Acceleration of Electrons and Ions by an “Almost” Astrophysical Shock in the
Heliosphere
Immanuel Christopher Jebaraj1 , Oleksiy Agapitov2 , Vladimir Krasnoselskikh2,3 , Laura Vuorinen1 , Michael Gedalin4 ,
Kyung-Eun Choi2 , Erika Palmerio5 , Nicolas Wijsen6 , Nina Dresing1 , Christina Cohen7 , Athanasios Kouloumvakos8 ,
Michael Balikhin9 , Rami Vainio1 , Emilia Kilpua10 , Alexandr Afanasiev1 , Jaye Verniero11 , John Grant Mitchell11 ,
Domenico Trotta12 , Matthew Hill8 , Nour Raouafi8 , and Stuart D. Bale2,13
1 Department of Physics and Astronomy, University of Turku, 20500 Turku, Finland; immanuel.c.jebaraj@gmail.com
2 Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
3 LPC2E/CNRS, UMR 7328, 45071 Orléans, France
4 Department of Physics, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel
5 Predictive Science Inc., San Diego, CA 92121, USA
6 Centre for Mathematical Plasma Astrophysics, KU Leuven, 3001 Leuven, Belgium
7 California Institute of Technology, Pasadena, CA 91125, USA
8 The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA
9 University of Sheffield, Sheffield, S10 2TN, UK
10 Department of Physics, University of Helsinki, 00014 Helsinki, Finland
11 Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
12 The Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2AZ, UK
13 Physics Department, University of California, Berkeley, CA 94720, USA
Received 2024 April 24; revised 2024 May 9; accepted 2024 May 18; published 2024 June 6
Abstract
Collisionless shock waves, ubiquitous in the Universe, are crucial for particle acceleration in various astrophysical
systems. Currently, the heliosphere is the only natural environment available for their in situ study. In this work, we
showcase the collective acceleration of electrons and ions by one of the fastest in situ shocks ever recorded,
observed by the pioneering Parker Solar Probe at only 34.5 million km from the Sun. Our analysis of this
unprecedented, near-parallel shock shows electron acceleration up to 6MeV amidst intense multiscale
electromagnetic wave emissions. We also present evidence of a variable shock structure capable of injecting
and accelerating ions from the solar wind to high energies through a self-consistent process. The exceptional
capability of the probe’s instruments to measure electromagnetic fields in a shock traveling at 1% the speed of light
has enabled us, for the first time, to confirm that the structure of a strong heliospheric shock aligns with theoretical
models of strong shocks observed in astrophysical environments. This alignment offers viable avenues for
understanding astrophysical shock processes and the self-consistent acceleration of charged particles.
Unified Astronomy Thesaurus concepts: Interplanetary shocks (829); Solar energetic particles (1491); Solar
coronal mass ejection shocks (1997); Interplanetary particle acceleration (826)
1. Introduction
Collisionless shock waves (CSWs), resulting from conver-
ging flows in tenuous plasma, are a fundamental phenomenon
in plasma physics (Sagdeev 1966; Galeev 1976; Lembege et al.
2004) capable of heating the plasma and accelerating charged
particles (Kennel et al. 1985; Blandford & Eichler 1987). While
ubiquitous in diverse environments, from planetary bow shocks
to supernova remnants (SNRs), our comprehension of particle
energization (heating and acceleration) at these shocks remains
incomplete (Malkov & Drury 2001; Lembege et al. 2004). It is
mostly the radiation generated by energized electrons that
makes the detection of CSWs, like those in SNRs, possible
(Helder et al. 2012). Direct in situ examination of astrophysical
shocks is currently not possible, leading to a limited under-
standing of the exact mechanisms behind particle acceleration
and the ensuing radiation. At present, heliospheric shocks are
the only natural CSWs accessible for direct in situ study,
making them essential for comprehending shock structure,
evolution, and particle energization mechanisms. In particular,
the shock transition, which marks the finite region between the
upstream and downstream flows, plays a crucial role in
understanding the redistribution of kinetic energy (Balikhin
et al. 1993; Krasnosselskikh et al. 1995; Agapitov et al. 2023).
