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Geophysical Research Letters

RESEARCH LETTER Currents and associated electron scattering
10.1002/2016GL068359
and bouncing near the diffusion region
Special Section: at Earth’s magnetopause
First results from NASA's
Magnetospheric Multiscale B. Lavraud1,2, Y. C. Zhang1,2,3, Y. Vernisse1,2, D. J. Gershman4,5, J. Dorelli4, P. A. Cassak6, J. Dargent1,2,7,
(MMS) Mission C. Pollock4, B. Giles4, N. Aunai7, M. Argall8, L. Avanov4,5, A. Barrie4,9, J. Burch10, M. Chandler11,
L.-J. Chen4, G. Clark12, I. Cohen12, V. Coffey11, J. P. Eastwood13, J. Egedal14, S. Eriksson15, R. Ergun15,
Key Points: C. J. Farrugia8, S. A. Fuselier10, V. Génot1,2, D. Graham16, E. Grigorenko17, H. Hasegawa18, C. Jacquey1,2,
• Observation of Hall current-associated
I. Kacem1,2, Y. Khotyaintsev16, E. MacDonald4, W. Magnes19, A. Marchaudon1,2, B. Mauk12, T. E. Moore4,
electron dynamics near the
diffusion region T. Mukai18, R. Nakamura19, W. Paterson4, E. Penou1,2, T. D. Phan20, A. Rager4,21, A. Retino7, Z. J. Rong22,
• Confirmation of low-energy electron C. T. Russell23, Y. Saito18, J.-A. Sauvaud1,2, S. J. Schwartz13,15, C. Shen24, S. Smith4,21, R. Strangeway23,
scattering by curved magnetic
S. Toledo-Redondo25, R. Torbert8, D. L. Turner26, S. Wang9, and S. Yokota18
field lines
• Simultaneous observation of 1
Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, Toulouse, France, 2Centre National de la
inflowing and outflowing,
bouncing populations Recherche Scientifique, UMR 5277, Toulouse, France, 3State Key Laboratory of Space Weather, NSSC/CAS, Beijing, China,
4
NASA Goddard Space Flight Center, Greenbelt, Maryland, USA, 5Department of Astronomy, University of Maryland, College
Park, Maryland, USA, 6Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia, USA,
Supporting Information: 7
Laboratoire de Physique des Plasmas, Palaiseau, France, 8Physics Department, University of New Hampshire, Durham,
• Supporting Information S1
New Hampshire, USA, 9Millenium Engineering and Integration Company, Arlington, Virginia, USA, 10Southwest Research
Correspondence to: Institute, San Antonio, Texas, USA, 11NASA Marshall Space Flight Center, Huntsville, Alabama, USA, 12The Johns Hopkins
B. Lavraud, University Applied Physics Laboratory, Laurel, Maryland, USA, 13The Blackett Laboratory, Imperial College, London, UK,
14
Benoit.Lavraud@irap.omp.eu Department of Physics, University of Wisconsin, Madison, Wisconsin, USA, 15Laboratory for Atmospheric and Space
Physics, University of Colorado Boulder, Boulder, Colorado, USA, 16Swedish Institute of Space Physics, Uppsala, Sweden,
17
Space Research Institute of the Russian Academy of Sciences, Moscow, Russia, 18Institute of Space and Astronautical
Citation:
Lavraud, B., et al. (2016), Currents and Science, JAXA, Sagamihara, Japan, 19Space Research Institute, Austrian Academy of Sciences, Graz, Austria, 20Space Sciences
associated electron scattering and Laboratory, Berkeley, California, USA, 21Department of Physics, Catholic University of America, Washington, District of
bouncing near the diffusion region at Columbia, USA, 22Key Laboratory of Earth and Planetary Physics, IGG/CAS, Beijing, China, 23Department of Earth and Space
Earth’s magnetopause, Geophys. Res.
Sciences, University of California, Los Angeles, California, USA, 24Harbin Institute of Technology, Shenzhen, China, 25ESAC/ESA,
Lett., 43, 3042–3050, doi:10.1002/
2016GL068359. Villafranca del Castillo, Spain, 26The Aerospace Corporation, El Segundo, California, USA

