) provides the best opportunity to evaluate the electric field sources. Figure 5 shows the evaluation of the terms on the right‐hand side of the generalized Ohm's law and comparison with the measured electric fields for the same time period as Figure 4. Plotted in Figure 5 from top to bottom are the following: (a) vector B at the centroid of the four spacecraft, (b) current from curl B, (c) E inertia = (m /e)dv /dt, (d) −Div P /en, (e) E Hall = J × B/en, (f) the total RHS of Ohm's law, (g) E' = E + v  × B at the centroid, (h) J · E' at the centroid, (i) the M component of E′, and (j) the M component of the RHS of Ohm's law.

Figure 5

Middle column: evaluation of the terms on the right‐hand side (RHS) of the generalized Ohm's law based on MMS measurements in boundary‐normal coordinates. (a) Centroid magnetic field, (b) current from curl B, (c) E inertia = (m /e)dv /dt, (d) −div P /en, (e) E Hall = J × B/en, (f) RHS of Ohm's law, (g) E′ (E + v  × B) at barycenter, (h) J · E', (i) E M, and (j) M component of RHS of Ohm's law. Left column: DF polar plots from MMS2, MMS3, and MMS4 at time of left vertical line with format the same as for Figures 3i and 3j). Right column: Same as left panel except for the time at the right vertical line.

The same two vertical lines of reference as in Figure 4 are shown in Figure 5 with electron DFs at the left and right, respectively, for the two selected times. Since MMS1 DFs were plotted in Figure 4 for these same two times, DFs for only the other three spacecraft are shown in Figure 5. At the first time marker, when the spacecraft were located just upstream of the BL reversal (closest to the X‐line), the DFs in the perpendicular plane for MMS2 and MMS3 show agyrotropic distributions resembling the crescent‐shaped distributions described by Burch et al. (2016). The perpendicular‐plane DF for MMS4 shows a generally gyrotropic distribution as was the case for MMS1 (in Figure 4), while in the plane containing B all four spacecraft detected intense electron beams along +v par, which is indicative of a southward reconnection jet with a source in the X‐line region. As indicated by the DFs from two of the spacecraft (MMS2 and MMS3), they were near or within the upstream edge of the EDR, and this conclusion is supported by the line plots in Figure 5 (middle column). At the first vertical time marker Figure 5g shows the strongest E' component being E while the strongest currents (Figure 5b) are directed along −M and +L. Comparison of Figures 5i and j shows that E is generally well predicted by the RHS of Ohm's law with the strongest contribution being from the pressure tensor divergence (Figure 5d) with a significant Hall‐field contribution with the opposite polarity (Figure 5e). Between the two vertical lines EM is also well predicted as shown with an expanded vertical scale in Figures 5i and 5j.

Referring to the second time marker in Figure 5, which is in the region of electron stagnation on the magnetosphere side of the X‐line and also near the apex of the rising‐tone whistler mode chorus emissions, we see that electron DFs from all four spacecraft are similar and as described for Figure 4 with a beam (southward electron jet) along −v par and magnetospheric electrons flowing along +v par. As noted in the discussion of Figure 4l, the perpendicular temperature gradient appears to be supported by escape of magnetospheric electrons along a recently opened magnetic field line. Although only weak electric fields and dissipation are observed at the time marker, there is a significant dissipation peak at about 0.1 s later, and this peak will be shown to have existed at all four spacecraft in the next two figures.

Wave Generation Mechanisms

Wave Data Description

Figure 6 shows a detailed view of magnetic and electric fields, high‐rate electric and magnetic wave data, and electron distribution functions for a 0.6 s time period beginning at 07:49:35.4 on 23 November 2016. Plotted in Figures 6a–6f are B, Te, v , E, and E and B frequency‐time spectrograms using sample rates of 65,536/s and 16,384/s, respectively. Fce, Fpi, and Flh are plotted in black, red, and blue, respectively. Fuh (upper hybrid frequency) is located just off the top of the plots at about 28 kHz. The two dashed vertical lines at 074935.781 and 074935.811 UT note the time range of the DF plots in the right side of Figure 6, which have the same format as used in Figure 4. As in Figure 4, the DF in the perpendicular plane (Figure 4g) is gyrotropic while in both parallel cuts shown in (Figures 4h and 4i) the same loss of high‐energy electrons is noted, which causes Teperp/Tepar > 0 as seen clearly in Figure 4b.

