# Relativistic electron precipitation events driven by solar wind impact on
the Earth’s magnetosphere

###### Abstract

Certain forms of solar wind transients contain significant enhancements of
dynamic pressure and may effectively drive magnetosphere dynamics, including
substorms and storms. An integral element of such driving is the generation of
a wide range of electromagnetic waves within the inner magnetosphere, either
by compressionally heated plasma or by substorm plasma sheet injections.
Consequently, solar wind transient impacts are traditionally associated with
energetic electron scattering and losses into the atmosphere by
electromagnetic waves. In this study, we show the first direct measurements of
two such transient-driven precipitation events as measured by the low-altitude
Electron Losses and Fields Investigation (ELFIN) CubeSats. The first event
demonstrates storm-time generated electromagnetic ion cyclotron waves
efficiently precipitating relativistic electrons from $>300$ keV to $2$ MeV at
the duskside. The second event demonstrates whistler-mode waves leading to
scattering of electrons from $50$ keV to $700$ keV on the dawnside. These
observations confirm the importance of solar wind transients in driving
energetic electron losses and subsequent dynamics in the ionosphere.

JGR: Space Physics

ISR Space Science and Applications Group, Los Alamos National Laboratory, Los
Alamos, New Mexico, USA Department of Earth, Planetary, and Space Sciences,
University of California, Los Angeles, Los Angeles, California, USA Department
of Physics, University of Texas at Dallas, Richardson, Texas, USA Department
of Atmospheric and Oceanic Sciences, University of California, Los Angeles,
Los Angeles, California, USA Center for Space Physics, Boston University,
Boston, Massachusetts, USA Institut für Geophysik und Extraterrestrische
Physik, Technische Universität Braunschweig, Braunschweig, Germany Space
Research Institute, Austrian Academy of Science, Graz, Austria

Alexandra<EMAIL_ADDRESS>
A CIR and ICME, both including interplanetary shocks, are observed resulting
in relativistic electron precipitation from low-altitude orbit

Duskside precipitation after CIR impact is driven by intense EMIC waves,
showing distinct energy-$L$ dispersion from magnetic field distortion

Dawnside precipitation after ICME impact is driven by intense whistler-mode
waves resonating with electrons at high latitudes

##  1 Introduction

The dynamics of the Earth’s magnetosphere, especially those of the Earth’s
inner magnetosphere, are largely controlled by solar wind impacts [Kivelson
Russell (1995)]. The most intense and sudden types of impact are those which
include interplanetary (IP) shock waves, which result from the interaction of
fast and slow solar wind streams and manifest as the upstream shock structures
accompanying the larger geoeffective solar wind transient phenomena, such as
interplanetary coronal mass ejections (ICMEs) and corotating interaction
regions (CIRs) [Gopalswamy . (2003), Nitta . (2021), Gosling (1996), Heber .
(1999), Richardson (2018)]. Such impacts have the ability to trigger rapid,
large-scale redistribution of energetic particle fluxes in the radiation belts
[<]e.g.,¿Blake97, Lyons05, Tsurutani95:solarwind,Tsurutani11:jastp. This
redistribution involves significant adiabatic effects related to magnetic
field reconfiguration, as well as kinetic effects related to plasma wave
generation and energetic particle scattering.

The impact of the strongly intensified solar wind dynamic pressure that is
characteristic to the large-scale solar wind transients (sometimes seen as
distinct pulses of augmented pressure) compresses the Earth’s dayside
magnetosphere and has an immediate influence on charged particle dynamics.
This includes the formation of unstable (anisotropic) particle velocity
distributions [<]e.g.,¿[and references therein]Zhao22:drift&swpressure as well
as electron flux dropouts and enhancements
[<]e.g.,¿Ma21:dynamics_pressure_decrease,DaSilva23:chorus_cme. The basic
mechanism for the formation of unstable particle distributions consists of the
adiabatic heating of ions and electrons via induction electric fields. Such
heating is usually more effective for equatorial particles, resulting in the
formation of perpendicularly anisotropic particle populations which are
unstable to whistler-mode waves [<]see¿Sagdeev&Shafranov61,Kennel66 and
electromagnetic ion cyclotron (EMIC) waves [<]see,
e.g.,¿Liu22:emic&solarwind,Yan23:emicIS,Zuxiang23:ws_emic,ThorneKennel71.

Indeed, in-situ spacecraft measurements have detected many cases of whistler-
mode chorus [<]e.g.,¿Zhou15:chorus&shock,Zhou23:chorus_pressure and EMIC wave
[<]e.g.,¿Usanova12 generation in response to solar wind dynamic pressure
increases, e.g., during an interplanetary shock wave’s arrival to the Earth’s
magnetosphere. A detailed multi-case study by Yue17:whistler&solarwind
demonstrated that IP shock impact can significantly increase the intensity of
whistler-mode chorus waves in the outer radiation belt, outside of the
plasmapause. Although this type of wave intensity enhancement is typical for
any positive pulses (i.e., increases) of the solar wind dynamic pressure, IP
shocks often provide the strongest effect [Jin . (2022)]. Interestingly, wave
intensity increases not only around the equatorial plane, where the chorus
generation region is located [<]see reviews by¿[and references
therein]Tao20,Omura21:review, but in low-altitude regions as well [Bezděková .
(2021)]. This suggests that the more intense whistler-mode waves driven by IP
shock impact are not damped by suprathermal electron fluxes [Bortnik . (2007),
L. Chen . (2013)] and can propagate to high latitudes, thus significantly
increasing their global efficiency in scattering relativistic electrons [<]see
discussion in¿Chen21:frontiers,Chen22:microbursts,Artemyev21:jgr:ducts.