Received 19 FEB 2016

Accepted 22 MAR 2016
Abstract Based on high-resolution measurements from NASA’s Magnetospheric Multiscale mission, we
Accepted article online 28 MAR 2016 present the dynamics of electrons associated with current systems observed near the diffusion region of
Published online 6 APR 2016 magnetic reconnection at Earth’s magnetopause. Using pitch angle distributions (PAD) and magnetic curvature
analysis, we demonstrate the occurrence of electron scattering in the curved magnetic field of the diffusion
region down to energies of 20 eV. We show that scattering occurs closer to the current sheet as the electron
energy decreases. The scattering of inflowing electrons, associated with field-aligned electrostatic potentials
and Hall currents, produces a new population of scattered electrons with broader PAD which bounce back
and forth in the exhaust. Except at the center of the diffusion region the two populations are collocated and
appear to behave adiabatically: the inflowing electron PAD focuses inward (toward lower magnetic field),
while the bouncing population PAD gradually peaks at 90° away from the center (where it mirrors owing to
higher magnetic field and probable field-aligned potentials).

1. Introduction
The process of magnetic reconnection is ubiquitous in the plasma universe. Although it has major large-scale
implications on the surrounding media, the key processes that drive magnetic reconnection occur at very
small scales in a region known as the diffusion region (where magnetic fields diffuse and reconnect with a
new topology) [e.g., Priest and Forbes, 2000]. In proton-electron plasmas, as observed near Earth, for instance,
the vastly different particle masses lead to a structured region wherein the ions (with larger gyroradius) decouple
from the magnetic field farther from the X line (where the topology changes) than electrons. This separation
©2016. American Geophysical Union. leads to the formation of an ion diffusion region with characteristic Hall currents and magnetic fields embedding
All Rights Reserved. a much smaller electron diffusion region [e.g., Øieroset et al., 2001; Mozer et al., 2002]. While missions such as the

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 Geophysical Research Letters 10.1002/2016GL068359

multispacecraft Cluster mission have instrumentation and interspacecraft separation on the order of the typical
ion scales at Earth’s magnetopause, the recently launched Magnetospheric Multiscale (MMS) mission has been
designed to measure the details of electron dynamics to understand electron-scale physics in the vicinity of these
diffusion regions [Burch et al., 2015].
Electron dynamics in collisionless magnetic reconnection has been studied mostly using test particle [Speiser,
1965] and particle-in-cell simulations [e.g., Hoshino et al., 2001; Fu et al., 2006; Pritchett, 2006; Drake et al., 2008;
Wan et al., 2008; Hesse et al., 2014]. For the present study, of particular interest is the prediction that particle
pitch angle scattering should occur when the gyroradius of a particle is on the order of the scale of the local
magnetic field curvature. With Rc the local magnetic field curvature and Rg the particle gyroradius, one can
define an adiabatic parameter κ by κ2 = Rc/Rg. Based on this parameter, theory predicts that particle scatter-
ing (of ions or electrons) occurs when κ2 approaches 25 and that particle dynamics becomes chaotic for
values below 10 [Sergeev et al., 1983; Büchner and Zelenyi, 1989; Young et al., 2008]. Observations of proton
dynamics in the radiation belts and ring current have, for instance, been attributed to scattering by curved
magnetic field configurations [Zou et al., 2011; Shen et al., 2014]. Regarding electrons, simulations have mostly
been used to study their dynamics in the vicinity of magnetic reconnection regions, with more chaotic
behaviors identified near the X line where the local magnetic field line curvature becomes comparable to
the electron gyroradius [e.g., Wang et al., 2010]. In the magnetotail ion diffusion region, isotropic electron
observations at energies of a few keV were explained by local electric fields and magnetic curvature pitch
angle scattering [Egedal et al., 2005; Wang et al., 2010]. Although recent theory and numerical modeling have
predicted complex behaviors at electron scales as well [Ng et al., 2011, 2012; Bessho et al., 2014, 2015;
Haggerty et al., 2015; Wang et al., 2016], no appropriate spacecraft observations have been available. The
present paper is devoted to novel observations of currents in the Hall region and associated electron
demagnetization, scattering and bouncing down to the smallest scales near the diffusion region, which will
contribute to our understanding of the fine structure and dynamics of magnetic reconnection.