Figure 6

High‐rate data from MMS1 on 23 November 2016 in boundary‐normal coordinates: (a) vector magnetic field; (b) electron temperature, Tpar in blue and Tperp in red; (c) electron velocity; (d) DC electric field at 8,192/s; (e) frequency‐time spectrogram of AC electric field data; (f) frequency‐time spectrogram of AC magnetic field data; (g) same as Figure 3(i) except for 07:49:35.796 UT; (h) same as Figure 3 (j) except for 07:49:35.796 UT; (i) polar plot of electron velocity space distribution with the horizontal axis along B and the vertical axis (v ⊥2) with cuts through the distributions shown for the field‐aligned sectors shown in black and red on the polar plots and for Figure 6i an additional cut along v ⊥2. Correction for the spacecraft potential of 4.4 V and a four bi‐Maxwellian fit to the field‐aligned distributions is added to Figure 6i with (1) a stationary background population with T = 6 eV, n = 3 cm−3, and Tperp/Tpar = 1, (2) a drifting Maxwellian with T = 4 eV, n = 1.0 cm−3, Tperp/Tpar = 4.0, and Vdrift/Vth = −2.95 (flow along −B), (3) a drifting Maxwellian with T = 60 eV, n = 5 cm−3, Tperp/Tpar = 2.2, and Vdrift/Vth = 0.28, and (4) a stationary population with T = 45 eV, n = 1 cm−3, and Tperp/Tpar = 1. The green curve fit in Figure 6i is the sum of (1), (2), and (4), while the blue curve is the sum of (1), (3), and (4). The purpose of showing the 90° distribution (the green data, which are not included in the field‐aligned fits) is to illustrate the source of the Tperp/Tpar anisotropy shown in the line plot in Figure 6b.

Polarization Analysis

As noted by Gary and Karimabadi (2006) an electron temperature anisotropy is a likely cause of whistler mode emissions, including the chorus‐type emission shown in Figure 6, which coincides with the significant temperature anisotropy shown in Figure 6b. Based on the previous results of Fuselier et al. (1985) and Graham, Khotyaintsev, Vaivads, et al. (2017), we expect the high‐frequency electrostatic waves to be associated with beam‐plasma instabilities. Thus, we performed a polarization analysis and a dispersion analysis in order to determine the characteristics and generation mechanisms for the whistler mode waves and higher‐frequency electrostatic waves. Figure 7 shows the E‐field polarization analysis for the 0.8 s time period starting at 074935 UT. Figure 7a repeats the electric field wave power spectrogram showing the upper and lower bands of whistler mode chorus and the electrostatic waves near and above 10 kHz, with these features appearing more clearly in the second half of the plot. Figure 7b shows the degree of polarization to be near 1.0 for the electrostatic waves and lower band chorus and also for the upper band chorus where it is most intense. The wave‐normal angle in Figure 7c shows values near 0° (field aligned) for the lower band chorus but becoming more oblique for the upper band. Both the ellipticity and the helicity show fairly high positive values for the lower band chorus (right handed and nearly circular), while the results are less clear for the upper band. Such differences between the lower and upper chorus bands are well known and have recently been analyzed by Li et al. (2013).

Figure 7

Results of electric field polarization analysis: (a) electric power spectral density (PSD) versus frequency, (b) degree of polarization, (c) wave normal angle, (d) wave ellipticity, and (e) wave helicity.