Magnetospheric impact by strong solar wind transient IP shocks plays a
similarly significant role in the intensification of EMIC waves [Yan .
(2023)]. Blum21:emic&shock described a CME event that led to a series of
compressions of the dayside magnetosphere by pulses of solar wind dynamic
pressure; each of such compressions resulted in proton adiabatic heating and
near-equatorial EMIC wave generation. The effects of EMIC wave generation due
to IP shock impact on the Earth’s magnetosphere can be even more evident, such
as in the stark ion flux enhancements observed by Li22:emic&shock and
Zuxiang23:ws_emic. Moreover, EMIC wave intensity enhancements in response to
solar wind pulses may also be observed simultaneously on the day and night
sides of the Earth, as when coinciding with plasma sheet ion injections driven
by substorm activities [Xue . (2022), Yan . (2023)]. For EMIC wave generation
in particular, the solar wind impact may consist of two independent processes:
(1) direct proton heating by magnetic field compression within the inner
magnetosphere and (2) injection of hot, anisotropic protons into the inner
magnetosphere by flow bursts and dipolarizing flux bundles arising from
localized reconnection in the magnetotail [<]see discussion and comparison of
these two processes in, e.g.,¿Chen20:emic_statistics,Upadhyay22.

Although whistler-mode and EMIC wave generation caused by interplanetary shock
waves and solar wind dynamic pressure pulses has been previously reported, as
it is commonly observed by near-equatorial spacecraft, details on the
influence of these waves on radiation belt dynamics have yet to be fully
investigated. One expected effect of importance is the scattering and
resultant precipitation of energetic electrons by intense whistler-mode and
EMIC waves. However, such electron precipitation can only be observed by low-
altitude spacecraft (i.e., taking advantage of finite, $\sim 20$ deg, pitch-
angle resolution measurements of electron distributions within a large, i.e.,
many tens of degrees, loss-cone) or ground-based measurements of X-ray
emission [<]see, e.g., example in¿Breneman20:losses&swpressure. Direct
measurements of precipitating electron fluxes in response to solar wind
dynamic pressure enhancements can therefore be highly useful for understanding
the importance of transients, including IP shocks, in magnetosphere-ionosphere
coupling and radiation belt depletion.

Here, we describe two events in which large-scale solar wind structures impact
the Earth’s magnetosphere and drive relativistic electron losses. Both
precipitation events were captured by the low-altitude measurements of the
Electron Losses and Fields Investigation (ELFIN) CubeSats [Angelopoulos .
(2020)]. The first event consists of a magnetospheric impact by a CIR (with an
embedded IP shock and prominent solar wind discontinuities) that drives a
magnetospheric storm and strong relativistic electron precipitation by EMIC
waves on the duskside; the second event consists of a separate ICME impact,
adjoined by a prominent IP shock, that drives strong energetic electron
precipitation, extending to relativistic energies, by whistler-mode waves on
the dawnside. We describe the satellite observations of the solar wind, inner
magnetosphere, and low-altitude space region in Section 2. In Sections 2.1 and
2.2, we examine the first and second events, respectively. In Section 3, we
discuss our results and the likely characteristics of the specific waves
responsible for the two electron precipitation events. Finally, we summarize
our results and present conclusions in Section 4.

##  2 Observations

We examine two specific events of electron precipitation, observed from the
low-altitude vantage point of ELFIN, driven by interplanetary shock
interaction with the terrestrial magnetosphere: the first event (S#1) occurred
on 6 March 2021, and the second event (S#2) occurred on 12 May 2021. We use
ELFIN observations of precipitating (inside the local bounce loss-cone) and
locally trapped (outside the local bounce loss-cone) fluxes within the energy
range of 50-6000 keV (16 energy channels) at 3 s time resolution (ELFIN spin
rate) [Angelopoulos . (2020)]. We also use the precipitating-to-trapped flux
ratio as an effective measure of the intensity of electron precipitation
[<]see examples in¿Mourenas21:jgr:ELFIN,Tsai22,Zhang22:natcom.

To monitor the solar wind and magnetospheric conditions for perturbations
indicative of transient and accompanying shock arrival, we utilize
observations from the Time History of Events and Macroscale Interactions
during Substorms (THEMIS) mission and The Geostationary Operational
Environmental Satellite (GOES). Measurements of the upstream solar wind, where
an approaching IP shock is first observable as a sharp gradient of solar wind
velocity and magnetic field magnitude, are taken from the Acceleration,
Reconnection, Turbulence, and Electrodynamics of the Moon’s Interaction with
the Sun (ARTEMIS) subset of THEMIS spacecraft (specifically, ARTEMIS P2 also
know as THEMIS C, with the latter designation utilized hereafter). The ARTEMIS
satellites orbit the moon and measure the solar wind magnetic field [Auster .
(2008)] and plasma [McFadden . (2008), Artemyev . (2018)]. The three other
THEMIS spacecraft (A, D, and E) orbit the Earth with an apogee of $\sim
12R_{E}$ [Angelopoulos (2008)]. We use THEMIS A magnetic field and plasma
measurements ( 3-4 s spin resolution) to monitor the near-Earth dayside
magnetosheath and foreshock response to the arriving interplanetary shock.
Additionally, to identify plasma injections we check energetic ion and
electron measurements made by the GOES-16 and GOES-17 space weather suite of
instruments [Dichter . (2015), Boudouridis . (2020)]. Figure 1 shows the
orbits of THEMIS, GOES, and ELFIN spacecraft relative to the nominal, modelled
magnetopause and bow shock [Shue . (1997), Wu . (2000), King Papitashvili
(2005)], as well as the geomagnetic activity, as represented by Sym-H and AE
indices, around the time of each event.

