# Statistical Characteristics of the Electron Isotropy Boundary

###### Abstract

Utilizing particle data from the ELFIN satellites, we present a statistical
study of $\sim$2000 events from 2019-2020 characterizing the occurrence in
magnetic local time and latitude of $\geq$50 keV electron isotropy boundaries
(IBs), and the dependence of associated precipitation on geomagnetic activity.
The isotropy boundary for an electron of a given energy is the magnetic
latitude poleward of which persistent isotropized pitch-angle distributions
($J_{prec}/J_{perp}\sim 1$) are first observed to occur. The boundary is
interpreted as resulting from magnetic field-line curvature scattering (FLCS)
in the equatorial magnetosphere, a process that violates the first adiabatic
invariant of particle motion. The FLCS isotropization mechanism is readily
recognizable over a wide range of electron energies (10s of keV to several
MeV) in the often highly dynamic transition region between the outer radiation
belt and plasma sheet, where such populations are commonly found. We find that
electron IBs can be well-recognized on the nightside from dusk until dawn,
under all geomagnetic activity conditions, with a peak occurrence rate
(averaged over all activity levels) of almost 90% near $\sim$22 hours in
magnetic local time (MLT), and remaining above 80% from pre- to post-midnight
(21 to 01 MLT). The IBs span a wide range of IGRF magnetic latitudes from
$60^{\circ}$-$74^{\circ}$, with a maximum occurrence between
$66^{\circ}$-$71^{\circ}$ (L of 6-8), shifting to lower latitudes and pre-
midnight local times as geomagnetic activity increases. The precipitating
energy flux of $\geq$50 keV electrons averaged over the IB-associated
latitudes varies over four orders of magnitude, up to $\sim$1 erg/cm2-s, and
often includes electrons of energy exceeding 1 MeV. The local time
distribution of IB-associated electron energies and precipitating fluxes also
exhibit peak values near midnight for low activity, shifting toward pre-
midnight for elevated activity. The percentage of the total energy deposited
over the high-latitude regions ($55^{\circ}$ to $80^{\circ}$; or IGRF
$L\gtrsim 3$) attributed to IBs is 10-20%, on average, or about 10 MW of total
atmospheric power input. The IB-associated electron energy deposition, while
narrow in latitude, can however be up to $\sim$100% of the total $\geq$50 keV
electron energy deposition over the entire sub-auroral and auroral zone
region, at times exceeding 1 GW in total atmospheric power input. Both the
total IB-associated precipitating flux intensity and its relative contribution
to the total precipitating energy over the sub-auroral and auroral zone
increase with AE, $|$Dst$|$, and Kp. We discuss implications of these results
for atmospheric energy deposition, ionospheric conductivity enhancement,
magnetospheric electron losses and magnetic field mapping.

JGR: Space Physics

Department of Earth, Planetary, and Space Sciences, UCLA

Colin<EMAIL_ADDRESS>
Using observations by the ELFIN CubeSats in 2019 and 2020 we statistically
characterize the properties of 50 keV to $\sim$5 MeV electron isotropy
boundaries (IBs), including occurrence rates, spatial distribution, and
associated precipitating energy fluxes versus magnetic local time, latitude,
and geomagnetic activity indices

We found that electron IBs occur over a wide range of nightside local times
and latitudes under any geomagnetic conditions, and exhibit four orders of
magnitude variation in electron precipitation due to geomagnetic activity.
They contribute on average up to 20% of the total high-latitude nightside
$\geq$50 keV electron precipitation, at times becoming the predominant
contributor to such precipitation

We discuss implications of IB precipitation for selected magnetospheric and
ionospheric processes, global atmospheric power input, and applications of IB
observations to magnetic field and particle flux modeling

## Plain Language Summary

In Earth’s magnetosphere, energetic electrons are often trapped by the
geomagnetic field, which can shield the planet and orbiting satellites from
potentially dangerous effects. However under certain conditions, especially on
the nightside of the magnetosphere, the magnetic field can become too weak or
curved to maintain such trapping, and electrons can be lost to the atmosphere,
where they collide and give up their energy (i.e., precipitate). On a poleward
moving satellite, the magnetic latitude at which the flux of precipitating and
magnetically-reflected (locally trapped) electrons of some energy first become
equal is known as its isotropy boundary (IB) latitude for that energy. This
happens because at that latitude the magnetic field intensity at the
magnetically conjugate equator becomes too small and thus unable to maintain
the particle’s cyclical motion, allowing it to scatter in its pitch-angle with
respect to the field direction. The electron distribution consequently
randomizes in pitch-angle and many electrons thus precipitate. This latitude
varies with electron energy and local time, and with geomagnetic activity,
which affects the underlying magnetic topology near Earth. Isotropy boundaries
for various energies can be observed by low-altitude polar-orbiting satellite
missions equipped with particle detectors able to discriminate the electron
flux as a function of pitch-angle and energy, such as ELFIN. Here, we
characterize statistically the properties of IBs, such as their occurrence
rate versus longitude and latitude, as well as the energy they deposit into
the atmosphere at different geomagnetic activity levels. This ultimately
allows for better understanding and predictive capability of space weather
effects, as well as for improvement in magnetic field and electron flux
models.

##  1 Introduction

###  1.1 Background

A major objective in the study of Earth’s magnetosphere-ionosphere system is
to characterize the space processes leading to the precipitation of energetic
charged particles. One such process is magnetic field-line curvature
scattering (FLCS; occasionally referred-to as “current-sheet scattering”), in
which the increased curvature and decreased strength in the equatorial
magnetic field at large distances can scatter particles above a certain energy
non-adiabatically in pitch-angle, isotropizing their flux distributions. Both
electrons and ions (including heavy ions) can be affected in this way, though
at different distances from Earth. The result of this flux isotropization is
that precipitating and mirroring fluxes become comparable (i.e.,
$J_{prec}/J_{perp}\sim 1$), for particle energies that have equatorial gyro-
radii exceeding a critical threshold [Gray Lee (1982), V. Sergeev . (1983),
Birmingham (1984), Delcourt . (1996), Martin . (2000), Young (2002)]. For
electrons, such FLCS-isotropization can happen at energies as low as a few 10s
of keV and upward, including the 100s of keV to multi-MeV electrons found in
the vicinity of the outer radiation belts [W. Imhof . (1979)]. Furthermore,
due to the nightside equatorial near-Earth magnetic field often exhibiting a
gradual change in intensity and curvature versus radial distance near the
dipole-tail transition region, it is possible for this scattering process to
act on different minimum energy particles over an extended range of L-shells,
magnetically mapping to an extended range of latitudes in the ionosphere [V.
Sergeev Tsyganenko (1982)]. Fluxes which have been isotropized by this process
can be detected by polar-orbit satellites traversing a range of field-lines
connected to the equatorial scattering region. The magnetic latitude
corresponding to the onset of isotropy as a function of increasing (absolute)
latitude for a particular particle species and energy is known as the
_isotropy boundary_ (or “IB”) for that species and energy [V. Sergeev .
(1983)]. Given its ability to rapidly fill the loss cone over a wide energy
range, local time, and latitudinal range, the process of curvature scattering
presents a potentially significant means by which energetic particles and
their associated kinetic energy can be deposited into the atmosphere in the
vicinity of IBs.

Contrary to proton IBs, whose properties have been well-explored previously
[V. Sergeev Tsyganenko (1982), V. Sergeev . (1983), Newell . (1998), Donovan
(2003), Yue . (2014), VA. Sergeev, Chernyaeva . (2015), Dubyagin . (2018)],
the electron IBs have received less attention and their occurrence and
properties have been poorly investigated [VA. Sergeev . (2018), Capannolo .
(2022)]. This has largely been due to observational constraints of past
studies, which have contended with limited latitudinal coverage (e.g. RadSat,
UARS, Van Allen Probes, GOES, Geotail, THEMIS, etc.), or issues with particle
detection capability, such as insufficient electron pitch-angle resolution and
energy range, dynamic range or sensitivity, uncertainties in sensor cross-
calibration between look directions, and cross-species contamination (e.g.
POES, DMSP). Because energetic electron IBs are found as high as $74^{\circ}$,
exhibit orders of magnitude variation in flux and precipitation energy, and
often appear poleward of proton IBs, previous studies were ill-equipped to
fully characterize their properties. To address these issues, we used recently
acquired data from the Electron Losses and Fields Investigation (ELFIN)
satellites [Angelopoulos . (2020)], whose observations from circular polar Low
Earth Orbit (LEO) provide latitudinal coverage spanning 55∘ to 80∘, 24 hours
in aggregate local time, and electron energies between $\sim$50 keV and
$\sim$5 MeV, with a single, low-noise, high-sensitivity, proton-rejecting
electron sensor used to measure fluxes over all pitch-angles during each spin
(once per 2.8 seconds).