Similar results for the B field are shown in Figure 8. An interesting feature in Figure 8a is the connection (or bridge) between the upper and lower chorus bands that occurs at three different times between 0.5 s and 0.7 s, which show the upper part of the lower band rising in frequency to form the upper band. We note that Kurita et al. (2012) have reported instances from THEMIS (Time History of Events and Macroscale Interactions during Substorms) of chorus without a 0.5 Fce gap. In addition, the magnetic ellipticity and helicity are shown in Figures 8d and 8e to have values close to 1.0 indicating circular polarization for the lower chorus band but changing to zero helicity and negative ellipticity near Fce indicating left‐hand polarization, which may be a reflection or cutoff effect needing further investigation.

Figure 8

Same as for Figure 6 except for magnetic field.

The results of a Poynting flux analysis of the whistler mode chorus waves are shown in Figure 9 where Figure 9a shows the magnitude of the Poynting flux while Figure 9b shows the angle between B and the Poynting vector. We conclude from Figure 9 that while the lower band chorus waves are propagating primarily parallel to B (AngBS < 20°) the upper band waves tend to be more oblique with AngBS > 60° for some intervals.

Figure 9

(a) Poynting flux magnitude versus frequency for MMS1 at same time period as for Figures 6 and 7. (b) Angle between B and S (the Poynting vector) showing that the lower band chorus waves are parallel propagating (<20°), while the upper band waves tend to be more oblique (>60°).

Dispersion Analysis

In order to investigate the causes of the observed whistler mode and electrostatic waves we used the program WHAMP (Rönnmark, 1982), which performs a linear dispersion analysis for multiple drifting bi‐Maxwellian plasmas. Plotted in Figure 6i is a green curve and a blue curve that were derived from a fit to the parallel component of four bi‐Maxwellian distributions: (1) a stationary background population with T = 6 eV, n = 3 cm−3 and Tperp/Tpar = 1, (2) a drifting Maxwellian with T = 4 eV, n = 1.0 cm−3 Tperp/Tpar = 4.0 and Vdrift /Vth = −2.95 (flow along −B), (3) a drifting Maxwellian with T = 60 eV, n = 5 cm−3, Tperp/Tpar = 2.2 and Vdrift/Vth = 0.28, and (4) a stationary population with T = 45 eV, n = 1 cm−3, and Tperp/Tpar = 1. The green curve (antiparallel to B) in Figure 6i is the sum of (1), (2), and (4), while the blue curve (parallel distribution) is the sum of (1), (3), and (4). The purpose of showing the 90° distribution (the green curve, which as expected is not reproduced by the parallel fit) is to illustrate the source of the Tperp/Tpar anisotropy shown in the line plot in Figure 6b. The features in Figures 6g–6i persisted throughout the time period containing the whistler mode chorus emissions (07:49:35.40–07:49:35.84 UT), and the four‐Maxwellian fit is valid throughout that region.

Figure 10 shows the dispersion relation and normalized growth rate versus wave number and frequency for the four‐Maxwellian model. Figures 10a and 10c show the dispersion relation (blue curve) and normalized growth rates (red curves) for whistler mode waves. The characteristic growth‐rate peak near 0.5 Fce is clearly seen in Figure 10c as is the sharp drop at higher frequencies.

Figure 10

Results of a dispersion analysis for the electron distribution shown in Figure 6i. Four bi‐Maxwellian distributions, as described in the text and the caption of Figure 6, were used as input to a WHAMP analysis (Rönnmark, 1982). (a and c) Results for the whistler mode. (b and d) Beam mode results for electrostatic waves. Results are for parallel propagation (k⊥ = 0) with the dispersion relations shown by the blue curves and the normalized growth rates by the red curves.

Results for the higher‐frequency electrostatic waves are shown in Figures 10b and 10d. Positive wave growth (imaginary frequency component greater than 0) is shown for k⊥ = 0 (parallel propagation) over a range of k∥ values from 0 to ~0.05 m−1, while for larger values strong damping is observed. The dispersion relation in Figure 10b has the characteristic shape of waves generated by the unstable beam mode (Dum, 1989). Finally, Figure 10d plots the wave growth versus frequency with a broad peak centered at ~0.4 Fpe.

