# Intermittent Electron-Only Reconnection at Lunar Mini-Magnetospheres

A. Stanier Los Alamos National Laboratory, Los Alamos, New Mexico, USA
<EMAIL_ADDRESS>Li-Jen Chen NASA Goddard Space Flight Center, Greenbelt, MD,
USA  A. Le Los Alamos National Laboratory, Los Alamos, New Mexico, USA  J.
Halekas Department of Physics and Astronomy, University of Iowa, Iowa City,
IA, USA  R. Sawyer Department of Physics and Astronomy, University of Iowa,
Iowa City, IA, USA

###### Abstract

Lunar crustal magnetic anomalies (LCMA) are sub-ion-gyroradius structures that
have been shown to stand off the solar wind (SW) plasma from the Moon’s
surface, forming shock-like discontinuities and reflecting incident SW
protons. In this letter, the results of high-resolution, two-dimensional fully
kinetic simulations show a bursty electron-only magnetic reconnection in the
SW-LCMA interaction region, characterized by the quasi-periodic formation and
ejection of magnetic islands and strong parallel electron flows along the
X-point separator lines. The islands are observed to modify the magnetic
pressure pile-up and Hall electric field above the LCMA, leading to sharp
increases in reflected protons that drive electromagnetic fluctuations
downstream and short distances upstream in the SW.

Moon — magnetic fields — shock waves — plasmas — solar wind

##  1 Introduction

The Moon does not have a global-scale magnetic field dipole to shield it from
charged particles in the solar wind (SW). To lowest order, the SW particles
are incident on and absorbed by the lunar surface to leave a deep void in the
downstream wake (Lyon et al., 1967; Colburn et al., 1967). The interplanetary
magnetic field (IMF) passes through the Moon with only a weak enhancement in
the downstream wake (Colburn et al., 1967), that is supported by diamagnetic
currents at the wake boundaries (Owen et al., 1996; Fatemi et al., 2013).

However, this lowest order description is enriched by the presence lunar
crustal magnetic anomalies (LCMAs), which are distributed in a complex and
multi-polar pattern over the Moon’s surface (Coleman et al., 1972; Purucker &
Nicholas, 2010). The scale size of these anomalies varies between $1-1000$ km
(Dyal et al., 1974) with surface magnetic field strengths of up to a few
hundred $nT$, falling to a few $nT$ at $100$ km altitude.

Despite their small scale, LCMA can have an significant impact on the incident
solar wind. Spacecraft measurements have detected reflection of up to 50% of
incident solar wind protons above LCMA (Futaana et al., 2003; Lue et al.,
2011), some of which can be energized by the convective electric field and
even gyrate into the deepest part of the near-Moon wake (Nishino et al., 2009;
Xu et al., 2020). This strong modulation of the solar wind flux at the LCMA
can affect the surface albedo and cause the bright lunar swirl patterns
visible on the lunar regolith (Hood & Schubert, 1980; Deca et al., 2018).
Further, sharp enhancements of the magnetic field have been measured
downstream of the LCMAs close to the limb – so-called “limb-compressions”
(Russell & Lichtenstein, 1975; Lin et al., 1998; Halekas et al., 2017), that
are suggestive of a shock-like structures forming upstream of the LCMA (Lin et
al., 1998; Halekas et al., 2014).

The SW-LCMA interaction has been investigated by numerical simulation using a
variety of different plasma models. Early efforts used a single-fluid
magnetohydrodynamics (MHD) description (Harnett & Winglee, 2003). With the
size of the interaction region being less than the ion skin depth,
$d_{i}=c/\omega_{pi}$ with $c$ the speed of light and $\omega_{pi}$ the ion
plasma frequency, this motivated studies using Hall-MHD (Xie et al., 2015),
hybrid kinetic-ion fluid-electron (Giacalone & Hood, 2015; Fatemi et al.,
2014), and fully kinetic (Deca et al., 2014, 2015; Bamford et al., 2016)
models.