2. Mission and Instrumentation

The four NASA MMS [Burch et al., 2015] spacecraft were launched together on 12 March 2015 on an Atlas V
launch vehicle into a highly elliptical 28° inclination orbit with perigee at 1.2 Earth radii (RE) and apogee at
12 RE. The main requirements for the mission objectives were the following: (1) four spacecraft in a close
tetrahedron formation with adjustable separations down to 10 km, (2) accurate three-axis electric and
magnetic field measurements for estimating spatial gradients and time variations, and (3) three-dimensional
electron and ion distribution functions at the highest time resolution ever achieved (30 ms for electrons and
150 ms for ions). For the present paper, we primarily focus on ion and electron measurements from the Fast
Plasma Instruments [Pollock et al., 2016] and magnetic field measurements from the fluxgate magnetometers
[Russell et al., 2015]. We primarily show data from the MMS4 spacecraft, except when using multispacecraft
methods or measurements as stated in the text.

3. Diffusion Region Observations

To study the current systems and the occurrence of electron pitch angle scattering and bouncing in the vicinity of
the diffusion region of magnetic reconnection, the magnetopause crossings of 3 October 2015 (near 14:07:00 UT)
and 16 October 2015 (near 10:33:30 UT) are presented in Figure 1. The figure shows the former event in
Figures 1a–1h and the latter in Figures 1i–1p. For the events, we perform a minimum variance analysis
[Sonnerup and Scheible, 1998] on the intervals 14:46:58–14:47:03 UT and 10:33:22–10:33:37 UT, respectively,
which is used to transform the ion velocities and magnetic fields in Figures 1d and 1f into boundary normal
LMN coordinates (where N points outward into the magnetosheath and L has a positive ZGSE component).
Figures 2a and 2b display the out-of-plane (Hall) magnetic field and the parallel currents, respectively, from a full
particle-in-cell simulation performed for typical asymmetric magnetopause conditions. These simulation figures
are merely used here for illustration purposes, but their description is given in the associated supporting informa-
tion for completeness. The notional virtual spacecraft trajectory in the vicinity of the X line is depicted for the two
events in Figure 2a based on the following description.
Figures 1a–1h from 3 October 2015 display the typical signatures of the crossing of an ion diffusion region, i.e.,
with Hall magnetic field (BM) and current signatures. The region labeled 1 in Figure 1d for this event shows a

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 Geophysical Research Letters 10.1002/2016GL068359

Figure 1. MMS plasma and magnetic field observations from two ion diffusion region crossings (3 October 2015 and 16 October 2015). (a–h) The ion energy-time
spectrogram, electron energy-time spectrogram, 200 eV electron PAD spectrogram, ion velocity and magnetic field components in LMN coordinates, the parallel
and perpendicular currents from the four-spacecraft Curlometer method (Figure 1f) and from the particles measurements (Figure 1g; average of the currents from the
four spacecraft), and finally the parallel and perpendicular electron temperatures (Figure 1h). (i–p) The same but for the second event on 16 October 2015. Several key
regions, as identified in the text, are numbered in black and red for each event. These regions are also reported in the simulation illustration in Figure 2a.

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Figure 2. (a) The out-of-plane Hall BM magnetic field component and parallel component of the currents with overlaid
magnetic field lines in black from a particle-in-cell simulation described in the supporting information. The parallel
currents are related to parallel electrostatic potentials, while perpendicular currents drive the classic out-of-plane Hall
magnetic field signature of Figure 2a. The notional relative spacecraft paths for the two events, with various identified
regions numbered as described in the text, are shown in these simulation plots for illustration purposes only. The properties
of the parallel currents are sketched in Figure 2b.