Beyond characterization of the electron IB proper, the properties and role of
isotropic $\geq$100 keV electrons associated with IBs in several important
magnetospheric and ionospheric processes have remained similarly veiled. For
example, because FLCS-isotropized electrons can include populations of tens of
keV and up to the MeV range, they can penetrate to lower altitudes into the
high-latitude atmosphere than typical auroral fluxes, potentially increasing
conductivity and chemical reactivity at altitudes as low as the ionospheric
D-region [Fang . (2010)]. Additionally, because the FLCS isotropization
mechanism can act rapidly (on the order of a bounce period) in the equatorial
region where inward radial diffusion transports particles into the outer
radiation belt, it can potentially prevent such particles from ever becoming
trapped. These flux losses would not be accounted for as part of outer
radiation belt precipitation due to being outside the trapped flux region.
Such efforts are also confounded by the fact that the isotropy boundary is
difficult to recognize on equatorial spacecraft traversing the tail-dipole
transition region, because the loss cone at the equator is only $\sim$1∘, too
small to resolve by typical particle instruments; thus their fluxes are not
accounted for in energetic precipitation modeling and prediction based on such
data. Further, knowledge of the IB location as a function of time can be a
useful tool for near-instantaneous remote-sensing of the equatorial magnetic
field configuration, and of the particle populations residing there. This can
help refine equatorial magnetic field and particle flux models, especially
when paired with equatorial satellites [VA. Sergeev . (1993), VA. Sergeev,
Chernyaev . (2015), Ilie . (2015), Shevchenko . (2010)]. Here, we expand on
preceding observational results, which have reported the presence of both
isotropic electrons and protons with energies above typical plasma sheet
auroral processes ($>$10s of keV) throughout the magnetosphere, but especially
on the nightside.

For electrons in particular, past studies have reported isotropic
precipitation structures often found within $\pm$4 hours of midnight,
persisting for multiple spacecraft orbits (timescales of hours) with well-
populated (filled) loss cones up to several MeV in energy [WL. Imhof . (1977),
W. Imhof . (1979), WL. Imhof . (1997)]. The most striking feature of these
structures was the energy-latitude dispersion in the onset of isotropy: higher
energies were monotonically isotropized at lower latitudes than lower energies
[WL. Imhof . (1997)]. These combined properties suggested that the underlying
generation mechanism must persist over a wide range a geomagnetic conditions,
and could not be due to transient processes, such as wave-particle scattering.
It was proposed that such long-lasting isotropy structures were likely the
result of particle scattering by the curvature of the background magnetic
field within the cross-tail current, which extends both in latitude and in
local time around midnight. Similar isotropy boundary effects for protons have
been reported to occur at lower latitudes, the latter characteristic explained
as due to the larger gyro-radii of protons. Interestingly, intense localized
peaks in energetic proton precipitation were found to often occur in close
poleward proximity to the proton IB (itself close to the auroral oval), with
an apparent pre-midnight peak occurrence [Newell . (1998)]. This suggests that
the IB precipitation may be replenished by repeated instances of freshly
accelerated and transported particles from the magnetotail. The equivalent
properties for electron IBs are addressed in this work. For completeness, we
note that interactions with magnetopause may give rise to similar dispersive
isotropic particle scattering onto Earth-connected field lines [Lyons .
(1987)], although these cases are not the focus of this study, and have been
excised from our database.

###  1.2 Model of energetic electron isotropization

Isotropy boundaries emerge when freshly accelerated (heated) particles convect
or drift through the near-earth equatorial magnetosphere near locations of
strong equatorial magnetic field curvature or weakened strength. After
traversing the equator, the resulting modification of a particle’s pitch-angle
depends highly on the ratio of its incoming gyroradius ($r_{L}$) to the local
scale length of variations in the background magnetic field. On the nightside
in particular, as the distance from Earth increases, the most significant
magnetic scale variations correspond to the smallest (sharpest) magnetic
curvature radius $R_{C}=|\hat{\bf b}\cdot\nabla\hat{\bf b}|^{-1}$ of the
field, where $\hat{\bf b}={\bf B}/B$ is the unit tangent vector to the
magnetic field ${\bf B}$. The most pronounced effects can be expected at the
close Earthward vicinity of the cross-tail current, which marks a transition
from a dipole-like field to an extended tail and is also accompanied by a
local field strength gradient. If the particle gyroradius is much smaller than
the field line curvature (i.e. $r_{L}\ll R_{C}$), the particle retains its
first adiabatic invariant $\mu$ (possibly imparting an impulsive change in
gyro-phase), and executes traditional guiding-center bounce and drift motions
about the equatorial plane. However, if the particle gyroradius begins to
approach the local equatorial radius of curvature (e.g., for higher energy
particles), non-adiabatic effects emerge [Gray Lee (1982), Young (2002)].

When equatorial particle crossings become non-adiabatic due to the local
geometry of the background magnetic field (as above), the resulting motion
depends further on the ratio of the minimum magnetic curvature radius to the
maximum equatorial particle gyroradius, defined in prevailing literature as
$\kappa^{2}=R_{C}/r_{L}$ [V. Sergeev Tsyganenko (1982), Martin . (2000)], as
well as the particle’s incident gyrophase. The case of $\kappa^{2}\sim 1$
results in Speiser-like motion [Speiser (1965)], while the range
$3\lesssim\kappa^{2}\leq\kappa^{2}_{cr}$ results in strong diffusive pitch-
angle scattering, leading to isotropy upon repeated crossings of the
equatorial plane (i.e. $J_{prec}/J_{perp}\sim 1$). Owing to the strong
diffusion, only a few crossings are usually required to achieve isotropy. The
particular critical value of $\kappa^{2}_{cr}$ required for efficient
isotropization is independent of particle species and varies only with the
magnetic field configuration in the scattering region, although at a fixed
location (and field-line curvature) electrons isotropize at a higher minimum-
energy than protons due to their smaller mass and smaller gyroradius. A
threshold of $\kappa^{2}_{cr}=8$ is commonly taken as an _a priori_ value
based on a Harris-type current sheet with constant $B_{normal}$ [Gray Lee
(1982), V. Sergeev . (1983)], though it can take on values between 3 and 33
over the range of possible magnetotail configurations [Ilie . (2015)]

Upon isotropization by equatorial curvature scattering, particles typically
resume motion toward Earth along field lines, where they can be profiled in
latitude by low-altitude polar spacecraft such as ELFIN. To provide a
theoretical reference of the particle energy versus latitude at which FLCS-
based isotropy could be expected to appear, we re-cast the critical
$R_{c}\leq\kappa^{2}_{cr}r_{L}$ relationship in terms of a minimum required
particle kinetic energy $E_{min}^{iso}$ for isotropic field-line scattering,
computing it based on model-mapped equatorial magnetic field properties at the
crossing location:

$E_{min}^{iso}=\left(\gamma_{min}^{iso}-1\right)mc^{2}=\left[\left(1+\left(\frac{qBR_{C}}{\kappa^{2}_{cr}mc}\right)^{2}\right)^{1/2}-1\right]mc^{2}$
(1)

where $\gamma_{min}^{iso}$ is the minimum particle Lorentz factor
corresponding to the minimum required particle energy for isotropization, $q$
is the particle’s charge, $B$ is the equatorial magnetic field strength,
$R_{C}$ is the equatorial radius of curvature, $\kappa^{2}_{cr}=8$ as
explained above, $m$ is the mass of the particle, and $c$ is the speed of
light.