Figure 1: Equatorially-projected positions of THEMIS, GOES, and ELFIN
spacecraft (a, d), relative to the modelled nominal magnetopause (dashed
curve) and bow shock (dotted curve). ARTEMIS (THEMIS B and C) is located in
the solar wind, out of frame. For each orbit, the start time is marked with a
triangle while the end time is marked with an asterisk; the tick marks between
represent hour intervals for THEMIS and GOES satellites and minute intervals
for ELFIN. The bottom panels show Sym-H (b, e) and AE (c, f) indexes for the
two-day interval encompassing each event. The orbits of observation and
geomagnetic indices for the first event (S#1) are shown in the left panels,
while those of the second event (S#2) are shown on the right. The stars mark
the approximate locations and times for the different shock observations made
by ARTEMIS, THEMIS, and ELFIN.

###  2.1 First event: EMIC wave-driven precipitation

Our first event occurred on 6 March 2021. Figure 2 shows an overview of
ARTEMIS (THEMIS C) and THEMIS A observations. THEMIS C observes the large-
scale solar wind perturbations of a corotating interaction region (CIR)
[<]see¿Gosling96:cir,Heber99:cir,Richardson18:cir, starting at $\sim$ 01:00 UT
with a slight jump of solar wind speed (panel (b)). Simultaneous variations of
magnetic field magnitude (panel (a)) and plasma density (panel (b)) show the
series of rotational discontinuities (rotation of ${\bf B}$ components with
$|{\bf B}|\approx const$) associated with an interplanetary shock wave ($|{\bf
B}|$ variation) embedded in a CIR [<]see detailed discussion in¿Gosling96:cir.
Distinct from the initial fine structure of solar wind perturbations, the
large scale magnetic field and solar wind discontinuities, seen prominently in
the ion spectra variation around 05:40-06:00 UT in panel (c), are expected to
compress the Earth’s magnetosphere and drive a geomagnetic storm
[<]see¿Gonzalez99:storms,Alves06. Indeed, Sym-H and AE indexes in Figure 1
show moderately depressed Sym-H, indicative of storm-like activity, along with
so-called high-intensity, long-duration, continuous AE activity, [<]as
described in¿Tsurutani04, Tsurutani06. Activity starts with magnetosphere
compression from 01:00-02:00 UT (positive Sym-H) and continues to a moderately
negative Sym-H of around $-20$ nT with recurrent substorms (AL minimum
reaching $\sim-800$ nT). The substorm around 03:00 UT is associated with a
strong ion injection observed at GOES-16 in the pre-midnight sector (not
shown). Such events are usually characterized by an increased level of
relativistic electrons in the inner magnetosphere [Hajra . (2014), Hajra .
(2015)], but have not been studied in the context of relativistic electron
precipitation.

During THEMIS C observations of the CIR, THEMIS A, located inside the
magnetosheath (see Figure 1), detects multiple strong magnetic field
perturbations accompanied by density variations and hot magnetospheric plasma
bursts. Such variations of density and cold/hot plasma flux are indicative of
multiple magnetopause crossings due to magnetopause surface waves
[<]e.g.,¿Agapitov09,Archer19 or Kelvin-Helmholtz waves [<]e.g.,¿Hasegawa04.
$B_{z}$ changes sign multiple times, i.e., the magnetosheath is filled by
negative polarity $B_{z}$ variations that potentially drive magnetopause
reconnection [Paschmann . (1979), Paschmann . (2013), Phan . (2014), Burch .
(2016)]; multiple plasma jets ($v_{z}$ excursions from the ambient sheath
flow) are also seen. Thus, THEMIS A confirms the strong driving of the Earth’s
magnetosphere by the CIR after its arrival at $\sim$01:00 UT.

At $\sim$06:47 UT, near the time of the observed Sym-H minimum (1 hour after
THEMIS C detects the ending edge of the CIR with a large increase of the solar
wind speed), and still well within the prolonged, albeit weak, storm main
phase, ELFIN A crosses the dusk flank (MLT$\sim 18$) and observes strong
precipitation of relativistic electrons. Figure 3 shows an overview of flux
observations capturing this precipitation. The precipitation burst covers a
wide range of magnetic latitudes, $MLAT\in[61.4,59.4^{\circ}]$ (corresponding
to a wide $L$-shell range in the equatorial region of electron scattering,
$\Delta L\sim 1$), between the plasma sheet region (before 06:47:30 UT; region
with only $<300$ keV electron fluxes; see detailed analysis of such ELFIN
observations in, e.g., Artemyev22:jgr:ELFIN&THEMIS) and plasmasphere (after
06:48:30 UT; region with characteristic depletion of $\sim 100-200$ keV fluxes
due to scattering by plasmaspheric hiss waves; see detailed analysis of such
ELFIN observations in, e.g., Mourenas21:jgr:ELFIN). The precipitating-to-
trapped electron flux ratio maximizes at $>300$ keV and stays $\sim 1$ for
energies up to $\sim 2-3$ MeV. Relativistic electron precipitation distinctly
lacking in energies $<300$ keV is the characteristic feature of electron
resonant scattering by EMIC waves [<]see detailed description of such events
in, e.g.,¿An22:prl,Grach22:elfin,Capannolo23:elfin,Angelopoulos23:ssr, as the
minimum resonance energy for such scattering is typically $\gtrsim 0.5$ MeV
[Summers Thorne (2003), Kersten . (2014), Ni . (2015)]. Meanwhile, GOES-17,
located in the pre-midnight sector, observes a strong $B_{z}$ depletion of
$\sim-50$ nT (not shown) that is associated with a ring current injected ion
population [Daglis . (1999)], the principal source of EMIC waves
[<]e.g.,¿Chen10:emic,Chen11:emic. The duskside location of the precipitation
event further supports characterization as EMIC-driven scattering, as this is
the primary region of EMIC wave generation, with aforementioned hot plasma
sheet (ring current) ions drifting duskward after being injected at the
nightside [Thorne Kennel (1971), Jun . (2019), Jun . (2021)].