negative VL component, consistent with the location of region 1 for this event as shown in Figure 2a along the
black dashed arrow displaying the spacecraft trajectory. Going forward in time for this event, region 2 corre-
sponds to the passage from the left-hand side of the X line to its right-hand side, so that region 2 is where
VL switches sign to a positive value. The spacecraft then enters the negative BM Hall magnetic field in region
3 and exits the region through the opposite polarity Hall magnetic field in region 4 (positive BM in Figure 1e).
A short time later the satellite returns to the positive Hall magnetic field region (region 5). After region 5, the
satellite exits into the magnetosheath, characterized by a large southward magnetic field, consistent with the
crossing of an ion diffusion region at a reconnecting, large magnetic shear magnetopause.
The Hall magnetic field signatures are confirmed by the independent calculations of the currents based on
the multispacecraft curlometer method [Robert et al., 1998] in Figure 1f and the direct particle measurements
in Figure 1g, i.e., J = Nq(Vi Ve) (where J is the current density vector, N is the plasma density, q is the electric
charge, and Vi and Ve, respectively, are the ion and electron velocity vectors). The current from particle
measurements in Figure 1g is the average over the four spacecraft individual measurements and is thus
directly comparable with that estimated from the curlometer over the tetrahedron (note that for the two
events studied the interspacecraft separation is on the order of 10 km). Only the parallel and perpendicular
currents are displayed for more direct comparison with the simulation results in Figures 2a and 2b. As can
be seen, these two independent measures of the currents match each other extremely well, demonstrating
the unprecedented level of accuracy in particle measurements reached by MMS.
Strong perpendicular currents consistent with the Hall currents are observed throughout the region contain-
ing the out-of-plane BM magnetic field signature. Strong parallel currents are also measured as the spacecraft
crosses the Hall region. The parallel current changes sign across the midplane (where BZ changes sign),
consistent with outward flowing currents and with strong inward acceleration of field-aligned electrons.
This acceleration is most likely the result of field-aligned potentials accelerating electrons inward [Egedal
et al., 2005, 2008] but may also be involving Fermi-type acceleration [e.g., Drake et al., 2009]. These observa-
tions are also consistent with the increased parallel electron temperature observed at the edges of the
exhaust in Figure 1h, as also observed from simulations [Le et al., 2010; Wang et al., 2016]. More intermixed