Consequently, heliospheric shocks, which may in many aspects
be similar to young SNR shocks, have become a key focus of
research (Terasawa 2003).
In magnetized CSWs, such as those found in SNRs and the
heliosphere, particle motion is determined by the angle θBn
between the upstream magnetic field and the shock normal.
CSWs are classified into quasi-parallel (θBn< 45°) and quasi-
perpendicular (θBn> 45°) based on this angle. Observational
surveys have often found the brightest radio and X-ray
synchrotron emissions in regions of SNRs where the shock is
quasi-parallel (e.g., Giuffrida et al. 2022; Vink et al. 2022).
They are also thought to be the most efficient particle
accelerators (Vink 2020) and are of particular interest for
in situ exploration. Quasi-parallel shocks have been understood
for nearly eight decades (Moiseev & Sagdeev 1963; Sagdeev
1966; Quest 1988), but observational efforts have not yet
yielded conclusive results (Burgess et al. 2005, and references
therein). Another critical parameter in the study of CSWs is the
The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 https://doi.org/10.3847/2041-8213/ad4daa
© 2024. The Author(s). Published by the American Astronomical Society.
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1
Alfvén Mach number (MA), which is directly related to the
proportion of flow kinetic energy dissipated at the shock. It is
defined as the ratio of the upstream flow speed to the
characteristic wave speed in highly magnetized plasma, known
as the Alfvén speed (vA). Typically, heliospheric shocks exhibit
MA values of less than 10
2 (Masters et al. 2013a), while SNR
shocks can reach MA values of around 10
3 (Vink 2020). A final
important parameter is the plasma-β, which is the ratio of
kinetic plasma pressure to magnetic field pressure. It is
generally believed to control the evolutionary characteristics
of shocks. Those developing in a low plasma-β regime tend to
exhibit large-amplitude overshoot magnetic fields (Russell
et al. 1982).
SNR shocks such as Tycho and Vela Jr. expand with
velocities of around 3000 km s−1 and are established accel-
erators of cosmic rays >1014 eV (100 TeV) by channeling up to
∼10% of their kinetic energy into particle acceleration (Helder
et al. 2009). A key factor in the acceleration of high-energy
particles is the shock’s ability to confine particles between
converging scattering centers, such as electromagnetic waves,
on either side of the CSW. These scattering centers,
fundamental to the theory of diffusive shock acceleration
(DSA), enable particles to repeatedly cross the shock and gain
energy in the process (Axford et al. 1977; Krymskii 1977;
Bell 1978; Blandford & Ostriker 1978). This energy acquisition
process persists until the particles can escape the shock’s
influence, conventionally dubbed the duration of particle
confinement (Hillas 1984). Planetary bow shocks, the strongest
heliospheric shocks, are incapable of confining particles long
enough to accelerate relativistic particles due to their small size
(Hoppe & Russell 1982; Terasawa 2011).
CSWs driven by solar eruptive events such as coronal mass
ejections (CMEs) can occasionally accelerate particles to
energies of …109 eV (GeV; Reames 1999). The most significant
acceleration occurs in the relatively denser solar atmosphere
when these shocks are fast but not very large, highlighting the
importance of their early evolution (Afanasiev et al. 2018). This
process is somewhat analogous to that of young SNR shocks,
which are capable of accelerating particles to 1015 eV (PeV)
during their rapid evolution within a dense medium (Vieu et al.
2022). A recent statistical study of the strongest CME-driven
shocks from the past decade suggests that high-energy electrons
are likely accelerated by the shock through a mechanism similar
to that affecting ions (Dresing et al. 2022). This draws attention
to the precise process of shock-induced particle injection and
acceleration through DSA, processes that are actively studied
(Malkov & Völk 1998; Malkov & Drury 2001). The complexity
of this process is exacerbated by the significant mass disparity
between ions and electrons, with protons being 1836 times
heavier. This separation of scales necessitates distinct processes
for the energization of protons and electrons at their respective
scales (Lembege et al. 2004).