Although there was no direct magnetic conjunction of ELFIN with near-
equatorial spacecraft during the first event, the geostationary GEO-KOMPSAT-2A
[Seon . (2020)] satellite was traveling along the dusk flank around the time
of ELFIN electron precipitation observations and observed several intense
bursts of helium band EMIC waves. Figure 4 shows KOMPSAT fluxgate magnetometer
measurements (1 s resolution; Magnes20:KOMPSAT_fgm,Constantinescu20:KOMPSAT)
during the interval of 05:00-09:00 UT. There are clear EMIC wave bursts
(bottom panel) around 05:10, 06:10, and 08:00-09:00 UT, covering an MLT range
that extends from 13 up to 18 hours. These time intervals and MLT locations do
not exactly overlap with ELFIN measurements at $\sim$06:50 UT, MLT$\sim 18$,
but instead provide a good context for ELFIN measurements. KOMPSAT shows that
a large part of the dusk flank is filled by EMIC wave source regions at the
times surrounding our observations; these regions can survive for a long time
and be quite extended in MLT [<]see¿Engebretson15,Blum20. Thus, the
observation of multiple EMIC wave source regions in close spatial and temporal
proximity to ELFIN observations of relativistic electron precipitation follows
our interpretation of EMIC wave scattering.

Interestingly, EMIC wave-driven precipitation is quite long lasting (multiple
ELFIN spins covering almost $\Delta L\sim 1$ and reaching the upper limit of
the range of sizes expected for an equatorial EMIC wave source region [Blum .
(2016), Blum . (2017)]). Our first event additionally includes two types of
$dE/dL$ (or $dE/dMLAT$) gradients: one around 06:47:30 UT, with the minimum
precipitating electron energy increasing as $L$-shell decreases ($dE/dL<0$),
and a second around 06:47:45 UT, when the minimum precipitating electron
energy decreases as $L$-shell decreases ($dE/dL>0$). The $dE/dL$ gradient is
likely provided by the dependence of the minimum resonance energy on the
equatorial ratio of the plasma frequency and the gyrofrequency, $E\propto
f_{ce}/f_{pe}$ [Summers Thorne (2003)]. In the unperturbed dipole magnetic
field $f_{ce}\propto L^{-3}$ and $f_{pe}\propto L^{-2}$ [<]see the empirical
model in¿Sheeley01, which will give $E\propto L^{-1}$ with $dE/dL<0$ (observed
at larger $L$, around 06:47:30 UT). Substorm injections, however, transport
hot ion populations [Birn . (2015), Gkioulidou . (2014), Gkioulidou . (2016),
Ukhorskiy . (2017), Ukhorskiy . (2018)] that may form localized regions of
magnetic field depletion [<]so-called magnetic
dips,¿Xia19:magnetic_hole,Zhu21:magnetic_holes filled by EMIC waves
[<]see¿He17:emic,Yin22:magnetic_holes&emic,Yu23:magnetic_holesemic,Zhao23:emic_dips.
This magnetic field depletion will result in a weaker radial gradient of
$f_{ce}$, that is $f_{ce}\propto L^{-3+q}$ with $q>0$ [Xia . (2019), Zhu .
(2021)], and this effect may make $f_{ce}/f_{pe}\propto L^{-1+q}$ increase
with decreasing $L$ (i.e., $dE/dL>0$, observed around 06:47:45 UT). Therefore,
the inverse gradient of the precipitating energies ($dE/dL>0$, seen in Fig. 3)
corroborates that here a strong ion injection is penetrating deep into the
plasmapause and driving significant losses of relativistic electrons. Indeed,
KOMPSAT magnetic field measurements around MLT $\sim 13.3$ and $\sim 17$ show
a significant magnetic field depletion within the source region of EMIC waves
(Figure 4, top panel; for MLT $\sim 17$, depletion is seen also in the
gyrofrequency profile of the bottom panel below).

Figure 2: Overview of ARTEMIS (THEMIS C) and THEMIS A observations for event 1
on 6 March 2021: THEMIS C magnetic field (a), plasma density (b), plasma flow
speed (c), and ion energy spectrum (d) and THEMIS A magnetic field (e), plasma
density (f), plasma flow speed (g), and ion energy spectrum (h), with the
colorbar showing flux in [cm-2s-1sr-1eV-1]. At the bottom of each set of
panels (a-d, e-h) are location and time information, including the X, Y, and Z
positions in the GSE coordinate system, L and MLT values, and the hour (hh)
and minute (mm) for the day of the event. The beginning of the primary
disturbances caused by the shock are indicated by the dashed lines across
panels (a-d) and (e-h), as observed by THEMIS C and THEMIS A, respectively.
Figure 3: Overview of ELFIN observations for event 1 on 6 March 2021:
precipitating electron fluxes (a), trapped fluxes (b), precipitating-to-
trapped flux ratios (c), and omnidirectional fluxes (d). In panels (a), (b),
and (d) the colorbar shows flux in [cm-2s-1sr-1MeV-1]. The dashed lines
demarcate the time interval in which electron precipitation is primarily
observed, as indicated in the enhancement of the precipitating-to-trapped
ratio (i.e., ratio approaches unity).  Figure 4: An overview of KOMPSAT
magnetic field measurements at the dusk flank around the time of event 1:
magnetic field components (top panel) and magnetic field spectrum for EMIC
wave frequency range (bottom panel). The two white lines depict helium (He)
and oxygen (O) gyrofrequencies.