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parallel and perpendicular components of the currents are measured in the center of the region. Analysis of
the detailed interplay between various processes in this complex current system is left for future work.
Of specific interest for the present study is Figure 1c, which shows the pitch angle distribution (PAD) of 200 eV
electrons. While these electrons show clear anisotropies in the magnetosphere (bidirectional to the left) and
magnetosheath (unidirectional at 0° to the right), in the identified ion diffusion region these 200 eV electrons
appear much more isotropic. This is also observed in measured electron temperatures in Figure 1h.
To further quantify the properties of this crossing, we used a multispacecraft timing method [e.g., Russell et al.,
1983] to determine the magnetopause normal direction—based on the BZ component reversal (zero crossing
times)—which we found as (0.90; 0.36; 0.24)GSE with a normal speed of 65 km/s. Given a full diffusion region
duration of about 3 s, the spatial thickness of the region is 195 km. With a density of 12 cm 3 as observed just
outside in the magnetosheath (not shown), the typical ion skin depth λi is estimated as 66 km. The ion
diffusion region thickness is thus about 3λi. Assuming fast reconnection with a diffusion region aspect ratio
of 0.1 (ratio of the thickness to width of the region), the crossing distance to the X line is estimated as 15λi
(or ~987 km), as roughly represented by the spacecraft trajectory in Figure 2a.
A similar overview of the 16 October event is now described based on Figures 1i–1p. The spacecraft sampling
of the X line vicinity is illustrated with the red dashed arrow in the simulation plot of Figure 2b. As with the
first event, the magnetopause crossing starts on the magnetospheric side with a negative VL components
(region 1 in Figures 1l and 2b). Unlike the first event, however, the spacecraft does not cross to the other side
of the X line, as shown by the continuously VL component throughout the event (Figure 1l), and the consis-
tently reversed polarity (compared to the first event) of the Hall magnetic field and currents (Figures 1m–1o),
identified as regions 2 and 3. Note that the positive Hall BM upon entry is rather weak in the present event,
but such asymmetry is not unusual at the asymmetric magnetopause [Mozer et al., 2008]. For this event again
the currents are independently and accurately estimated by the curlometer and particle measurements, with
parallel and perpendicular components consistent with expectations from previous work and simulations
(Figure 2b). As for the first event, strong parallel currents and enhanced (parallel) temperature anisotropy are
observed at the edges of the exhaust, suggestive of parallel electrostatic potentials and Fermi acceleration.
After region 3, the spacecraft does not exit into the magnetosheath but apparently comes back toward
the magnetopause (region 4) before a final exit at 10:33:37 UT. Given the particularly low magnetic field
and the absence of a strong Hall magnetic field signature in region 4, it is possible that the spacecraft
approaches the electron diffusion region during this period. This is also confirmed by the estimation of the
distance to the X line: 6.5 ion skin depths. This estimation was performed as for the first event using a normal
vector (0.92; 0.02; 0.4)GSE from multispacecraft timing, a normal speed of 12 km/s, and a magnetosheath
density of 20 cm 3. Note that given the proximity to the X line, the determination of the timing was complex
in this case. The estimated normal speed likely varies over time as exemplified by the second reentry into the
diffusion region, for instance.
Whether the event of 16 October 2015 is an actual electron diffusion region is not addressed further here, as
the focus of the present paper is on current systems and electron pitch angle scattering and bouncing in the
vicinity of this region, rather than in specifically studying the electron diffusion region. The reader is referred
to ongoing MMS studies on this topic which will soon be published. As further detailed in section 4, Figure 1k
shows again enhanced isotropy in the 200 eV electron PAD in the identified diffusion region as compared to
the surrounding magnetospheric and magnetosheath electron populations (which are again, respectively,
bidirectional and unidirectional at this energy).

4. Electron Focusing and Bouncing in the Hall Region

The event on 3 October 2015 above was presented first as a textbook case of ion diffusion region crossing
and to highlight the observation of broader PAD at various distances from the X line. Now we focus on the
more detailed observation of electron focusing and bouncing in the vicinity of the X line based on the 16
October 2015 event. This event is chosen for more detailed analysis because the spacecraft likely approached
closer to the X line on that day than on 3 October 2015, and the slow crossing (cf. section 3) better empha-
sizes key transitions, namely, (1) the gradual focusing and bouncing of electrons and (2) the spatial separation
of the scattering as a function of electron energy.

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Figure 3. MMS observations zoomed on an interval of interest during the event of 16 October 2015. (a) The magnetic field magnitude and (b) the 200 eV electron
PAD. Figure 3b also shows with a thick dashed line the pitch angle focusing expected from adiabatic behavior (cf. text for details). (c–f) PAD spectrograms at four
electron energies of about >600 eV, 400 eV, 100 eV, and 20 eV. The thick vertical lines mark the passage from an anisotropic population (peaked at 0° and/or 180°) to
2
an isotropic population for each energy. (g–i) The magnetic field radius of curvature, the error associated with the method, and the adiabatic parameter κ for four
different energies based on the results of a magnetic curvature analysis (MCA; cf. text and supporting information for details).