On 2023 March 13, during its 15th perihelion, NASA’s
Parker Solar Probe (PSP) mission (Fox et al. 2016) encountered
an extraordinary interplanetary (IP) shock at merely 0.24 au
from the Sun. This CME-driven shock, one of the fastest IP
shocks ever recorded in situ, was traveling at 1% the speed of
light and exhibited a near-parallel geometry. In this study, we
detail the distinct features observed in the transition region of
this shock and its impact on particle behavior, enhancing our
understanding of strong shocks in both heliospheric and
astrophysical contexts. This investigation was enabled by
PSP overcoming the engineering challenges of entering the
Sun’s atmosphere, coupled with the exceptional capabilities of
its high-fidelity instrument suites to measure such phenomena
in great detail. Information about PSP’s instrument suites used
in this study can be found in Appendix A.
2. Results from the Analysis
2.1. One of the Fastest IP Shocks Observed In Situ to Date
In Figures 1(A) and (B), we present magnetic field and ion
measurements during a 9 hr period (03:00–12:00 UT) on 2023
March 13. The coordinate system used throughout the manuscript
is the inertial radial–tangential–normal (RTN) system, where the
radial component R is oriented along the Sun–spacecraft line; the
transverse component T is defined to be orthogonal to the
rotational axis of the Sun and the radial component, i.e.,
T=Ωe×R; and the normal component N completes the
orthogonal right-handed triad and, in this case, is aligned with
the normal of the ecliptic plane. The two panels provide details
on the preevent conditions and the in situ arrival of the shock
driven by a large magnetic structure, the CME. The upstream
bulk flow speed, measured by the Solar Probe ANalyzer for Ions
(SPAN-i), remains consistent throughout the period, averaging
410± 40 km s−1 in the 15 minutes prior to the shock’s arrival.
However, this consistency does not extend to the number density,
which is underestimated, as detailed in Appendix B.2. Similarly,
the upstream magnetic field is averaged over the same period,
while the downstream magnetic field is averaged over a
subsequent 10 minute period; both are listed in Table 1.
PSP observed the shock propagating almost exactly radially
outward, as indicated by the estimated shock normal nRTN( ˆ ), which
is also listed in the table. Figures 1(C)–(E) provide a zoomed-in
view of the shock’s arrival at 07:13UT, marked by a vertical line,
and cover the 75minutes leading up to it. During the shock’s
passage, the downstream plasma flow exceeded SPAN-i’s
measurement capabilities, as depicted in Figures 1(B), (D), and
(E). By combining data from SPAN-i and EPI-Lo and utilizing
the principle of mass flux conservation across the shock (detailed
in Appendix C.3), we calculate the shock speed to be
∼2800± 300 km s−1 in the spacecraft frame. This classifies it as
one of the fastest shocks ever recorded in situ, placing it in the same
category as the one described in Russell et al. (2013). Additionally,
the occurrence of such a strong shock (MA∼ 9.1± 1.35) in a low-
β plasma environment (∼0.16± 0.031), along with its near-parallel
geometry (8°± 4°), makes it an exceptionally rare in situ
observation. A list of the most relevant plasma and shock
parameters along with their uncertainties is presented in Table 1.
The uncertainty for each parameter is subsequently propagated
when estimating related parameters, following the general fractional
error propagation. For instance, the shock normal is derived as an
average from minimum variance analysis (MVA) and the magnetic
coplanarity theorem (MCT), detailed in Appendix C.1. Addition-
ally, unorthodox methodologies employed to estimate plasma
density contribute to the uncertainty of the shock parameters, as
discussed in Appendix B.2.
A notable characteristic of quasi-parallel shocks is the
patchwork of complex magnetic structures making up an
extended transition region, typically in the order of hundreds of
ion inertial lengths (λi, the characteristic distance over which
ions respond to electromagnetic changes; Burgess et al. 2005).