An important question regarding SW-LCMA interaction concerns the possible
occurrence and effects of magnetic reconnection (Ji et al., 2022) between the
IMF and the LCMA fields. Earlier kinetic simulations noted the lack of typical
reconnection signatures (Deca et al., 2014, 2015) such as bi-directional
reconnection outflow jets. However, recent data from ARTEMIS at $15$ km
altitude (Sawyer et al., 2023) have measured the Hall electric field at LCMA,
as well as the presence of solar wind electrons on closed magnetic field-lines
– an indication of reconnection having occurred between the IMF and the LCMA
fields. Reconnection has also been observed at Mars (Eastwood et al., 2008;
Halekas et al., 2009) – another body without a global dipole field – with the
MAVEN spacecraft detecting reconnection occuring above a Martian crustal
magnetic anomaly (Harada et al., 2018). If reconnection can indeed occur
between the solar wind IMF and the LCMA, the sub-ion scale-size of the
interaction region suggests that demagnetized ions would not form the
characteristic bipolar reconnection outflow jets, and the regime may be more
similar to electron-only reconnection observed in the Earth’s magnetosheath
(Phan et al., 2018).

In this paper, we report 2D kinetic particle-in-cell simulation results that
show a bursty electron-only magnetic reconnection occurring in the SW-LCMA
interaction region, characterized by the quasi-periodic formation and ejection
of magnetic islands and parallel electron flows along the separator lines of
the magnetic X-points. These islands were found to form only for simulations
with close to realistic values of the proton-electron mass ratio, such that
the electrons are strongly magnetized and the aspect ratio of the current
layer is large enough to become tearing unstable. The presence of these
islands is found to modify the pressure balance between the LCMA and the solar
wind inflow, increasing both the magnetic field pile-up strength and the Hall
electric field. The resulting quasi-periodic increases in the reflected ion
fraction produce observable “spike” features in the simulated ion density
profiles, as well as rapidly varying magnetic field enhancements that can
propagate both downstream and a short distance upstream of the LCMA.

##  2 Numerical Simulations

In this paper, results are presented from 2D electromagnetic particle-in-cell
simulations of the solar wind-LCMA interaction. The simulations are performed
using the Vector Particle-In-Cell (VPIC) code (Bowers et al., 2008; Bird et
al., 2021).

###  2.1 Simulation set-up and boundary conditions

The solar wind plasma and interplanetary magnetic field are injected at a
constant rate and orientation from the $x=0$ inflow boundary. The solar wind
velocity vector is in the $+x$ direction,
$\boldsymbol{v}_{SW}=v_{SW}\boldsymbol{\hat{x}}$, and the IMF lies in the
$x-y$ plane making an angle
$\theta_{IMF}=\arctan{\left(\frac{B_{y,IMF}}{B_{x,IMF}}\right)}$ from the
solar wind direction.

For the inflow boundary at $x=0$, and the top/bottom boundaries of the
simulation domain (at $y=0,L_{y}$), we choose boundary conditions based upon
the initial solar wind/IMF values. Particles colliding with these domain
boundaries are absorbed, and new particles are sourced at the boundary at each
step based upon the drifting Maxwellian distribution function used for the
solar wind. The VPIC code uses a typical Yee-mesh (Yee, 1966; Birdsall &
Langdon, 2004) scheme for spatial discretization of the electromagnetic fields
that is staggered in space, such that only the tangential electric field and
normal magnetic field components lie exactly on the domain boundaries. The
components are fixed equal to their initial values as
$B_{n}=\boldsymbol{\hat{n}}\cdot\boldsymbol{B}_{IMF}(t=0)$ and
$E_{t}=-v_{SW}\boldsymbol{\hat{x}}\times\boldsymbol{B}_{IMF}(t=0)$. (It was
found that setting additional field components such as $B_{t}$ gave rise to
unphysical fluctuations in the inflowing plasma). The spatial domain was
sufficiently large (see below) that the locally strong LCMA fields become
negligible at the domain boundaries, and the SW and IMF parameters there match
the initial and boundary values used.

All particles incident on the Moon and the outflow boundary at $x=L_{x}$ are
absorbed, with their accumulated surface charge $\rho_{\textrm{surface}}$
being used to correct
$\boldsymbol{\nabla}\cdot\boldsymbol{E}=\left(\rho_{\textrm{surface}}+\rho_{\textrm{plasma}}\right)/\epsilon_{0}$,
and no particles (e.g. photoelectrons) are presently sourced from the Moon’s
surface. The IMF is allowed to pass freely through the Moon and the outflow
boundary ($x=L_{x}$).