Using this relation, an example spatial profile of minimum electron kinetic
energies for efficient isotropization due to FLCS is shown in Fig. 1 over the
50 keV to 5 MeV energy range, using the combined IGRF and T89 field models
[Alken . (2021), Tsyganenko (1989)] at midnight local time (GSM coordinate xz-
cut) for $\kappa^{2}_{cr}=8$ and $K_{p}=2$ on 2020-09-02/14:22 UT. The profile
shows that the regions capable of isotropizing 50 keV to 5 MeV electrons are
confined to the equatorial plane at distances beyond several earth radii,
corresponding to the dipole-tail transition from a dipole-like field to that
of an extended magnetotail. The model-computed isotropy boundary field-line
traces for 50 keV and 5 MeV energies are shown as blue and pink traces,
respectively.

The above model predicts that on an equator-to-pole traversal of the pertinent
field lines, as seen from a LEO polar satellite vantage point, the highest
energies are isotropized first, at the lowest latitudes (smallest equatorial
distances), due to their larger gyroradius and corresponding ratio to the
equatorial curvature. The minimum energy of isotropization decreases
monotonically as the vantage point latitude increases. This energy-latitude
dispersion, characteristic of IBs, is a consequence of the field-line mapping
progressively further away from Earth (especially on the nightside), where the
equatorial field strength and/or radius of curvature are reduced and, as a
result, the minimum required energy for isotropic scattering by Eqn. 1 is also
reduced. In Fig. 1, the equatorial region corresponding to the portions of the
IB dispersion ELFIN could observe is shaded yellow. The mint and light blue
lines are the poleward and equatorward boundaries, respectively, of the IB
dispersion region observable by ELFIN, corresponding to the ELFIN energetic
particle detector’s energy limits.

These dispersed energy-latitude isotropy signatures are the basis of IB event
identification and modeling in our study. The modeled dispersion slope and
minimum field-line scattering energy at a given latitude depend on the choice
of magnetic field model and the quantity $\kappa^{2}_{cr}$. Although the data
may have significant uncertainties associated with true field-line mapping,
and the field model of choice may not fully represent the instantaneous
magnetic topology, we assume that both IB crossings and model exhibit a
monotonic energy-latitude dispersion for event-identification and modeling
purposes. We note also that this model predicts that electrons exceeding the
minimum required scattering energy continue to be isotropized at latitudes
extending beyond their IB; however, in reality as the mapped field-line
distance increases appreciably beyond the IB dispersion region, the electron
dynamics can become intertwined with other plasma sheet processes.

###  1.3 Outline

In the following, we first describe the ELFIN dataset and then discuss the
methods used to determine the presence of isotropy boundaries and the
intensity of the associated precipitation. We next report observations of the
IB occurrence rates versus MLT, L-shell, magnetic latitude and geomagnetic
activity indices, alongside the observed electron energy ranges and slope of
IB energy-latitude dispersion. We then discuss the computation methods and
interpretation of the deposited electron energy flux associated with the
IB/FLCS-dominated region. We finally summarize our findings and discuss their
implications, potential applications, and the next steps in this line of
investigations.

##  2 Methods and dataset

###  2.1 ELFIN dataset

We use data collected by the Energetic Particle Detector for electrons (EPD-E)
instrument aboard each of the two Electron Losses and Fields Investigation
(ELFIN) CubeSats. The satellites were in polar LEO (at $\sim$450 km altitude),
drifting about 1 hour in magnetic local time per month. The EPD-E instruments
have an energy range of approximately 50 keV to 5 MeV, sub-divided into 16
logarithmically-spaced energy channels of width less than 40% (i.e. $dE/E\leq
0.4$), with a $22^{\circ}$ field of view and geometric factor of $\sim$1
cm2-str. The satellites were spinning with a nominal rotation period of 2.8 s
about an axis nearly perpendicular to the background magnetic field, allowing
for pitch-angle determination of incident particles. The particle data
collected in each spin period was subdivided in time into 16 spin sectors
($\Delta t\sim 175$ ms) by the on-board data processing unit, which were
combined in ground processing with IGRF and attitude data to determine the
local pitch-angle distributions. The attitude of the spacecraft typically
allows for resolution of both the loss cone and locally-mirroring particle
populations. Proton contamination was mitigated by an absorbant aperture foil,
while side-penetrating particles were rejected by a combination of dense
shielding and detector coincidence logic. The data and processing tools are
publicly available using the ELFIN routines within the SPEDAS framework
[Angelopoulos . (2019)].

To form the statistical event database, a list of $\sim$2600 ELFIN science
zone crossings ($\sim$6-7 minute data collections encompassing outer-belt and
auroral zone crossings) were identified and subjected to preliminary event-
selection criteria. Since the FLCS mechanism depends on the large-scale
background magnetic field configuration and bulk particle transport, which can
vary on the timescale of tens of minutes to hours, each science zone
collection can be regarded as an instantaneous snapshot of IB properties.
These science zones were collected as a part of ELFIN’s Outer Belt
Observations (OBO) mode, which is designed to extend between $55^{\circ}$ to
$80^{\circ}$ in (absolute) magnetic latitude in a single hemisphere (L-shells
$\gtrsim 3$), computed using the International Geophysical Reference Field
(IGRF) model, though the start and stop limits of each individual collection
can vary by up to several degrees due to the operational implementation
method. The data in our study were obtained in 2019 and 2020, spanning the
full range of magnetic local times (MLTs). We binned these data in 1 hour
magnetic local time intervals, encompassing $>$40 collections in each MLT bin.
Significantly more science zone collections were available near midnight and
on the dayside than at other MLTs, requiring normalization by residence time
to remove this observational bias. The collections spanned a wide range of
geomagnetic activity, including storms and substorms. Because in the early
part of the mission satellite spin-axis attitude was not controlled to be
orbit-normal (which would provide the widest pitch-angle coverage), but,
rather, science zones were targeted based on attitude being closest to ideal,
further checks of our dataset were necessary to ensure the loss-cone was
cleanly measured. We inspected and culled the above preliminary database to
ascertain that the satellite attitude permitted sufficient pitch-angle
resolution to compute precipitating-to-perp flux ratios (only a few events had
to be eliminated by this process). To limit the possibility of under-counting
high-latitude IB events, we also required that all science zones spanned an
(IGRF-computed) L-shell exceeding $L=8$. Finally, we eliminated all events
with known instrument performance issues (evident in quality flags). These
constraints collectively reduced the qualifying science zones (QSZ) available
for further analysis to 1922; these formed our final event database.

###  2.2 Prototypical electron isotropy boundary crossing

A prototypical example of a qualifying ELFIN science zone collection
containing an IB crossing is shown in Figure 2. During this $\sim$6 minute QSZ
window the ELFIN-B satellite moved southward from the northern polar cap
toward the magnetic equator. The top two panels show the in-situ perpendicular
($J_{perp}$) and precipitating ($J_{prec})$ energy flux spectrograms for 50
keV to 5 MeV electrons. The energy-time spectrogram of flux isotropy ratio
$R_{I}=J_{prec}/J_{perp}$ in Panel 3, is computed from the ratio of Panels 1
and 2. Until shortly before 14:21 UT, only relatively low energy ($\leq 200$
keV) electrons are present and exhibit a high isotropy ratio ($\sim$1),
suggesting a traversal of an extended electron plasma sheet. That the
electrons are isotropic signifies a source location poleward of the isotropy
boundary, where their energies exceed the threshold for field-line scattering.
At around 14:21 UT, a rapid rise in energetic ($\geq 300$ keV) isotropized
electron fluxes is observed, suggesting that the satellite entered the
transition region between the inner edge of the electron plasma sheet and
outer radiation belt, or tail-dipole transition region (herein dubbed the
“PS2ORB” interface, and adhering to a specific observational definition to be
introduced later). The emergence of isotropic fluxes over such a high energy
range not typically found in the plasma sheet, nor associated with any known
persistent wave-particle acceleration process, is consistent with the
satellite being on field lines connected to a dynamical transition region
dominated by field-line scattering poleward of but in close proximity to the
isotropy boundary. Around 14:22 UT, an abrupt transition from isotropic to
anisotropic fluxes over the energy range from 50 keV to 4 MeV is observed.
Viewed in reverse-time (i.e., from increasing latitude), the latitude where
flux anisotropy transitions to flux isotropy at each energy (i.e., the
isotropy boundary at that fixed energy) increases as the energy decreases.
This inverse (negative) latitude-energy dispersion is exactly what is expected
for the isotropy boundary dispersion with energy, in which higher energies
isotropize first, at lower latitudes. Based on this, we conclude that this QSZ
interval contains an IB crossing.