This contrasts with quasi-perpendicular shocks, known for their
sharp transition in the form of a ramp and overshoot
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(Krasnoselskikh et al. 2013). This complexity of quasi-parallel
shocks is illustrated in Figures 1(F)–(H), which display the
magnetic field, its fluctuations, and the ion temperature over a 2
minute interval (07:12–07:14 UT). As we approach the shock
transition, marked by the vertical line, there is a noticeable
increase in the amplitude of magnetic field fluctuations (δB/B),
indicative of intense upstream wave activity. The data also
show that the magnitude of the magnetic field intensifies before
the transition, likely as a result of shock mediation by energetic
particles. This amplification of the magnetic field and the
intensification of the relative fluctuations is also predicted by
theoretical models of strictly parallel shocks (e.g., Wang et al.
2022). The shock transition is characterized by δB/B… 0.5,
preceding the ramp-overshoot region, which exhibits δB/B… 2.
Figure 1(H) displays a sudden rise in ion temperature at the
transition, consistent with the expected behavior for magneto-
hydrodynamic (MHD) shocks (Kennel 1988). While it is
evident that the temperature sharply increases at the transition,
the SPAN-i measurements do not accurately reflect down-
stream conditions.
2.2. Electron Acceleration to Ultrarelativistic Energies
A particularly notable and unprecedented observation
concerning this strong quasi-parallel shock is the local
Figure 1. Magnetic field and plasma measurements during the shock encounter. Panels (A) and (B) provide a 9 hr overview of the magnetic field and the 1D proton
energy flux, capturing the preevent solar wind, the in situ shock passage, the following sheath region, and the initial portion of the associated CME ejecta. The SPAN-i
data downstream of the shock do not accurately represent reality, as the flow is largely deflected away from the detector’s FOV. Panels (C)–(E) offer an 80 minute
close-up leading to the shock arrival, showing variations in the bulk ion distribution as captured by the SPAN-i and EPI-Lo instruments. Finally, panels (F)–(H) focus
on a 2 minute snapshot close to the shock transition, emphasizing fluctuations in the total magnetic field as well as the change in proton temperature. The downstream
proton temperature is marked with hatching due to significant instrumental uncertainties.
Table 1
List of Relevant Plasma and Shock Parameters Associated with the 2023
March 13 Event
Parameter Data
Shock normal (MVA, MCT), nRTNˆ [0.984 ± 0.01, −0.07 ± 0.036,
−0.128 ± 0.096]
Shock angle, θBn (deg) 8° ± 4°
Shock speed, vsh 2800 ± 300 km s
−1
Upstream magnetic field, Bu 90 ± 5 nT
Downstream magnetic field, Bd 140 ± 7 nT
Overshoot magnetic field, Bmax 330 nT
Magnetic compression, rB 1.55 ± 0.1
Upstream electron density (RFS), nu 46.5 ± 15 cm
−3
Downstream electron density
(RFS), nd
184 ± 35 cm−3
Density compression, rgas 4
Upstream ion inertial length, λi 32.5 ± 3 km
Upstream bulk flow speed, vu 410 ± 40 km s
−1
Downstream bulk flow speed, vd 2200 ± 200 km s
−1
Upstream Alfvén speed, vA 268 ± 20 km s
−1
Upstream ion beta, βu 0.16 ± 0.031
Alfvén Mach number, MA 9.1 ± 1.35
Sonic Mach number, Ms 25.4 ± 4.5
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acceleration of electrons, with energies ranging from tens of
keV (subrelativistic) to 6 MeV (ultrarelativistic). Observation
of the local acceleration of relativistic electrons (300 keV to
3MeV) is exceptionally rare in IP shocks (Jebaraj et al. 2023;
Talebpour Sheshvan et al. 2023) and is even less frequent at
planetary bow shocks, regardless of their strength (Masters
et al. 2013b). The occurrence of ultrarelativistic electrons at
these shocks has never been documented before. The rarity of
local electron acceleration at IP shocks can be attributed to a
combination of scale-related challenges and a lack of high-
fidelity instrumentation. Physical challenges, such as the
energization of electrons from a thermal core, require specific
processes that affect electrons at scales close to their
gyrofrequency (ωce). These processes are related to funda-
mental issues of energy redistribution in CSWs (Balikhin et al.