###  2.2 Solar wind and LCMA parameters

Solar wind plasma parameters and IMF strength are chosen based upon ARTEMIS
spacecraft observations (Halekas et al., 2014) of shock-like compression
features being detected at high altitude (periselene $~{}420$ km) above the
Lunar surface. The density of the solar wind $n_{SW}=12.5$ cm-3, the solar
wind velocity $v_{SW}=300$ km sec-1, and the proton and electron temperatures
are $T_{p}=T_{e}=7$ eV. The IMF strength is $|B_{IMF}|=7.5$ nT, where the
orientation angle $\theta_{IMF}=-30^{\circ}$. In terms of dimensionless
parameters, these give an Alfvén Mach number $M_{A}=6.7$, and solar wind
plasma beta $\beta_{i}=\beta_{e}=0.6$. The mass ratio is $m_{i}/m_{e}=1836$.
The ratio of the electron plasma to cyclotron frequencies is set to the value
of $\omega_{pe}/\Omega_{ce}=2$ in the results presented below, but we have
checked the sensitivity of the results up to $\omega_{pe}/\Omega_{ce}=8$ (at
lower mass ratio) without finding significant qualitative differences in the
results.

The 2D LCMA fields are applied via line-dipole currents below the surface. For
a 3D (ring) magnetic dipole with strength $3\times 10^{13}Am^{-2}$ this would
stand-off the solar wind at a distance of $D_{p}=35\textrm{km}=0.55d_{i}$ from
the dipole center, using the solar wind parameters specified above, and have a
strength of $2$ nT at 100 km altitude. Here, for our 2D model, we determine
the line dipole strength by matching this pressure stand-off distance to the
3D value. The line-dipole is buried $15$ km $=0.23d_{i}$ below the surface of
the Moon, such that the effective pressure stand-off distance would be $20$ km
$(0.32d_{i})$ above the surface. The LCMA is at a solar zenith angle of
$-45^{\circ}$.

The spatial domain used is $12.5\times 12.5d_{i}$ ($536\times 536d_{e}$ with
$1d_{e}\approx 1.5$ km). This is resolved with $8192\times 8192$ cells to give
a constant mesh size of $\Delta x=0.065d_{e}=0.24\lambda_{D}$, where $d_{e}$
is the electron skin depth and $\lambda_{D}$ is the electron Debye length.
There are an average of $50$ particles per cell for each species. The
simulation is run a significant time prior to the presented results
($t\Omega_{ci}>8$), so that the solar wind passes through the domain and
carries away any initial transients associated with the initial conditions.

##  3 Results

Figure 1: Ion density (color scale) normalized by the solar wind density
$n_{\textrm{SW}}$, and magnetic field lines (white), shown at four snapshots
separated by $0.05\Omega_{ci}^{-1}=92\Omega_{ce}^{-1}$. The Moon (gray) is at
the upper right corner of each plot. The spatial coordinates are given in
electron skin depths ($1d_{e}\approx 1.5$ km). The region shown is only a
small part of the full domain.

Figure 1 shows the formation and ejection of a magnetic island, occuring on
electron time-scale in the SW-LCMA interaction region. In the initial plot
(1a), the X-point is located above the LCMA dipole-center line and close to
the surface of the Moon. This X-point position is displaced upwards from the
vacuum field location, indicative of large currents in the SW-LCMA interaction
region, and this displacement is found to be noticeably larger for simulations
with $m_{i}/m_{e}\gtrsim 400$. A tearing instability, with an associated
electron stagnation point flow (see below), leads to the formation of a
magnetic island (1b), which grows in size due to the reconnection of magnetic
flux at the upper and lower X-points (1c). At its largest size the magnetic
island is elongated with semi-major radius $25d_{e}$ and semi-minor axis
$12.5d_{e}$. The magnetic island is then ejected downwards and reconnects with
the open magnetic field-lines coming from the southern pole of the LCMA. These
field-lines are strongly perturbed from their initial orientation parallel to
the Moon’s surface (1d), to generate a small-scale disturbance that propagates
downstream above the Moon’s surface (see below). The total time taken for the
formation and ejection of the magnetic island is $\approx
0.2\Omega_{ci}^{-1}\approx 367\Omega_{ce}^{-1}$ based upon the interplanetary
magnetic field strength $B_{\textrm{IMF}}$.

Figure 2: Line integral convolution (LIC) of the ion bulk velocity field
(left) and the electron bulk velocity field (right). The ion plot is colored
by the ratio of the ion to solar wind speed, and the electron plot is colored
by the ratio of the electron parallel velocity to the solar wind speed. The
white contours show the magnetic field lines and the Moon (gray) is in the
upper right corner. The spatial coordinates are given in electron skin depth
($1d_{e}\approx 1.5$ km).