###  2.2 Second event: whistler-mode wave-driven precipitation

The second event occurred on 12 May 2021. THEMIS C, in the solar wind ahead of
the Earth’s bow shock, observes the IP shock of an impinging ICME [Gopalswamy
. (2003), Nitta . (2021)] around 06:25 UT. Figure 5(a-d) shows the strong
gradient of the magnetic field magnitude, a plasma density jump from 8 cm-3 to
$\sim$40 cm-3, and an intensification of solar wind flow from $\sim-300$ km/s
to $\sim-450$ km/s; the ion spectrum also shows conspicuous flow and thermal
energy increases across the shock. Compared with the first event (S#1, Figure
2), the IP shock of the second event is much more distinct in form, with
sharper gradients between upstream and downstream regions.

Prior to the IP shock’s arrival to the Earth’s magnetosphere, THEMIS A was
inside the magnetosphere and observed hot stagnant ions (i.e., ion energy is
above $1$ keV and ion flow is around zero, see Figure 5(e-h)). The shock
impact compresses the magnetosphere and moves the magnetopause toward the
Earth, such that THEMIS A momentarily appears to be located within the
magnetosheath, with high density plasma flow observed onward from 06:40 UT.
The spacecraft returns to the magnetosphere around 07:00 UT, the magnetopause
evidently moving out closer to its pre-shock configuration. However, THEMIS A
undergoes multiple apparent magnetopause crossings over the subsequent $\sim
3$ hours; such crossings are seen as plasma density increases along with
alternating recurrences of hot rarefied and cold dense ion populations in the
flux spectrum shown in Figure 5(h). These successive magnetopause crossings
are likely caused by magnetopause oscillation, driven by both IP shock impact
and the arrival of subsequent trailing solar transients that compose the
extent of CME (observed by THEMIS C behind the initial IP shock) [<]see,
e.g.,¿Agapitov09,Archer19. During the entire interval of 06:00-10:00 UT,
THEMIS A was at $L\sim 14$; thus observations of magnetopause crossings after
07:00 UT highlight the large amplitude character of the magnetopause
oscillations.

Figure 5: Overview of ARTEMIS (THEMIS C) and THEMIS A observations for event 2
on 12 May 2021: THEMIS C magnetic field (a), plasma density (b), plasma flow
speed (c), and ion energy spectrum (d) and THEMIS A magnetic field (e), plasma
density (f), plasma flow speed (g), and ion energy spectrum (h), with the
colorbar showing flux in [cm-2s-1sr-1eV-1]. At the bottom of each set of
panels (a-d, e-h) are location and time information, including the X, Y, and Z
positions in the GSE coordinate system, L and MLT values, and the hour (hh)
and minute (mm) for the day of the event. The beginning of the primary
disturbances caused by the shock are indicated by the dashed lines across
panels (a-d) and (e-h), as observed by THEMIS C and THEMIS A, respectively.

Figure 1 shows that the IP shock compresses the magnetosphere (evidenced by
the long interval of increased, positive Sym-H for S#2) and drives a substorm
with AE$\sim-700$ nT (both GOES-16 and 17 observe strong plasma sheet
injections at 06:40 UT on the nightside; not shown). Additionally, after 11:00
UT there are prolonged storm activities with Sym-H around $-60$ nT [<]expected
for CME impact; see¿[and references therein]Tsurutani03:cme,Koehn22, similar
to what we observe for the first event, albeit more intense here. Focusing on
the initial compressing shock impact at 07:00 UT, we see ELFIN B crossing the
dawn-flank magnetosphere when it observes a very intense burst of electron
precipitation. Figure 6 shows ELFIN detecting the relativistic electron
precipitation burst around $L\sim 5.7$, with an upper energy of $\sim 800$ keV
and the precipitating-to-trapped flux ratio reaching 1 for approximately the
entire energy range. This burst is localized between the plasma sheet
(distinguished by the absence of trapped fluxes ¿ 300 keV and the presence of
isotropic fluxes $<300$ keV for electrons observed before 06:55 UT) and the
plasmapause (recognized by the disappearance of $\sim 300$ keV fluxes after
06:56 UT; see discussions of this feature in ELFIN observations by
Mourenas21:jgr:ELFIN,Angelopoulos23:ssr). Therefore, this precipitation burst
occurred in the outer radiation belt, where electrons are scattered by intense
whistler-mode waves in the dawn region [<]strong precipitation of $\sim 50$
keV electrons is the defining characteristic of whistler-mode wave scattering,
see, e.g.,¿Tsai22,Chen22:microbursts. This precipitation burst covers four
ELFIN spins, i.e., it lasts much longer than microburst precipitation duration
[<]e.g.,¿OBrien04,Shumko21. Considering these features in totality, we
interpret this instance of relativistic electron precipitation, localized
within the outer radiation belt, as an equatorial intensification of whistler-
mode waves due to IP shock-induced magnetospheric compression [<]see,
e.g.,¿Yue17:whistler&solarwind,Jin22:chorusshock.