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Figure 3a shows the magnetic field strength, while Figure 3b displays the PAD for electrons at 200 eV for the
interval of interest on 16 October 2015. As mentioned previously, while these 200 eV electrons show clear
anisotropies at the beginning of the interval (in the magnetosphere) and at the end of the interval (in the
magnetosheath), much more isotropic PADs are observed in the low magnetic field regions. Superimposed
on the electron PAD spectrogram we show with a thick dashed line the expected narrowing/broadening
of both field-aligned and anti–field-aligned electron populations as a function of magnetic field strength
assuming conservation of the first adiabatic invariant. We take for this purpose an outer magnetic field
strength of 30 nT (chosen to best match the observed pitch angle focusing), which we consider as a mirror
point (BMIRROR; this corresponds to where the dashed line ends on the left-hand side), and calculate the
expected focusing/broadening of an adiabatic electron population as follows: α = sin 1(√(|B|/|BMIRROR|)).
The dashed line shows that field-aligned and anti–field-aligned electrons follow the expected
focusing/broadening. Going forward in time from the left-hand side of the dashed line, however, a new
electron population centered on 90° pitch angle appears at 10:33:26.5 UT. This population gradually broad-
ens as the magnetic field magnitude decreases. A faint demarcation (slightly lower fluxes) between this
population and the more field-aligned population is observed throughout the event. This demarcation is
particularly clear in the interval 10:33:34–10:33:37 UT, for instance. This latter interval is remarkable for
demonstrating that in fact, the pitch angle extent of both the (anti–)field-aligned and 90°-centered popula-
tions follow the thick dashed line. Thus, the broad, nearly isotropic population observed in the regions of
lowest magnetic field strength also obeys an adiabatic behavior. It gradually peaks and thus mirrors at 90°
pitch angle, as the electrons try to exit the low magnetic field region. This population is thus bouncing
(quasi-trapped) in the low magnetic field region near the X line in the ion diffusion region. Given the
expected topology in the vicinity of an X line, the 90°-centered population is only quasi-trapped because it
will eventually convect away from the X line vicinity where the magnetic field typically does not show as
prominent magnetic field minima (so this population cannot remain trapped indefinitely as reconnected field
lines propagate in the outflow direction).
Our interpretation of the above observations is as follows. The out-of-plane BM magnetic field signature is
induced by the observed perpendicular Hall currents throughout the region. The field-aligned and anti–
field-aligned populations just outside the lowest magnetic field region correspond to those carrying the out-
ward field-aligned currents measured at the edges of the region (with enhanced parallel temperatures).
These strong parallel currents may result from combined field-aligned electrostatic potentials and Fermi-type
acceleration. This is supported by increased parallel electron temperatures at these locations and past
simulations. Estimates of the parallel electrostatic potentials are, however, left for future work. The inflowing
population gets more and more focused along the magnetic field that threads the diffusion region as the
magnetic field strength decreases. The appearance of the 90°-peaked population (e.g., 10:33:26.5 or
10:30:37.0 UT) is interpreted, on the other hand, as a locally mirroring population which comes from near
the vicinity of the X line or main current sheet where the magnetic field strength is very low but the magnetic
field curvature very high. Scattering, and possibly additional energization, of the field-aligned electrons is
thus expected to occur close to the X line and main current sheet. The electrons scattered there are able
to travel outward some distance along the magnetic field before mirroring back toward the X line. They bounce
back and forth as long as a sufficient magnetic field minimum or parallel electrostatic potential remains in the
vicinity of the main current sheet. This explains both the colocation of the two electron populations and their
adiabatic behavior (PADs “bordered” by the thick dashed line) in the Hall region where they are largely mag-
netized. The bouncing mechanisms (adiabatic mirroring and parallel potentials) and pitch angle observations
suggest the existence of a loss-cone effect whereby only part of the initially scattered distribution function
(nonparallel electrons) can be trapped while parallel electrons are lost along the field lines.

5. Electron Scattering in Highly Curved Magnetic Field Lines

We now focus on a more detailed investigation of where and how the scattering occurs. Figures 3c–3i show
MMS data zoomed on the first entry into the ion diffusion region for the 16 October 2015 event. The four first
panels (Figures 3a–3d) show electron PADs at four different energies (>600 eV, 500 eV, 100 eV, and 20 eV).
The next panels (Figures 3g–3i) show the results of a Magnetic Curvature Analysis (MCA) performed on this
interval, the details of which are presented in Shen et al. [2003] and in the supporting information associated
with this paper. The errors related with the method have been shown to be on the order of the ratio of the

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spatial scale of the tetrahedron (spacecraft separation of order ~10 km for this event) to the spatial scale of the
structure (here the local magnetic field curvature radius). It should be noted that the MCA has been used in
many previous studies and has shown its ability to produce meaningful curvature estimates at all scales that
could be reached with past missions: current sheets and plasmoids [Shen et al., 2008; Rong et al., 2011; Zhang
et al., 2013; Yang et al., 2014], as well as larger scale structures such as the ring current [Shen et al., 2014].