Figure 2 shows line integral convolution (LIC) plots of the ion and electron
bulk velocities around the SW-LCMA interaction region in the presence of a
magnetic island. Due to the small scale size of the LCMA compared with the ion
kinetic scales, the bulk ion flows are only weakly deflected by the LCMA
fields and magnetic island, although they are decelerated to a minimum
velocity of $u_{x}\approx 0.2v_{SW}$ along a line that passes through the
vertical center of the dipole source. In particular, there are no discernible
ion outflow jets associated with reconnection occurring at the X-points. In
contrast, the electron flows are strongly modified by the magnetic topology.
There are strong parallel flows of electrons along the topological separators
of both of the X-points that reach about $3v_{SW}$ at times when there is an
island present.

Figure 3: Top: Contours show magnetic field-lines and the color scale shows
ion density. Bottom: Ion velocity distribution functions $F(v_{x})$ computed
along the horizontal line. The white vertical lines correspond to the green
dots in the top plots. The magenta lines show the predicted $v_{x}$ for
$v_{x}(t=0)=v_{\textrm{SW}}$ which is accelerated/decelerated by an electric
field $E_{x}=-\partial_{x}B_{y}^{2}/(2\mu_{0}n_{e}e)$. The left column is
without an magnetic island, and the right column has an island present with
radius $\sim 0.25d_{i}$.

Figure 3 shows a comparison of the reduced ion distribution function,
$f(x,v_{x}),$ at two times - without (left) and with (right) a magnetic island
present in the interaction region. In both cases, the incoming solar wind
population with mean $\overline{v}_{x}=v_{SW}$ experiences significant
reflection at the boundary of the closed LCMA field-lines. However, the
fraction of ions reflected is significantly more when the magnetic island is
present. The large number of reflected ions gives a visible ‘spike’ feature in
the plasma density (top right), which is locally increased to $\approx
3\times$ the background value. By integrating inflowing and reflected parts of
the distribution function over the $y$-extent of the LCMA dipole field, the
total fraction of ions reflected at the location of the density spike feature
is $40\%$ without the island, and increasing to $70\%$ in the case where the
island is present.

At both times, with or without the island present, we find that the ions are
reflected by Hall electric fields resulting from the different magnetizations
of the ions and electrons. The electrons, being magnetized, are frozen into
the magnetic field and deflected by the magnetic barrier, while the ions
having a large gyro-radius do not experience significant magnetic deflection.
However, as described below, the resulting strong Hall electric fields can
slow down and reflect the ions.

Consider an ion with mass $m_{i}$ and charge $q_{i}$ moving with the mean
solar wind velocity $v_{x0}=v_{SW}$. If it is assumed that the ion is
sufficiently unmagnetized, the velocity change in response to an electric
field is given by

$v_{x}\approx v_{x0}+(q_{i}/m_{i})\int{E_{x}dt}.$ (1)

Now, assuming that the electron fluid obeys the frozen-in condition, the Hall
electric field has dominant term given by

$E_{x}\approx-\frac{j_{z}B_{y}}{en_{e}}\approx-\frac{\partial_{x}B_{y}^{2}}{2n_{e}\mu_{0}e}.$
(2)

(This expression can also be derived as
$\boldsymbol{E}=-\boldsymbol{\nabla}\phi$ using the electrostatic potential
$\phi$ derived in Bamford et al. (2012); Cruz et al. (2017)).

The magenta dashed line plotted in the bottom panels of Fig. 3 is found by
integrating Eq. (1) with the Hall electric field from Eq. (2), and closely
matches the shape of the distribution functions. Thus, the Hall electric field
is responsible for the decelerations and accelerations of ions in the
calculated distribution function. For the snapshot with the magnetic island,
the IMF magnetic field first piles-up to increase $B_{y}^{2}$ on the left edge
of the magnetic island, passes through zero at the island center, before again
piling up at the LCMA closed field boundary. This is the cause of the small
dip in the inflowing ion velocities at $x=228d_{e}$, followed by the
subsequent acceleration up to $x=235d_{e}$ and final deceleration/reflection
features. Even though there is no magnetic island in the left hand plots, the
displacement of the X-point up towards the Moon’s surface gives similar
qualitative magnetic field-line profiles along the magenta horizontal line
where the distribution function is calculated. The presence of the magnetic
island however gives stronger increase of $B_{y}^{2}$ due to pile-up, thus
giving stronger deceleration/acceleration features, and reflecting a larger
fraction of ions back upstream.