Panel 5 shows the isotropy boundary location (red) as a function of energy and
latitude, as determined by an automated procedure. The jagged (occasionally
non-monotonic) nature of the curve is a consequence of poor counting
statistics at the highest energies. Also shown in the same panel is a model-
based prediction of the boundary location, obtained by equatorial footpoint
tracing of the ELFIN orbit with the Tsyganenko 1989 field model, and using
$\kappa^{2}_{cr}=8$ for the isotropy boundary determination for each energy.
The blue line results from a direct application of the model, which is earlier
in time (hence poleward in magnetic latitude) by $\sim$15 s ($\sim$1∘)
compared to observations due to model mapping uncertainties. This implies the
equatorial peak cross-tail current density was apparently further away from
Earth in reality at the collection time, causing the tail-dipole transition in
the model to be further away from Earth and map to a higher latitude. By
fitting a constant latitudinal offset to the model energy-latitude dispersion
(blue line) to best match the observation (red line), we obtain the green
line. The latitude-shift required to match the observations is a measure of
how far the model peak cross-tail current distance from Earth deviates from
the actual. For this event, the observed IB profile lasts $\sim$15 s across
all energies, and is in good agreement with the modeled-then-shifted IB
profile (errors less than 1 spin period of latitudinal uncertainty). The
latitudinal shift required to co-locate the IB crossings provides valuable
information for further investigation and model improvements that are beyond
the scope of this work.

After crossing the IB, the satellite moved into the outer radiation belt and
subsequently in the trough (where locally-trapped relativistic electron fluxes
subsided). Around 14:22:30 UT and 14:22:50 UT, near-isotropic fluxes were
again observed but only at the lowest energies, $<$300 keV, despite the fact
that locally-mirrored fluxes were abundant at all energies up to $\sim$3 MeV.
This fact, and the lack of an energy-latitude dispersion, suggests the cause
of this precipitation is likely a process other than field-line scattering,
such as wave-particle interactions, and therefore unrelated to the IB. Panel 6
shows the net precipitating electron energy flux, integrated over energy and
solid angle within the loss cone. This is used to estimate both the relative
and total amounts of average precipitating energy flux associated with the
isotropy boundary. Panels 7-10 display the pitch-angle spectra for select
energy channel ranges, alongside horizontal bars indicating the local bounce-
loss/anti-loss cones. Panel 11 shows the IGRF magnetic field at the spacecraft
location, for reference.

###  2.3 Statistical characterization

To obtain the statistical results of the study, we performed the preceding
type of analysis on each ELFIN QSZ data collection. We then manually inspected
the events for the presence of an electron isotropy boundary. To assess
whether an IB was present we computed the flux isotropy ratio
$R_{I}=J_{prec}/J_{perp}$ and checked for energy-latitude dispersion
signatures consistent with the field-line curvature scattering mechanism (e.g.
as in Fig. 1). In order for a science zone to be marked as containing an IB
crossing, and to distinguish it from other potential precipitation processes,
the candidate crossings were required to satisfy several criteria: 1) a
poleward transition from anisotropy to isotropy (defined as $R_{I}\geq 0.6$)
for energy channels with non-zero counts, followed by persistently isotropic
flux $(R_{I}\sim 1)$ for at least 50% of the subsequent non-zero poleward data
samples; 2) at least three energy channels satisfying condition 1), and thus
usable towards identification of an IB dispersion signature; 3) a negative
data-fitted energy-latitude dispersion slope, one consistent with higher-
energy electrons becoming isotropized at lower latitudes (or, at most, at
apparently the same latitudes given the finite spin-period time-resolution of
ELFIN measurements). To limit the effects of low-counting statistics, the
quantity $R_{I}$ was assumed to be 0 for cases in which the measurement
uncertainty was more than a factor of 2. Additionally, we rejected IBs with
equatorial footpoints residing within 3 Earth radii (or outside of) a model
magnetopause [Fairfield (1971)]. This was done to eliminate false IB-like
particle signatures which may result from scattering at the magnetospheric
boundary (particularly on the dayside and flanks). For cases which satisfy all
of the preceding criteria, the event was marked as containing an IB crossing.

We next determined the occurrence rate distribution of IB crossings in our
database of ELFIN QSZ collections versus MLT, magnetic latitude (MLAT),
L-shell (IGRF or T89-based), and geomagnetic activity (based nominally on AE,
and including Dst and Kp for characterization of IB-associated energy fluxes).
We also binned likewise the IB-associated (latitude-averaged over the PS2ORB
interface), integral (over energies $\geq$50 keV) electron precipitating
energy flux. This average was presumed to be dominated by field-line curvature
scattering. To obtain the average flux precipitating due to field-line
scattering over the PS2ORB interface, we used the following operational
definition of the PS2ORB interface region: The equatorward-most PS2ORB
interface latitude was taken to be the IB for the maximum observable isotropic
electron energy, while the poleward-most PS2ORB interface latitude was taken
to be the omni-directional flux cutoff in $\geq$300 keV electrons poleward of
its IB (see the Results Section for rationale). For cases in which the 300 keV
electron channel was not present (or its IB could not be clearly identified),
the next-closest energy channel cutoff was used to mark the PS2ORB poleward-
most latitude. From these events we also determined the minimum and maximum
electron energies of the IB crossing dispersion, alongside the average energy-
latitude slope of the dispersion. We lastly computed the latitudinal width of
the combined IB plus PS2ORB interface region, which provides an estimate of
the spatial extent of the equatorial FLCS-dominated region at the collection
time.

##  3 Results

###  3.1 Occurrence, spatial distribution, and dispersion of electron IBs

To provide an initial picture of the spatial distribution of electron IBs in
our dataset, the equatorial footpoints corresponding to the minimum and
maximum L-shell of field-line traces bounding the IB dispersion region (based
on T89) are shown in Figure 3 as a scatter plot, projected in the equatorial
GSM xy-plane. The points marked $L_{min}$ represent the most Earthward
portions of the IB crossings (typically corresponding to the highest-present
electron energy IB; variable from event to event), and the point marked
$L_{max}$ similarly represents the furthest portion of the IB dispersion in
the crossings (almost always corresponding to the 50 keV electron IB). The
static reference-magnetopause based on [Fairfield (1971)] is shown (solid)
alongside the 3 earth radius cutoff (dashed) used to reject false IB
signatures, which are marked in silver and black (counted as non-IB but
otherwise valid events). It is evident that projected isotropy boundary
locations span a wide range of MLTs and mapped equatorial distances throughout
much of the nightside magnetosphere.

Figure 4 shows the electron IB spatial distribution. The top panel depicts the
histogram of isotropy boundary occurrence (absolute and normalized) versus MLT
in our database, binned with a bin size $\Delta MLT=1$ hour. Blue bars denote
the number distribution of all QSZ events in our database, orange bars depict
the number of events with an IB (both referring to the absolute numbers on the
left vertical axis), and red line is the normalized occurrence rate of IB
crossings versus MLT in the dataset (corresponding to the right vertical
axis), computed as the ratio of the orange to blue values. A running average
with $\pm$1-hour MLT window was applied to the data, to improve statistics and
reduce uncertainties, e.g., in field-line mappings.