Figure 6: Overview of ELFIN observations for event 2 on 12 May 2021:
precipitating electron fluxes (a), trapped fluxes (b), precipitating-to-
trapped flux ratios (c), and omnidirectional fluxes (d). In panels (a), (b),
and (d) the colorbar shows flux in [cm-2s-1sr-1MeV-1]. The dashed lines
demarcate the time interval in which electron precipitation is primarily
observed, as indicated in the enhancement of the precipitating-to-trapped
ratio (i.e., ratio approaches unity).

##  3 Discussion

We have presented two different events with EMIC and whistler-mode wave-driven
electron precipitation bursts (first event, S#1, and second event, S#2,
respectively). Both events are characterized by strong solar wind drivers that
either provide ion injections, followed by EMIC wave generation, or electron
compressional heating, followed by whistler-mode wave generation. We now
estimate the physical characteristics of EMIC and whistler-mode waves that
would be required to obtain the types of electron precipitation spectra we
observed for each event. We analyze two main aspects of wave generation: the
resonance conditions and the cold plasma dispersion relation. Firstly, we look
at these aspects for whistler-mode waves. The most intense whistler-mode waves
propagate along magnetic field lines [W. Li . (2011), Agapitov . (2013)], and
in cold dense plasma their dispersion relation takes the following form [Stix
(1962)]:

$\omega=\Omega_{ce}\left(\lambda\right)\cdot\left({1+\frac{{\Omega_{pe}^{2}\left(\lambda\right)}}{{k^{2}\left(\lambda\right)c^{2}}}}\right)$
(1)

or

$k\left(\lambda\right)=\frac{{\Omega_{pe}\left(\lambda\right)}}{c}\cdot\left({\frac{{\Omega_{ce}\left(\lambda\right)}}{\omega}-1}\right)^{-1/2}$

where the dispersion relation sets the wave number $k(\lambda)$ for a fixed
wave frequency, $\omega$. The electron gyrofrequency
$\Omega_{ce}=\Omega_{ce,eq}\sqrt{1+3\sin^{2}\lambda}/\cos^{6}\lambda$ is given
by the dipole magnetic field model ($\Omega_{ce,eq}$ is the equatorial
gyrofrequency; $\lambda$ is the magnetic latitude), and the plasma frequency
$\Omega_{pe}=\Omega_{pe,eq}\cos^{-5/2}\lambda$ is given by the Denton06 model
($\Omega_{pe,eq}$ is the equatorial plasma frequency; the ratio
$\Omega_{pe,eq}/\Omega_{ce,eq}$ is taken from the model presented in
Sheeley01). The resonance condition for field-aligned whistler-mode waves is:

$\gamma\omega-k\left(\lambda\right)p_{\parallel}\left(\lambda\right)/m_{e}=\Omega_{ce}\left(\lambda\right)$
(2)

where electron parallel momentum $p_{\parallel}$ can be written as a function
of electron energy $m_{e}c^{2}(\gamma-1)$ and equatorial pitch-angle
$\alpha_{eq}$:

$p_{\parallel}=-m_{e}c\sqrt{\gamma^{2}-1}\sqrt{1-\sin^{2}\alpha_{eq}\frac{{\Omega_{ce}\left(\lambda\right)}}{{\Omega_{ce,eq}}}}$
(3)

We are interested in electron precipitation, and thus the equatorial pitch-
angle should be defined by the loss-cone size, $\alpha_{LC}\approx
L^{-3/2}\cdot\left(4-3/L\right)^{-1/4}$, where $L$ (L-shell) is defined by the
radial distance (in Earth radii) of the equatorial crossing of Earth’s
magnetic field lines [Schulz Lanzerotti (1974)]. Combining the resonance
condition (2), dispersion relation (1), and equation for
$\alpha_{eq}=\alpha_{LC}$, we obtain the precipitating electron energy as a
function of magnetic latitude for a given $\Omega_{pe,eq}/\Omega_{ce,eq}$.

Turning next to EMIC wave generation, the dispersion relation of field-aligned
EMIC waves is [Stix (1962)]

$\frac{{k^{2}c^{2}}}{{\omega^{2}}}\approx
1-\frac{{\Omega_{pe}^{2}}}{{\omega\Omega_{ce}}}-\frac{{\Omega_{pe}^{2}}}{\omega}\frac{{m_{e}}}{{m_{p}}}\left({\frac{{\eta_{H}}}{{\omega-\Omega_{cp}}}+\frac{{\eta_{He}}}{{\omega-\Omega_{cp}/4}}+\frac{{\eta_{O}}}{{\omega-\Omega_{cp}/16}}}\right)$
(4)

where $\eta_{H}$, $\eta_{He}$, $\eta_{O}$ are the relative concentrations of
protons, helium ions, and oxygen ions, respectively (with
$\eta_{H}+\eta_{He}+\eta_{O}=1$), and $\Omega_{cp}=\Omega_{ce}m_{e}/m_{p}$ is
the proton gyrofrequency ($m_{e}$ and $m_{p}$ are the electron and proton
mass, respectively). For a purely proton-electron plasma, equation (4) can be
rewritten as:

$\omega=\Omega_{cp}\left(\lambda\right)\cdot\left({\frac{{k\left(\lambda\right)c}}{{\Omega_{pp}\left(\lambda\right)}}}\right)^{2}\cdot\left({-\frac{1}{2}+\sqrt{\frac{1}{4}+\left({\frac{{\Omega_{pp}\left(\lambda\right)}}{{k\left(\lambda\right)c}}}\right)^{2}}}\right)$
(5)

or

$k\left(\lambda\right)=\frac{\omega}{c}\sqrt{1+\frac{{\Omega_{pp}^{2}\left(\lambda\right)}}{{\Omega_{cp}\left(\lambda\right)\cdot\left({\Omega_{cp}\left(\lambda\right)-\omega}\right)}}}\approx\frac{\omega}{c}\frac{{\Omega_{pe}\left(\lambda\right)}}{{\Omega_{ce}\left(\lambda\right)}}\sqrt{\frac{{m_{p}}}{{m_{e}}}}\left({1-\frac{\omega}{{\Omega_{cp}\left(\lambda\right)}}}\right)^{-1/2}$

where $\Omega_{pp}^{2}=\Omega_{pe}^{2}m_{e}/m_{p}$. The resonance condition of
equation (2) can be rewritten for EMIC waves as

$\gamma\omega-k\left(\lambda\right)p_{\parallel}\left(\lambda\right)/m_{e}=-\Omega_{ce}\left(\lambda\right)$
(6)

Using these relations, we obtain resonance energies as a function of magnetic
latitude and wave frequency, as displayed in Figure 7. For EMIC wave
calculations we set $\Omega_{pe,eq}/\Omega_{ce,eq}=15$ [<]typical for EMIC
wave generation region outside the plasmasphere, see¿Zhang16:grl, while for
those of whistler-mode waves we set $\Omega_{pe,eq}/\Omega_{ce,eq}=5$
[<]typical for whistler-mode wave generation region within the dawn flank,
see¿Glauert&Horne05,Agapitov19:fpe. Calculations for EMIC waves (left panel)
show that to provide precipitation of both sub-relativistic ($<500$ keV) and
accompanying relativistic ($\geq 1$ MeV) electrons, as observed by ELFIN in
S#1 (see Fig. 3), the waves would likely need to be at a very high-frequency,
with $\omega/\Omega_{cp,eq}>0.8$ [<]see
also¿Ukhorskiy10,Denton19,Bashir22:grl. Such a high-frequency portion of EMIC
wave spectra is indeed observed around equator [<]see, e.g.,¿Zhang16:grl and
may provide the necessary precipitating-to-trapped flux ratio to induce the
sub-relativistic precipitation associated with EMIC-driven relativistic
electron precipitation
[<]see¿Angelopoulos23:ssr,Capannolo19:EMICSpatialExtent. Two additional
factors may facilitate such sub-relativistic precipitation by EMIC waves: (1)
enhanced plasma density with $\Omega_{pe,eq}/\Omega_{ce,eq}$ exceeding the
nominal (model) values [Summers Thorne (2003), Summers . (20072)] and/or (2)
non-resonant electron scattering occurring below the minimum resonance energy
[<]effective for short EMIC wavepackets,
see¿Chen16:nonresonant,An22:prl,Grach&Demekhov23:theory. Both these factors
may contribute to the precipitating electron spectra that demonstrate a weak
(precipitating-to-trapped ratio of $\sim 1/10$) but finite precipitation down
to $50$ keV, as seen in our first event.

Concerning whistler-mode waves, the precipitation of relativistic electrons
suggests a large local $\Omega_{ce}/\Omega_{pe}$ [Summers . (20071)],
indicating that such waves should propagate up to high latitudes. This is
indeed the case for the second event, as the precipitating-to-trapped electron
flux ratio is approximately 1 [<]i.e., at the strong diffusion limit,
see¿Kennel69 for energies up to $0.9$ MeV (Figure 7, right panel shows that
resonant latitudes are $\sim 40^{\circ}$ for such energies and typical wave
frequency $\omega/\Omega_{ce,eq}\sim 0.3$ [W. Li . (2011), Agapitov .
(2018)]). Empirical wave intensity models, such as those of Agapitov18:jgr and
Wang&Shprits19:latitudes, predict that wave intensity should decrease with
increasing magnetic latitude (i.e. farther away from the equator). This
possible wave damping [<]likely due to Landau resonance with suprathermal
electrons; see¿Bell02,Bortnik07:landau,Chen13 prevents effective scattering of
relativistic electrons. Thus, two possible scenarios can explain the observed
electron precipitation of the second event. The first scenario assumes that
electrons are scattered by whistler-mode waves ducted within a small-scale
density perturbation [Hosseini . (2021), Ke . (2021), R. Chen . (2021), Shen .
(2021)] that can trap waves and prevent their damping [<]see¿[for discussion
of the wave ducting effect on electron scattering
energies]Artemyev21:jgr:ducts,Chen22:microbursts. The second scenario assumes
that the electrons are scattered by very oblique whistler-mode waves
resonating with electrons near the equator via high-order resonance:
$\gamma\omega-k\left(\lambda\right)p_{\parallel}\left(\lambda\right)/m_{e}=n\Omega_{ce}\left(\lambda\right)$
with $|n|>1$ [<]e.g.,¿Lorentzen01,Mourenas12:JGR,Artemyev16:ssr. Such waves
can precipitate relativistic electrons even at low latitudes [<]see examples
in¿Gan23:grl_elfin, but require additional populations of field-aligned
suprathermal electron streams to supress Landau damping and thus allow very
oblique wave generation
[<]e.g.,¿Mourenas15,Li16,Artemyev&Mourenas20:jgr,Sauer20. Therefore, to
explain the dawn-flank relativistic electron precipitation as driven by
interplanetary shock wave impact, we would need to incorporate either strong
equatorial density gradients formed by convection electric fields, which could
duct whistler-mode waves, or an ionospheric outflow of secondary
(suprathermal, $\sim 100$ eV) electrons [Khazanov . (2014), Khazanov . (2022)]
to provide the conditions for very oblique whistler-mode wave generation.