A plot of electric power spectral density for the time of the distribution functions shown in Figure 6 appears in Figure 11. Noted in Figure 12 are the plasma frequency (Fpe) and the frequency of peak wave growth from Figure 10. The peak signal is also shown by the yellow pixels in the electric field wave spectrogram in Figure 6a. The electric and magnetic field wave spectrograms in Figure 6 show clearly the lower band and upper band of the whistler mode chorus emissions along with the well‐known gap near 0.5 Fce (e.g., Kurita et al., 2012). The fact that there is no wave growth shown in Figure 10 near Fce while a peak power spectral density at frequencies just below Fce is shown in Figure 11 supports the idea that a different wave generation process may be responsible for the upper band (Li et al., 2013). We note the similarity of Figure 11 to Figure 3 of Reinleitner et al. (1983) who attributed the coexistence of chorus waves and higher‐frequency electrostatic waves in the dayside outer magnetosphere to the trapping of electrons within the whistler waves and their acceleration into beams by Landau resonance.

Figure 11

Electric field power spectral density measured by MMS1 for the 30 ms time period beginning at 07:49:35.77 on 23 November 2016. The frequency at peak growth from the dispersion analysis and the electron plasma frequency are noted by the vertical lines. Note the lower chorus band near 500 Hz and the upper chorus band between 900 and 1,000 Hz.

Figure 12

(a) DC electric field at 8192/s in boundary‐normal coordinates, (b) current from electron and ion measurements at 7.5 ms resolution in boundary‐normal coordinates with ion currents (37.5 ms resolution) interpolated to match electron time resolution, (c) dissipation measured by J · (E + v  × B) at 7.5 ms resolution with average E. (d–f) electron velocity space distribution function in field‐aligned coordinates in (top) the plane normal to B with v⊥1 in the (b × v) × b direction, which is a proxy for E × B and, and v⊥2 in the E direction, with red and black lines showing sectors where distribution function cuts are made, (middle) the plane containing B and v⊥1, (bottom) the plane containing B and v⊥2.

Dissipation at the Electron Stagnation Point

Highest Resolution MMS Data

Beginning just after the crest of the chorus event, the character of the E signal in Figure 6d changed to an intense positive pulse of mostly EL and EM reaching up to 15 mV. This pulse resulted in significant dissipation as measured by J · E' as shown in Figure 12, which is a zoom‐in to an 0.08 s interval of Figure 6 when MMS1 had moved Earthward of the whistler mode chorus and electrostatic wave emissions. Figure 12a plots the electric field in boundary‐normal coordinates at the burst mode rate of 8,192/s, while Figure 12b shows the LMN components of the current measured by FPI at the enhanced rate of 7.5 ms for electrons and 37.5 ms for ions (Rager et al., 2018). The data points are plotted every 7.5 ms with the ion portion of the current interpolated to the faster electron sample rate. Figure 12c shows a peak of dissipation measured by J · (E + v  × B), which uses the current measured by the electron and ion distributions and E averaged over the 7.5 ms electron (and current) time resolution. The peak dissipation shown in Figure 12c is consistent with that shown in Figure 5h for the barycenter E + v  × B and J Curl derived for all four spacecraft.

Opening of Magnetic Field Lines

Referring to the sequence of three electron DF plots shown in Figures 12d–12f, we note that (1) the electron jet beam along −v∥ becomes weaker while the higher energy electron fluxes along −v∥ become stronger until by Figure 12f the fluxes are essentially equal along both field‐aligned directions indicating closed field lines. We conclude that the field lines opened up via reconnection at a time near the center of Figure 12 when the dissipation was highest.