We find that IB crossings occur in up to 90% of events near midnight, and
exhibit a sustained occurrence rate of $\geq$80% between 21 to 01 MLT. Their
occurrence rate gradually declines towards near-zero at pre-dawn (7 MLT) and
near dusk (16 MLT). Interestingly, the peak IB occurrence is not centered at
midnight but at pre-midnight, around 22 MLT. (We note that the apparent peaks
in event number around 01 and 15 MLT are due to the reduced ELFIN data
availability in the first two years of the mission used here; i.e., in the
2019-2020 period.) The associated spatial distribution of these IB events
binned by L-shell ($\Delta L=1$) and magnetic latitude ($\Delta$MLAT = 1∘)
using the IGRF model are shown in Fig. 4 middle and bottom, respectively. IGRF
alone, not T89, was used to compute the distribution in this case to provide a
static reference independent of the behavior of the magnetic field far from
earth, with the caveat that this will typically underestimate the true L-shell
and latitude mappings at the nightside as distances from Earth increase, and
for different solar wind driving. We see that electron IBs span a wide range
of L-shells (4 to beyond 12), and are most commonly found to span L-shells
6-8, typically corresponding to the tail-dipole transition region, or PS2ORB
interface region. As anticipated from the L-shell to $|$MLAT$|$ equivalence in
mapping, a similar trend is observed in magnetic latitude: a broad range of
occurrences between $60^{\circ}$ to $74^{\circ}$, with peaks around
$66^{\circ}$-$70^{\circ}$. Additionally, we checked the occurrence of IB
crossings versus the geomagnetic activity indices AE, Dst, and Kp (not shown),
and found them to not vary appreciably from the overall MLT distribution
described here.

In these events, we also characterized the minimum and maximum electron
energies of the observed dispersion in the IB crossings, alongside the
latitudinal spread and dispersive slope (“sharpness”), versus MLT and
activity. Given that the IB generation mechanism is based on the background
magnetic field configuration and the local availability of energetic particles
(e.g. injections), it is reasonable to expect that the level of geomagnetic
activity and solar driving at the time of (and preceding) the crossing would
affect the electron energies appearing in the IB, as well as the latitudinal
onset and sharpness of isotropic dispersion. In order to provide an assessment
of this activity-dependent behavior, we separated the dataset into two
categories: quiet-time intervals with 1 hour average AE less than 200 nT, and
non-quiet intervals with 1 hour average AE above 200 nT. This choice of
hourly-average AE split the dataset roughly in half and aimed to emphasize
high-latitude geoeffectivity while avoiding complications of the potential
time-delayed nature of other indices (such as Dst at storm time).

Figure 5 displays the activity-dependent minimum and maximum observed IB
electron energies versus MLT, where solid points represent the mean values and
error bars represent the occurrence-weighted standard deviation about the
mean. The top panel shows the minimum and maximum electron energies appearing
in the dispersion of IB crossings within the ELFIN EPD instrument sensitivity
and energy limits. For low activity (AE$<$200 nT) the electron energies span a
typical maximum of 700-800 keV, peaking at MLTs near midnight, and trailing
toward a lower average maximum in the 300-400 keV range near dawk and dusk.
For higher activity (AE$>$200 nT), the maximum energies rise dramatically to a
mean of 2 MeV, and are shifted in local time to pre-midnight (peaking around
22 MLT), with the maximum energies falling to 800-900 keV at MLTs approaching
dawn and dusk. The apparent shift in peak energy to the pre-midnight during
active times is consistent with the idea of the FLCS source being supplied by
frequent (possibly continual) local energetic flux injections in the tail at
these MLTs [Gabrielse . (2014), Liu . (2016)], which the background field
rapidly isotropizes. At both quiet and non-quiet times the low-energy minimum
of the IB is almost always the lowest energy channel resolvable by the ELFIN
EPD ($\sim$62 keV mean). This suggests that the IB likely extends to lower
energies than ELFIN can resolve, and that such fluxes are highly available in
the tail for FLCS at the rates reflected by IB occurrence in each MLT sector.

Using this activity criterion, we also determined the MLT-binned latitudinal
bounds and sharpness of the energy-latitude dispersion in the IB crossings.
The center row panels in Figure 5 show the IGRF L-shell distribution (left)
and magnetic latitudes (right) bounding the onset in isotropic dispersion
across all resolved energies. The quantities denoted “min” reflect the most
Earthward (i.e. lowest latitude, often highest-energy) portion of the
dispersion while the “max” values mark the more distant location at which the
lowest energy channel is first observed to become isotropic. The results show
that at low activity, there is a symmetric bowl-shape distribution with global
minimum around 22 MLT with $L_{min}\sim 7.1$, $L_{max}\sim 7.3$ and
$MLAT_{min}\sim 67.6^{\circ}$, $MLAT_{max}\sim 67.9^{\circ}$, rising to a
maximum of $L_{min}\sim 8.6$, $L_{max}\sim 8.9$ and $MLAT_{min}\sim
69.8^{\circ}$, $MLAT_{max}\sim 70.0^{\circ}$ at 5-6 MLT. Interestingly at both
activity levels the mean latitudinal width (max minus min) of the dispersion
in the crossings is nearly constant across MLT, suggesting a highly persistent
supply of injected particles of appropriate energies (top panel) and
appropriate background field configuration across many local times on the
nightside, such that they are repeatably affected by FLCS. At higher activity,
IB dispersion is found consistently at lower latitudes across all MLTs, with
the emergence of a break from the symmetric bowl-shape distribution around 22
MLT. This feature is again consistent with the appearance of energetic
electron injections at lower latitudes, e.g. during substorms. Rather than
being localized to a single MLT, the active time latitudinal onset minima are
instead spread between 20-23 MLT, taking on values of $L_{min}\sim 6.3$,
$L_{max}\sim 6.5$ and $MLAT_{min}\sim 65.9^{\circ}$, $MLAT_{max}\sim
66.5^{\circ}$ and maxima around 4-5 MLT of $L_{min}\sim 7.6$, $L_{max}\sim
8.0$ and $MLAT_{min}\sim 68.4^{\circ}$, $MLAT_{max}\sim 68.8^{\circ}$. We note
that MLT sectors with fewer than 5 IB events are not shown, which is the
reason there are no data points for MLT 5-6 at active time versus quiet time.

Based on the observed energy and latitudal ranges of the IB crossings, we
finally computed the linear energy-latitude dispersion slopes $dL/dE$ and
$dMLAT/dE$ versus activity and MLT in the top and center panels. The bottom
panel shows the dispersion slope in terms of L-shell (left) and MLAT (right).
The data reveal that during quiet intervals the MLT-based distribution is
similarly bowl-shaped with a minimum slope (i.e. steepest latitudinal change
in energy) around midnight. As with the energies and latitudes, the dispersion
slope extrema shift to the pre-midnight at active times, with a universal
trend toward apparently sharper IBs. Such values provide insight into both the
equatorial profile of the magnetic field under these conditions and the
typical energies available from injections there. We note again that while
IGRF provides a practical activity-independent spatial reference, the reported
IB latitudes and slopes would be quite different (especially away from
midnight) versus models containing magnetospheric currents, such as the
magnetotail and the ring current (e.g. T89).

###  3.2 Precipitation associated with electron IBs

Next, we seek to quantify the amount and distribution of precipitating energy
flux associated with electron isotropy boundaries. The isotropy boundary for
each energy is by definition an instantaneous transition latitude (separating
isotropy from anisotropy), and consequently does not capture the finite
spatial extent of precipitation associated with the FLCS isotropization, which
is expected to extend into adjacent poleward latitudes (as seen in Fig. 2).
This prompts us to use an operational definition of the poleward extent of the
near-isotropic precipitation associated with the IB. To achieve this, we rely
on the fact that the inner edge of the plasma sheet proper (for which particle
processes other than FLCS may become dominant) can be regarded as a proxy for
the poleward edge in FLCS-dominated fluxes. To identify this edge in the data,
we relied on the fact that the plasma sheet typically possesses a high-energy
cutoff in electron fluxes at both quiet and active times [Christon . (1989),
Christon . (1991)]. By statistically determining the most common maximum
electron energy at which omni-directional fluxes experience a sustained drop-
out at latitudes poleward of IBs, we were able to define an operational
definition of the poleward edge of the IB-associated precipitation region,
otherwise referred to here the plasma sheet-to-outer radiation belt interface
region (“PS2ORB”). We note that the specific upper plasma sheet cutoff energy
found by this method depends on the sensitivity and resolution of the
instrument used to measure it, and thus had to be determined using the ELFIN
dataset (akin to that performed with ISEE observations in Christon et al.).