As introduced previously, theory [Büchner and Zelenyi, 1989] predicts that particle scattering occurs when κ2
nears 25 and that the particle dynamics becomes chaotic for values below 10. Figure 3g shows the expected
high curvature in the lowest magnetic field region, as estimated from the MCA. Figure 3h shows the errors,
which are also reported in Figures 3g and 3i and increase as expected in the region of increased curvature.
Despite large errors, the scale of the MMS tetrahedron is sufficiently small to study the magnetic field
curvature down to the scale of low energy electrons. This is demonstrated in Figure 3i where the κ2 value for
five electron energies are shown. These energies correspond to those shown in the PAD spectrograms of
Figures 3c–3f (apart from 200 eV, for which the PAD is similar to that at 100 eV). Thick vertical black lines are
shown in the PAD for each energy, except for the highest energy where no distinction can be made regarding
the anisotropy owing in part to low count rates. Going forward in time from the left, these vertical lines show
the time at which anisotropic distributions with primarily field-aligned and anti–field-aligned populations
disappear, or in other words where these electrons have been scattered (in angles and possibly also in energy)
to other parts of velocity space. These vertical lines roughly correspond to the times at which the colored curves
(for each energy) in Figure 2i start to approach a κ2 value of 25, as predicted by theory for pitch angle scattering
in curved magnetic field lines. Near the center of the region with the lowest magnetic field and highest curvature,
electrons at all energies appear scattered and much more isotropic than at other times.

As can be seen for the 100 eV and 200 eV populations (Figures 3e and 3b), the time at which the field-aligned
population is scattered is later, i.e., closer to the X line or current sheet, than the time at which the broader
population peaks at 90°. This confirms the interpretation of section 4 that while scattering occurs close
to the X line, parts of the scattered electrons bounce back and forth in the outflow region and mirror at
significant distances so that a large part of the Hall region contains both populations simultaneously (both
contribute to the parallel/perpendicular current structure of the ion diffusion region). These high-resolution
electron observations bear a strong resemblance with recent simulation results [e.g., Ng et al., 2011; Bessho
et al., 2014, 2015; Haggerty et al., 2015; Egedal et al., 2015; Wang et al., 2016].

6. Conclusions
Thanks to unprecedented high-resolution electron measurements from NASA’s MMS mission, the intricate
dynamics of electron populations and associated currents in the vicinity of the diffusion region of magnetic
reconnection at Earth’s dayside magnetopause are revealed. We have shown that electrons are scattered
most likely by the highly curved geometry of the magnetic field lines in this region. This was demonstrated
by the scattering being observed closer to the X line as the energy of electrons decreases. With the small
separation of the MMS spacecraft, the local magnetic field curvature could be studied down to the electron
scale and down to energies as low as 20 eV. We showed that the scattering process, combined with trapping
mechanisms, leads to the superposition of two electron populations in parts of the Hall region: one inflowing
population (carrying outward field-aligned currents likely related to parallel electrostatic potentials and Fermi
acceleration) whose PAD width focuses as it approaches the main current sheet with lower magnetic field,
and one outflowing population, whose source is the inflowing population that has been scattered closer
to the X line or current sheet and then bounced back and forth in the magnetic field minimum of the ion
diffusion region and exhaust. This second population can reach the observing point, away from its scattering
location, as long as it is not forced to mirror back. The mirroring is observed as a gradual peaking toward 90°
pitch angle away from the magnetic field minimum and is expected to result from both adiabatic mirroring
in stronger magnetic field and trapping by parallel electrostatic potentials. We finally stress that while the
present study shows a strong relation between electron scattering and magnetic field line curvature, future
studies ought to investigate the relative role of electric fields and waves for a more complete description of
electron dynamics. These novel electron-scale observations have broad impact on our current understanding
of the fine structure of plasma populations in the vicinity of the reconnection region, in particular with regard
to magnetic reconnection theory and numerical modeling.

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Acknowledgments References
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