Figure 7: Resonance energy as a function of magnetic latitude $\lambda$ and
wave frequency $\omega$ for EMIC waves (left panel) and whistler-mode waves
(right panel). The parameters for calculation are shown at the top of each
panel; black lines represent contours of constant energies that approximately
coincide with upper and lower bounds of ELFIN precipitation observations.

##  4 Summary

In this study we explore the chain of events leading to relativistic electron
precipitation during two different cases when comprehensive observations were
available from the solar wind, the magnetosphere, and the ionosphere. The two
events are each characterized by strong solar wind drivers that impact and
compress the magnetosphere, triggering intense geomagnetic activity and
electromagnetic wave intensification and ultimately culminating in distinct
forms of electron precipitation. Through the combined multi-point observations
of ARTEMIS, THEMIS, and the geosynchronous, low-altitude ELFIN satellites, we
synthesize an explanatory model of the sequence of events that lead to the
observed characteristics of precipitation. Although the effects of EMIC and
whistler-mode wave activity enhancements due to solar wind transient impacts
have been well explored in various previous studies [Yue . (2017), Blum .
(2021), Jin . (2022), Xue . (2022), YX. Li . (2022), Yan . (2023), Zuxiang .
(2023)], the two events in this paper arguably represent the first direct
observations of relativistic electron losses as induced by solar wind-driven
waves.

In the first event, a corotating interaction region, containing an
interplanetary shock and multiple rotational discontinuities of the solar
wind, compresses the magnetosphere and drives a prolonged moderate storm with
multiple substorm injections. Such injections are known to be responsible for
hot ion transport into the inner magnetosphere, where the injected ion
population consequently drives EMIC wave generation. We have presented low-
altitude observations of resultant EMIC wave-driven strong losses
(precipitating-to-trapped flux ratio reaches one) of relativistic electrons,
spanning energies of $300$ keV to $\sim 2$ MeV within a wide latitudinal
($L$-shell) range. In the second event an interplanetary coronal mass
ejection, with a strong preceding interplanetary shock, impacts the
magnetosphere and significantly compresses it ($Sym-H$ reaches $40$ nT). Such
compression is known to drive whistler-mode waves, and we have presented low-
altitude observations of intense whistler wave-driven electron precipitation,
encompassing a wide energy range (from 50 to 700 keV) but very localized span
of latitudes ($L$-shells). We have examined resonance conditions and cold
plasma dispersion relations in order to evaluate the expected characteristics
of waves capable of producing each unique precipitation event. Using these
calculations, we have discussed plausible physical factors and scenarios which
could foster the proper conditions for the latitudinal distribution of these
waves.

This study was largely built around ELFIN’s low-altitude measurements of
electron precipitation, and further investigations would benefit from the
incorporation of additional near-equatorial spacecraft observations which
could directly identify specific wave modes and their drivers (e.g.,
anisotropic ion and electron populations). Moreover, a combination of global
magnetohydrodynamic (MHD) and test-particle simulations, outside the scope of
this study, would be needed to verify solar wind structure impact as the main
trigger for electron precipitation [<]see discussion in¿Ukhorskiy22:NatSR,
Chan23:frontiers. The application of such models is left for future work.

###### Acknowledgements.

We acknowledge support from NASA contract NAS5-02099. Work at Los Alamos
National Laboratory was performed under the auspices of the United States
Department of Energy. Q.M. would like to acknowledge the NASA grant
80NSSC20K0196 and NSF grant AGS-2225445. A.V.A and X.-J.Z. acknowledge support
from the NASA grants 80NSSC23K0108, 80NSSC23K0403, 80NSSC21K0729, and from the
NSF grant 2021749. V.A. and A.R. also acknowledge support from NSF grants
AGS-1242918, AGS-2019950. We are grateful to NASA’s CubeSat Launch Initiative
for ELFIN’s successful launch. We acknowledge early support of the ELFIN
project by the AFOSR, under its University Nanosat Program; by the UNP-8
project, contract FA9453-12-D-0285; and by the California Space Grant program.
We acknowledge the critical contributions of the numerous volunteer ELFIN team
student members. We acknowledge the GEO-KOMPSAT-2A magnetometer team (Ulrich
Auster, Dragos Constantinescu; Institut für Geophysik und Extraterrestrische
Physik, Technische Universität Braunschweig, Braunschweig, Germany) for their
high quality dataset. We also acknowledge the support of NASA contract
NAS5-02099 for the use of data from the THEMIS Mission, specifically K.
H.Glassmeier, U. Auster, and W. Baumjohann for the use of FGM data (provided
under the lead of the Technical University of Braunschweig and with financial
support through the German Ministry for Economy and Technology and the German
Center for Aviation and Space (DLR) under contract 50 OC 0302) and C. W.
Carlson, J. P. McFadden for the use of ESA data.

### Open Research

ELFIN data is available at https://data.elfin.ucla.edu/
THEMIS&ARTEMIS data is available at http://themis.ssl.berkeley.edu.
Sym-H and AE indexes were downloaded from https://supermag.jhuapl.edu/
GEO-KOMPSAT-2A (SOSMAG) data is made available via ESA’s Space Safety
Programme and its provision forms part of the ESA Space Weather Service System
at https://swe.ssa.esa.int/
Data access and processing was done using SPEDAS V3.1, see Angelopoulos19.

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