Figure 6 explores the energy-latitude dependence of omni-directional electron
flux cutoffs poleward of IBs in the ELFIN dataset, which are used to define
the operational outer edge of the PS2ORB region. The top panel depicts as a
function of energy the mean and median IGRF magnetic latitude of the lowest
latitude (highest energy) portion of all IB events for comparison with the
poleward cutoff in omni-directional electron fluxes. For energies $\geq$300
keV, there is a near-constant $\sim$$1^{\circ}$ separation in average magnetic
latitude between the lowest latitude portion of the IB crossings and of the
omni-directional flux dropouts. For energies $<$300 keV, this difference
begins to grow rapidly to $>$$3^{\circ}$, suggesting that a separate electron
population from the plasma sheet has been encountered. The bottom panel
repeats this analysis instead using the event-wise difference between the
lowest latitude IB and the poleward omni-flux cutoff. This value is also
around $1^{\circ}$ at $\geq$300 keV but suddenly increases with decreasing
energy, providing additional confirmation that the latitude of flux cutoff at
300 keV in each specific event is a reasonable proxy for the location of the
poleward boundary of the IB FLCS-dominated precipitation region. We thus
defined the poleward bounding latitude of the PS2ORB region as the latitude
beyond the IB at which $\geq$300 keV omni-directional fluxes first drop out.
Using this definition, the bottom panel shows the mean latitudinal width
$\Delta\theta$ of the PS2ORB region observed in the dataset versus local time
during quiet and non-quiet intervals. The data reveal that at quiet intervals,
the latitudinal width of the FLCS-dominated region is typically between
1-1.5∘, rising to 2-3∘ at non-quiet times. This is consistent at active times
with the IB/FLCS source having greater access to source particles to be
scattered (such as from injections and enhanced electric fields in the
magnetotail), as well as from modified equatorial background magnetic field
properties (such as during intervals of magnetospheric compression), which can
further shift and extend the FLCS-dominated region in latitude.

Using the above operational definition for the latitudinal bounds of the
PS2ORB interface region, we computed the average precipitating energy flux
within IB-associated latitudes from isotropic $\geq$50 keV electrons. We also
computed the net energy flux integrated over all latitudes including and
poleward of the PS2ORB region, and for the entire ELFIN science zone (from all
available latitudes – typically spanning $55^{\circ}$ to $80^{\circ}$). This
was done to provide a comparison of the relative magnitude of IB-associated
energy flux versus that which is sourced by other ELFIN-observable regions,
such as the outer radiation belts, electron plasma sheet, and the polar cap.
To compute the energy flux, we integrated the precipitating electron
distributions over energy and solid angle (pitch-angle and gyrophase), and
averaged over the number of data samples the spacecraft spent in each region
in each event. Figure 7 shows the distribution of energy flux in each of these
latitudinal ranges, including the entire science zone (blue), the IB crossing
and regions poleward of it (orange), and the IB/FLCS-dominated PS2ORB
interface region (green). We immediately see that the PS2ORB interface region
exhibits the highest average and maximum of the three categories. Comparing
the green and orange bars also reveals that the precipitation is confined in
latitude to the localized PS2ORB interface region adjacent to electron IBs,
rather than being evenly distributed over all poleward latitudes (e.g. in the
plasma sheet and polar cap).

To further investigate the occurrence and significance of IB-associated
precipitation, we computed the local time distribution of latitude-averaged
precipitating energy flux within the PS2ORB interface, as well as the fraction
of the net energy flux (over the entire ELFIN science zone) contributed by the
PS2ORB region. To assess how these quantities varied with geomagnetic
activity, they were also binned by the activity indices AE, Dst, and Kp, taken
independently of local time. We computed the total power deposition as the
product of the crossing time and average flux. This is because as a polar-
orbiting ELFIN satellite moves at roughly constant velocity across different
latitudes in space (approximately at the same longitude), the time-average of
the flux represents a line-integral over the latitudinal spatial dimension.
The resultant quantity is power deposited over an ionospheric swath along the
satellite track per unit cross-track distance (in ergs/s/cm or, re-scaled, in
Watts/km). Thus the time-average represents average power deposition at the
ionosphere at a given MLT, either over the entire science zone crossing, or
over the more limited PS2ORB region. Ratios of time-average total
precipitation in the PS2ORB region over that in the entire science zone
represent the fractional total energy per unit time, or fractional power, in
PS2ORB relative to the whole science zone. Figure 8 captures the total
fractional power (top) and average electron energy flux (bottom) of the
precipitation associated with the PS2ORB interface region (the IB FLCS
source). For each MLT sector (horizontal axis) the value in color (see color
bar) shows the fraction of the IB events possessing a value greater or equal
than shown vertical axis (i.e., cumulative proability). For example, we can
see in the top panel than 0.15 (or 15%) of PS2ORB events (orange color in
color bar) contribute, near midnight, $>$0.4 ($>$40%) of the total
precipitating power within their individual science zones, and we can see in
the bottom panel that 0.1 (or 10%) of PS2ORB events (yellow-green color) have,
near midnight, an average energy flux $\geq$10-1 erg/cm2-s. Note that here, as
with the IB occurrence vs MLT distribution, we performed a three-hour MLT
average on these values (central value plus and minus 1 hour). Pink lines in
the two panels represent means of relative precipitating power (top panel) and
average precipitating flux (bottom panel).

To summarize key features of these results, we see (top panel, pink line) that
within $\pm$4 hours of pre-midnight, the PS2ORB interface region precipitation
accounts for 0.1-0.2 (10%-20%) of the total precipitating power, on average.
While this is a small value, on average, the cumulative probability
distribution (top panel, color plot) shows that precipitating power $>$0.5
($>$50%) of the total within a science zone (vertical axis value: 0.5) occur,
near midnight, 15% of the time (yellow-orange colors: 0.15 in vertical color
bar). In extreme cases, near 22 MLT, up to $\sim$100% of the power can be
delivered by PS2ORB (albeit more rarely). The average total precipitating
energy fluxes (bottom panel) are found to span several orders of magnitude
across all MLTs. Interestingly, the peak relative and total amounts of
precipitating energy flux again occur in the pre-midnight sector around 22
MLT. As alluded to previously, this is likely due to preferential current
sheet thinning at pre-midnight, the related proximity of the cross-tail
current to Earth and the preponderance of substorm onset, and injections at
that location.

The results from Fig. 8 additionally allow for an estimate of the total global
atmospheric power input across all local times and latitudes from IB-
associated $\geq$50 keV electron precipitation. To determine the average
global power input across the dataset, we used the IB MLT and latitudinal
occurrence rates from Fig. 4 combined with the average PS2ORB latitudinal
extent from Fig. 7. Using the pink mean line from Fig. 8, we add up the
occurrence-weighted total energy flux in each 1 hour (15∘ longitude) MLT
sector scaled by the effective area of the PS2ORB projected onto the
atmosphere at the IB latitude, assuming 1∘ in latitude equates to 111 km
projected, and that both hemispheres contribute equally. This results in a
typical total atmospheric power deposition of around 10 MW at any given time.
However, in the most extreme (and rare) cases where energy fluxes approach 1
erg/cm2-s across several several hours in MLT, the total atmospheric power
input from IB-associated $\geq$50 keV electron precipitation can exceed 1
GW—possibly exceeding the input from auroral sources, and thus likely playing
an important role in ionospheric processes.