While a crescent‐shaped distribution (Burch et al., 2016) was observed in the DF plane perpendicular to B (particularly with MMS2 and MMS3) in the region just upstream of the X‐line (Figure 5), no such crescents were observed in the electron stagnation region shown in Figure 12. This absence of crescent distributions could have resulted from the strong positive EL and JL and to a lesser extent the positive EN and JN as shown in Figures 12a and 12b.

We note that electron crescent distributions were observed by MMS2 and MMS3 just upstream of the X‐line (Figure 5). As shown in Figure 5g, there was a strong EN component at the time of the crescent observation. As noted by Burch et al. (2016), acceleration of magnetosheath electrons across a plasma boundary (in that case the electron stagnation point) is an important mechanism for accelerating electrons into crescent distributions. The observation of crescents on the magnetosheath side of the X‐line in a region of strong EN suggests that the same mechanism can occur at different types of boundaries such as reconnection separatrices.

Summary and Conclusions

On 23 November 2016 MMS made multiple magnetopause crossings between 07:49 and 07:51 UT. Three of these crossings have been analyzed by Webster et al. (2017). The current study addresses a fourth crossing that occurred between 07:49:33.5 and 07:49:36.5 UT with a focus on reconnection dissipation near the X‐line and near the electron stagnation point, which bracket the electron diffusion region, and on wave phenomena and beam‐plasma interactions that occurred between these two locations. During this event the four MMS spacecraft were maintained in a tetrahedron formation with the closest average separation (7 km) that was implemented during Phase 1 (dayside magnetopause) of the mission. Within the region between the X‐line and the electron stagnation point the magnetic field data from the four spacecraft remained nearly identical, which was ideal for the generalized Ohm's law analysis that was performed using plasma moments and electric and magnetic field data. As shown in Figure 5f, for this event there were unusually strong EM and EN components extending Earthward of the peak positive EL component (near the electron stagnation region). Two regions of interest were identified: one near 07:49:33.9 UT, just Sunward of the X‐line, as defined by the sign reversal of BL, and the other near 07:49:35.8 near the electron stagnation point as indicated by a sharp increase in Teperp and decrease in Tepar.

Ohm's Law Analysis

Near the X‐line the strongest electric field signal and the best correlation with Ohm's law terms (Figure 5) was found for EN, which was primarily caused by the divergence of the electron pressure tensor. Similarly, in the space between the two regions of interest there was very good correlation between the measured EM and that derived from divergence of the electron pressure tensor. Calculation of J · (E + v  × B) using data from all four spacecraft at their barycenter indicated reconnection dissipation at each region of interest with the out‐of‐plane current as shown in Figure 5b at the first region being associated with crescent‐shaped distributions primarily at MMS2 and MMS3. The dissipation at the second region was associated primarily with magnetic field‐aligned currents and electric fields (Figure 12).

Wave Analysis

Most of the space between the two regions of interest was filled with significant wave activity including (1) electromagnetic lower hybrid waves, (2) rising‐tone whistler mode chorus, and (3) broadband electrostatic waves extending from Fce to near Fpe. This space was also characterized by field‐aligned electron beams, which we identify as electron jets moving southward from the X‐line and by electron anisotropy with typical Teperp/Tepar ~ 1.6. We showed via WHAMP dispersion analysis that the whistler mode chorus waves result from the electron temperature anisotropy, and the electron plasma oscillations resulted from a beam‐plasma instability driven by the electron jets coupled with the counterstreaming beams of magnetospheric electrons. By inspection of the electron distribution functions we confirmed a previous result from Cluster (Graham, Vaivads, et al., 2016; Stenberg et al., 2007; Vaivads et al., 2007) that the electron temperature anisotropy responsible for the whistler waves is caused by the escape of magnetospheric electrons into the magnetosheath.

Determination of Field Line Opening

Finally, we demonstrated by measurement of J · (E + v  × B) and by the observation of a mixture of magnetosheath and magnetosheric electrons within a flux tube that the onset of both the whistler waves and the whistler mode chorus waves on the Earthward side of the electron diffusion region is coincident with the opening of magnetic field lines via reconnection.