Figure 4: Left: Ion density (color scale) and magnetic field-lines (white) at
time $t\Omega_{ci}=10.15$ (when there is a magnetic island present). The
spatial coordinates are given in electron skin depth ($1\,d_{e}\approx 1.5$
km). Right: Absolute value of the magnetic field ($|\boldsymbol{B}|/B_{0}$)
sampled from the green line (top right plot) and red line (bottom right plot),
plotted against distance along each line from upstream to downstream
(horizontal axes) in ion-skin depths ($1\,d_{i}=\sqrt{1836}\,d_{e}$), and time
(vertical axes) in $\Omega_{ci}^{-1}$. The white lines indicate $v=v_{SW}$
(top) and $v=-v_{SW}$ (bottom).

Figure 4 shows how fluctutations in density (left plot) and magnetic field
strength (right plots), caused by the quasi-periodic formation of islands,
propagates downstream above the lunar surface (green line, top right plot),
and back upstream into the solar wind (red line, bottom right plot). A density
spike feature caused by reflected ions (see above) is visible next to the red
line in the left hand plot. The magnetic compressions are as large as
$\boldsymbol{B}/B_{IMF}\approx 5$ at the island but reduce to
$\boldsymbol{B}/B_{IMF}\approx 1.7$ by $\approx 2d_{i}$ downstream. The
perturbations are carried with the solar wind velocity $v_{SW}$ downstream
(white line). As shown in the bottom right panel, such magnetic compressions
might also be detected a short distance upstream of the LCMA fields, even in
the direction perpendicular to the inflowing IMF (red line), but these
signatures drop off to small values over a shorter distance ($\lesssim 15\%$
by $\approx 0.5d_{i}$ upstream). The white line shows a propagation velocity
$v=-v_{SW}$, suggesting that the disturbances propagate back upstream by the
reflected ion population. Note that for the simulation parameters specified in
Sec. 2.2, the characteristic velocities are well separated with

$\frac{v_{th,e}}{v_{SW}}(=3.6)\gg
1\gg\frac{v_{A}}{v_{SW}}(=0.15)\gg\frac{v_{th,i}}{v_{SW}}(=0.084).$

###  3.1 Discussion

The simulations described indicate the occurrence of a bursty electron only
reconnection due to the repeated formation and ejection of magnetic islands,
and the generation of strong electron parallel flows along the separator lines
of the X-points in the SW-LCMA interation region. Moreover, this system
exhibits interesting dynamical behavior that is not seen in more typically
studied magnetospheric systems with more separation between the shock and
reconnection physics. Namely, the quasi-periodic formation of islands leads to
a time variabilty of the solar wind stand-off and pressure balance, and gives
sharp modulations the proton reflectivity via changes in the Hall electric
field. These protons in turn drive increased fluctuations downstream and
upstream in the SW to generate observable magnetic field compressions.

Our simulations use a realistic mass-ratio and are the first to show
signatures of electron-only reconnection and the formation of magnetic islands
at sub-ion-scale crustal fields. For example, (Deca et al., 2014) report
having observed no signatures of magnetic reconnection from their simulations.
While our simulations also do not show the ion jets that are characteristic of
macroscopic reconnection, the formation of islands and accelerated parallel
electron flows along the X-point separator lines indicate electron-only
reconnection. There are several differences to our simulations that could
explain this discrepancy. Firstly, at lower values of the ion-to-electron mass
ratio $m_{i}/m_{e}<400$, we have observed that the formation of islands
becomes more marginal, and the SW-LCMA interaction region becomes stable for
lower values of $m_{i}/m_{e}\approx 100$. Although a formal boundary layer
analysis of the tearing mode is difficult for the LCMA current sheet, due to
the complex geometry of the fields and flows in the region and the lack of
scale separation that makes the calculation tractable, some insight can be
gained by modeling it as a Harris sheet with electron-scale thickness. By
neglecting additional stabilization mechanisms such as shear flows, a lower
bound for the instability threshold can be estimated when the parameter
$\Delta^{\prime}>0$, where