###  3.3 Energy flux variations with geomagnetic activity

Lastly, we explored the dependence of precipitation on geomagnetic activity.
Towards that goal we computed the distribution of relative precipitating power
and total energy flux in the PS2ORB interface region (IB-associated) versus
geomagnetic activity indices AE, Dst, and Kp. Figure 9 presents these results.
The top row corresponds to the PS2ORB interface region precipitating power
relative to the total power in the science zone (akin to Fig. 8 top) while the
bottom row contains the average precipitating energy flux (akin to Fig. 8
bottom). The AE values ($\Delta AE=100$ nT) were three-hour averaged leading
into the collection interval in order to capture longer-term activity trends
rather than individual short-term activity phases (e.g. as in substorms). The
final bin is integral covering the cases of AE$\geq$600 nT. The trend is for
both the relative power and total energy flux of PS2ORB precipitation to
increase with AE (for AE increase from 0 nT to 600 nT the relative power
increases by 30% and the total energy flux by several orders of magnitude). A
similar increase in PS2ORB precipitation is evident for relative power and for
total energy flux as Dst decreases from 0 nT (quiet times) to $<$-30 nT
(storm-like times), as shown in Figure 9 in increments of $\Delta Dst=10$ nT.
In this case there is also a rise for positive Dst values, which may
correspond to effects associated with Storm Sudden Commencements (SSCs). We
observed a similar relationship between Kp ($\Delta Kp=1$) and the
precipitating fluxes that was seen for AE: both the relative power and total
energy flux increase nearly monotonically with this index. There are also
changes in the slope of the relative intensities at Kp 2 and 5, indicating
that on average, magnetospheric dynamics may exhibit an increased preference
for FLCS over other processes under these conditions.

##  4 Summary and discussion

Using $\sim$1900 ELFIN-A and -B science zone collections from years 2019 and
2020 we have characterized the occurrence and spatial distribution of electron
isotropy boundaries and associated electron energies and precipitation from
$\geq$50 keV electrons due to magnetic field-line curvature scattering. We
examined the spatial distributions in MLT, L-shell, and magnetic latitude and
the dependence of precipitating power and energy flux on geomagnetic activity
indices AE, Dst, and Kp. We found that electron IBs are present under all
activity levels over nightside local times, from dusk through midnight to
dawn. They have $\sim$90% peak occurrence rate around 22 MLT, remaining above
80% occurrence rate between MLTs of 21 to 01. The most common latitudes
associated with IB energy-latitude dispersion are between 66∘-68∘ (IGRF), or
L-shells between 6 and 8, with a total observed latitudinal range between
$60^{\circ}$ and $74^{\circ}$, or $L\gtrsim 3.5$. The latitude-averaged
precipitating energy flux associated with IBs, as well as the contribution to
the total high-latitude precipitation power also peaks around 22 MLT, and has
an MLT distribution similar to that of the IB spatial occurrence rate. The
peaks in electron IB occurrence in MLT and magnetic latitude and in
precipitation energy are statistically collocated with substorm onset MLT and
latitude.

The evolution of electron IB latitude and peak energy with activity is also
consistent with the equatorward evolution of the edge of the oval during
active times. This suggests that geomagnetic activity is conducive to the
formation of better-defined IBs, which implies more intense fluxes at the
tail-dipole transition region. We interpret this as due to the availability of
intense fluxes over broad energies from 10s to 100s of keV (and often $>$1
MeV) of electrons injected to that region by reconnection outflows, as in
Gabrielse2014. The maximum average IB-associated energy flux observed was on
the order of $\sim$1 erg/cm2-s but varies considerably spanning four orders of
magnitude depending on geomagnetic activity. The IB/FLCS source contributes,
on average, between 10-20% of the total nightside high latitude power, but
contributes more than 50% of the total around 20% of the time (in rare cases
even approaching 100% of the total). The total global atmospheric power input
from the IB/FLCS source is on average around 10 MW, but can exceed 1 GW in the
most extreme cases. Both the total intensity and the relative contribution to
high-latitude precipitation of the equatorial FLCS source are seen to increase
with increasing AE, $|$Dst$|$, and Kp, suggesting that IBs may play an
important role in high-latitude energetic electron precipitation at active
times.

Our study establishes a baseline for further investigations of the effects of
energetic electron precipitation from IB-associated field-line scattering for
magnetospheric and ionospheric processes. While we do not expect the
precipitating power from the IB source to typically out-compete the total
power from lower-energy ($<$50 keV), higher number flux auroral sources at
higher latitudes (e.g. as in Newell2009), more than 50% of the IB events in
our database contained $\geq$500 keV precipitating electrons. This indicates
that on average the IB-associated source will tend to penetrate much deeper
into the atmosphere than 10s of keV particles, and it is therefore worth
considering in models of ionospheric conductivity and chemical reactivity at
lower altitudes. This also suggests that models of energetic particle
transport from the plasma sheet to the outer radiation belts should also
incorporate these results for a proper accounting of magnetospheric losses.
The electron IB properties are all found to be positively correlated with
geomagnetic activity as inferred from splitting the dataset about AE=200 nT.
Further investigation is needed to determine the causal relationship between
solar wind driving and magnetospheric responses that result in IB-related
precipitation. These studies could be further augmented by conjunctions with
equatorial spacecraft which may provide simultaneous equatorial observations
of the magnetic topology and electron populations, while also reducing field-
line mapping uncertainties.

Similar to the proton IBs (e.g. as in Newell1998), electron IBs exhibit peak
pre-midnight occurrence rate and precipitation intensity around 22 MLT. This
is presumably due to the proximity of the cross-tail current to Earth in that
region due to its magnitude being stronger at dusk than at dawn [Lu . (2018)].
This results in a tail-dipole transition region closer to Earth at dusk than
at dawn, which can be associated with sharper field-line curvature. Moreover,
we note that the highest energy portion of electron IBs is sometimes observed
to occur in the vicinity of characteristic signatures of electromagnetic ion
cyclotron (EMIC) wave scattering in ELFIN data. Such signatures are most
common at pre-midnight (where EMIC waves peak in occurrence rate). This
suggests that occasionally both mechanisms can act at the same location, and
may, in fact, share common driving: magnetotail injections. Beyond the
technique used to identify IB dispersion, we did not attempt to separate the
two processes in our analysis, but we note that in future studies it is
possible to distinguish the two thanks to the characteristic narrow-banded
energy and lower-latitude extent of EMIC precipitation.

Around 5% of events in our dataset exhibit unusually intense IB-like wide-
energy isotropic electron precipitation signatures at either very low
latitudes (appearing as low as L$\sim$4 near the plasmapause), or over a
highly extended latitudinal range (exceeding $10^{\circ}$ in apparent poleward
extent), corresponding to significantly disturbed magnetospheric conditions
during storms or strong substorms. We excluded such events from our database
because they did not exhibit the characteristic energy-latitude dispersion of
the isotropy boundary assumed in the study. Nonetheless, their properties
suggest that wave-particle scattering sources alone may not sufficiently
explain them, leaving FLCS as a potential cause. One possibility is that these
structures correspond to an active-time type of isotropy boundary in which the
equatorial magnetic field is varying over FLCS timescales, possibly
accompanied by rapid particle energization in vicinity of the scattering
region. Such signatures may be compatible with those of local tail $B_{z}$
minimum as reported e.g. by Sergeev2018, or of active tail reconfiguration,
which would appreciably vary the critical FLCS scattering threshold
$\kappa_{cr}^{2}$ and field-line mappings in real-time. Additionally, during
periods of moderate activity, strongly populated IB-like structures can also
sometimes be seen at dawn/dusk. A possible explanation may be that ULF waves
of appropriate frequency and comparable strength to the equatorial magnetic
field may allow for electron isotropization far away from midnight. This would
present an alternative mechanism to magnetopause scattering at the flanks,
effectively expanding the IB local time occurrence distribution to events that
were filtered out by the 3 earth radius magnetospheric boundary culling
criterion in our analysis, as well as substantially increasing the maximum
amount of precipitating energy flux contributed by IBs/FLCS. Further
simulation and observational work will be helpful in addressing these and
related questions.

In addition to its relevance for electron loss and atmospheric energy
deposition, our study also has implications for improvements in magnetic field
modeling. Such models are still far from encompassing dynamical variations of
the magnetotail in space and time. By forming an observational dataset of
isotropy boundary properties of the type used here, magnetic models can be
further constrained (e.g. as alluded in Sergeev1993), either by fine-tuning
their existing parameters (such as cross-tail current sheet thickness and
Earthward-most extent), or by direct value sampling in modern assimilative
models. This method becomes especially powerful when combined with equatorial
measurements of the magnetic field for mapping, constituting an avenue ripe
for future effort. We note that in this work, predictions based on magnetic
field models were only used as a qualitative estimate of the expected isotropy
boundary properties.

A final clarification concerns the extended isotropic precipitation region
associated with and poleward of the IBs, which we referred to as the “electron
plasma sheet-to-outer radiation belt”, PS2ORB. Using ELFIN data alone at a
single local time, it is not feasible to ascertain a definite instantaneous
inner edge to the electron plasma sheet, nor to infer the location of the
last-closed drift shells of the outer belt. We regard this region as the
transition in global background magnetic field from the outer to the inner
magnetosphere in which freshly injected plasma sheet electrons acquire
sufficient energy to be visible above the highest plasma sheet energies
($>$300 keV) and for which freshly injected, trapped or quasi-trapped outer
belt electrons curvature scatter on timescales faster than a drift period.
Both populations then manage to precipitate with high intensities prior to
reaching the low-latitude boundary layer or the magnetopause boundary (meeting
the phenomenological definition of a transition separating the plasma sheet
from outer belt). We envision that precipitation from FLCS in this region out-
competes other processes (as evidenced by the energy-latitude distribution of
flux cutoffs that dominates over other wave-associated particle spectral
shapes, e.g., due to whistler-mode chorus or EMIC waves). This assumption can
benefit from ELFIN comparison with in-situ equatorial measurements of electron
flux, wave power and magnetic field strengths, as well as from data-
constrained adaptive magnetic field models.

##  5 Open Research

The ELFIN data and software used in this study are part of the SPEDAS
framework [Angelopoulos . (2019)], which is freely available to the public at
the following url: http://spedas.org/wiki/index.php?title=Main_Page

###### Acknowledgements.

This work has been supported by NASA awards NNX14AN68G, 80NSSC19K1439, and NSF
grants AGS-1242918 and AGS-2021749. We are grateful to NASA’s CubeSat Launch
Initiative for ELFIN’s successful launch in the desired orbits. We acknowledge
early support of ELFIN project by the AFOSR, under its University Nanosat
Program, UNP-8 project, contract FA9453-12-D-0285, and by the California Space
Grant program. We acknowledge critical contributions of numerous ELFIN
undergraduate student interns and volunteers.

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Figure 1: Model-based spatial profile (GSM xz-cut) on 2020-09-02/14:22:00 of
equatorial source locations corresponding to minimum electron kinetic energies
for isotropization by field-line curvature scattering, resulting in an
isotropy boundary observed at LEO. The minimum required energy for scattering
is observed to be lowest at the center of the cross-tail current. The pink and
blue curves depict the field-line mappings for the 5 MeV and 50 keV IBs,
respectively. Clear energy-latitude dispersion is observed in the IB location
for a given energy, with more energetic particles isotropized closer to Earth.
The region shaded in yellow shows the set of field-lines mapping into the
equatorial energy-latitude dispersion region, while the mint and light blue
colors show the poleward and equatorward latitudinal extent ELFIN can
typically observe. The critical field geometry parameter $\kappa^{2}_{cr}$ was
taken to be 8. Figure 2: Example isotropy boundary crossing observed by the
ELFIN-B on 2020-09-02. The spacecraft began in the northern polar cap and
moved southward toward the equator, crossing first plasma sheet and then outer
radiation belt field lines. The top two panels show perpendicular (locally-
mirroring) and precipitating electron energy spectra, respectively. The third
panel shows the instantaneous flux isotropy ratio spectrogram
$R_{I}=J_{prec}/J_{perp}$ computed using data from Panels 1 and 2. This ratio
exhibits a clear (abrupt) poleward transition (backwards in time) from
anisotropy (low ratio) to isotropy (high ratio) at a given energy, at
$\sim$14:22 UT. The latitude of that transition is the IB for that energy. The
dispersion in energy versus IB (latitude) is clear and suggests that the 50
keV to 4 MeV electron IBs were crossed at around that time. Figure 3: Spatial
distribution of isotropy boundary locations in our dataset, observed by ELFIN
and magnetically mapped to the equator. Points marked in blue represent the
closest Earthward footpoint of each observed IB crossing (nominally
corresponding to the highest energy observed to have isotropized electrons).
Orange points represent the furthest footpoint in the IB dispersion signature
(almost always representing the onset of 50 keV electron isotropy – the lowest
energy ELFIN can measure). Points marked in gray and black represent the same
IB dispersion signatures as blue and orange, respectively, but are too close
to the magnetopause (solid red line). Those crossings (both gray and black)
have been rejected as likely being of magnetopause origin, based on the
criterion that the 50 keV IB (gray point) is farther from Earth than 3 Earth
radii inside of the magnetopause (dashed yellow line).

Figure 4: Occurrence rates of IB crossings versus MLT (top), L-shell (middle),
and magnetic latitude (bottom). Peak occurrence in MLT is at 22 MLT. Min and
max refer to the low and high latitude boundary of the IB-dispersion
signature. Median values for L-shell and MLAT are shown in the panels, and are
L of 6-8 and 66∘-68∘, respectively, regardless of which boundary (low or
high): the spread of these distributions due to geomagnetic activity and MLT
is much larger than the thickness of the IB-dispersion. As a result the
L-shell and MLAT distributions vary over wide ranges (several L-shells and
$\sim$7∘ in MLAT around the respective medians).

Figure 5: Activity-dependent mean and probability-weighted standard deviation
of IB dispersion region properties, including minimum and maximum energies
appearing in the dispersion (top), minimum and maximum L-shells and magnetic
latitudes (center), and slope of the dispersion in terms of L-shell and
magnetic latitude (bottom). The general trend with increasing geomagnetic
activity is for IBs to appear at lower latitudes and shift toward pre-
midnight, accompanied by an increase in maximum electron energies. MLTs for
which fewer than 5 events were observed were left blank.

Figure 6: Average absolute ELFIN-observed latitudinal profile of IB crossing
locations and omnidirectional flux cutoff versus electron energy alongside
average latitudinal extent from the IB crossing to omnidirectional flux cutoff
versus energy (top), alongside the event-wise difference between these
quantities (middle). A clear break in slopes is observed in the vicinity of
300 keV, suggesting a transition from the region of electrons dominated by
field-line curvature scattering to that of the electron plasma sheet
population (operationally used to define the latitudinal extent of the
“PS2ORB” region). The mean latitudinal extent of the PS2ORB region in each MLT
bin using the 300 keV cutoff criterion is shown in the bottom panel. The
latitudinal width of the region dominated by FLCS exhibits clear variations
with local time and activity. Figure 7: Distribution of latitude-averaged
precipitating energy flux from $\geq$50 keV electrons for three categories:
The entire ELFIN science zone (blue); IB crossing and latitudes poleward of it
(orange); and PS2ORB interface region (encompasses IB crossing). The quantity
$\Delta\bar{\theta}$ represents the average latitudinal extent of the ELFIN
observations in each region, while the corresponding quantity
$\left<J_{E,prec}\right>_{\Delta\theta}$ represents the mean latitude-averaged
integral energy flux over all events in erg/cm2-s (or “pfu”). The plot reveals
that the IB-associated latitudes have the highest average energy flux of the
latitude-mapped source regions under consideration.

Figure 8: Distribution of the precipitating kinetic energy flux of $\geq$50
keV electrons in the PS2ORB region versus MLT. Top: Fraction of the average
total precipitating electron energy flux $\geq$50 keV compared with all
latitudes observed in ELFIN science zones possessing an IB crossing. Bottom:
average total precipitating energy flux from precipitating electrons versus
MLT. The values were aggregated over all activity levels in the dataset, with
each column representing a separate MLT-binned cumulative row-wise probability
of occurrence.

Figure 9: Extension of Figure 7, binning by the geomagnetic activity indices
AE (3 hour mean; left), Dst (middle), and Kp (right), aggregated over all MLTs
containing IBs. Both the total and relative intensities of precipitation
contributed by IBs/FLCS are observed to increase with activity, suggesting
they can become even more significant during geomagetically-disturbed
intervals.