$\Delta^{\prime}=\frac{2}{\delta}\left(\frac{1}{k\delta}-k\delta\right).$ (3)

The longest wavelength mode corresponding to a single magnetic island has
$k=k_{\textrm{min}}=2\pi/L$ where $L$ is the length of the current sheet. Thus
$\Delta^{\prime}>0$ for $L>2\pi\delta$. In the time between the formation of
magnetic islands, we measure the FWHM thickness $\delta=1.2d_{e}$ and aspect
ratio $L/\delta\approx 12.5$, thus exceeding the $\Delta^{\prime}$-threshold
for a tearing instability. On the other hand, for a simulation with
$m_{i}/m_{e}=100$ and the same resolution ($\Delta x/d_{e}=0.06$), we find
$\delta\approx 1.3d_{e}$, but the length decreases to $6.2d_{e}$ (as the
length of the current distribution is limited by spatial-scale of the LCMA
fields that is set in terms of ion inertial lengths). This gives an aspect
ratio $L/\delta=4.8$ (below the threshold) that fits with the absence of
islands forming in that simulation. This may explain why islands have not been
seen in other kinetic simulations of sub-ion-gyroradius scale LCMA run with
lower values of $m_{i}/m_{e}$. We note that for mini-magnetospheres with
larger than ion-scale stand-off distances, magnetic islands have been observed
in PIC simulations (Cruz et al., 2017).

The quasi-neutral hybrid simulations of Giacalone & Hood (2015) use an IMF
angle such that a magnetic X-point forms to one side of the main LCMA field.
They find that strong magnetic gradients between the X-type neutral point and
the stronger LCMA surface field can generate an additional spatially separated
Hall electric field, and this is found to give rise to a distinct secondary
population of reflected protons. Our study supports the observation that the X
and O-type magnetic topological points can modify the Hall electric structure
and modulate the reflected proton flux. However, some of the main features
reported in this letter regarding the time dependence of the reflected proton
flux, the magnetic island formation, and the accelerated electron flows along
the magnetic field-lines were not observed in the kinetic-ion fluid-electron
hybrid simulations reported by Giacalone & Hood (2015), presumably because
these processes depend on electron kinetic physics that is not present in the
hybrid model (Winske et al., 2023).

The use of two-dimensional simulations allows us to simulate larger spatial
domains ($12.5\times 12.5d_{i}$, $8192\times 8192$ cells) and mass-ratios
($m_{i}/m_{e}=1836$) than would be feasible at present in 3D domains. However,
this does impose a key limitation: the effectively infinite extent of a line
dipole source in $Z$ in our 2D simulations constrains the electrons to flow
around the LCMA in the $X$-$Y$ plane only, whereas in 3D the strong electron
flow in the $Z$ direction would be limited in length by the extent of the LCMA
structure in that dimension. As the magnetic field becomes frozen into the
electron flows on sub-ion scales, it can experience different advection by
such flows, which can produce a different distribution of current about the
LCMA in 3D vs 2D. Future work will explore 3D effects on this process at
similar mass ratios to those used in our 2D study, and also study the
influence of more complex multiple-dipole models of the LCMA fields (as in
e.g. Harnett & Winglee, 2003; Xie et al., 2015), to give a larger length of
the SW-LCMA interaction region that may increase the likelihood of flux-rope
formation due to tearing instabilties.

It may be possible to observe the quasi-periodic propagating magnetic field
compressions and density spikes shown in Fig. 4 with the ARTEMIS spacecraft at
periapsis, as they can be distinguished from fluctuations in the background
solar wind through pitch-angle distributions. There may also a possibility to
experimentally study the formation of magnetic islands in kinetic scale
magnetic dipole configurations that resemble mini-magnetospheres, which can be
formed inside laser driven plasmas (Schaeffer et al., 2022). Indeed, small-
scale magnetic islands are becoming quite commonly measured in electron-scale
current sheets in other laboratory reconnection experiments (Olson et al.,
2016; Jara-Almonte et al., 2016; Kamio et al., 2018), including in the
electron-only regime (Olson et al., 2016).

This research was supported by the NASA MMS and HERMES missions, and by the
DOE Frontier Plasma Science Program. J.H. and R. S. were supported by the
THEMIS-ARTEMIS mission (NASA contract NAS5-02099), and the Solar System
Exploration Research Virtual Institute (80NSSC20M0022).

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