1993; Krasnosselskikh et al. 1995; Schwartz et al. 2011).
Additionally, their acceleration also necessitates the presence of
oblique waves across a wide range of frequencies. Figures 2(A)
and (B) present energetic electron observations during a 90
minute period surrounding the shock’s arrival. Figure 2(A)
displays the counts per second of relativistic electrons
(>1MeV) throughout this interval, while Figure 2(B) provides
differential energy fluxes of lower-energy electrons, ranging
from 50 to 350 keV. Notably, there is a significant increase in
electron fluxes and counts across a wide range of energy when
approaching the shock (between 06:40 and 07:13 UT), thus
illustrating its impact on electron acceleration.
The observed range of electron energies, spanning sub-
relativistic to ultrarelativistic, implies the presence of multiscale
electromagnetic structures in and around the shock transition,
affecting electrons across all these energies. Figure 2(B) shows
that while subrelativistic electrons are significantly affected by
the shock transition, relativistic and ultrarelativistic electrons
seem largely unaffected. This distinction arises from the
changing gyration radius (Larmor radius) of electrons relative
to the scale of the magnetic and electric field gradients in the
transition. The variations in these scales with respect to each
other may induce either adiabatic or nonadiabatic behavior in
the electrons, resulting in their energization (Balikhin et al.
1998). Regardless of the exact mechanism, once the electron
gyrations reach the scales at which they are affected by ion-
scale waves, they can diffuse similarly to ions (Malkov &
Drury 2001). The upstream data reveal fluctuations in electron
fluxes at distinct times, specifically at 06:00 UT and 06:40 UT,
suggesting localized upstream phenomena. Nonetheless, the
limited resolution of electron observations restricts a more
detailed analysis of these variations.
2.3. Self-consistent Injection and Acceleration of Solar
Wind Ions
In Figure 2(C), we showcase the ion fluxes measured by EPI-
Lo’s sunward-pointing detector (W3) at the shock, and up to
90minutes prior, to investigate the motion of energetic ions.
Measurements from all EPI-Lo wedges are presented in
Figures 8 and 9 of Appendix D. A striking observation is the
intense population of ions streaming ahead of the shock,
persisting for the entire 90 minute duration, peaking between
06:40 and 07:13 UT. Figure 2(D) illustrates the fluctuations in
the magnetic field (δB/B) on a characteristic timescale of τ= 1
minute, corresponding to a frequency of approximately 0.02 Hz.
This frequency roughly matches the resonance frequency for the
lowest energy of the streaming ions further from the shock,
namely, ∼1MeV. The fluctuations are categorized into
transversal (δB⊥/B) and parallel (δB∥/B) components, with the
former being significantly larger than the latter within the same
time frame. The technical details of these analyses can be found
in Appendix E.
Figure 2. Energetic particles and the evolution of the wave foreshock. Panels (A)–(D) show the time–energy plots for high-energy electron counts detected by EPI-Hi,
low-energy electron flux from EPI-Lo, proton flux from EPI-Lo, and the amplitude of transversal (⊥) and parallel (∥) magnetic fluctuations. In panel (E), we present
the proton intensity spectra for three selected times (06:40, 07:10, and at the shock, averaged as 07:13–07:15 UT) with an E−1 power law shown for reference, which
indicates the changes in energetic particle distribution. Panel (F) shows the Fourier power spectra of BR (estimating B∥ power) and the sum of BT and BN (estimating
B⊥ power) in the foreshock and the background. Variations in the proton flux and magnetic fluctuations over a 2 minute period surrounding the shock transition are
shown in panels (G) and (H).
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Another intriguing feature is the observed absence of flux at
energies below ∼1MeV, before 07:05 UT. This absence of flux
extends to higher energies further from the shock, especially
prior to 06:40 UT. In Figure 2(E), the omnidirectional intensity
spectra of protons are shown for three distinct time periods: at
the shock (07:13–07:15 UT), near-upstream (07:10 UT), and
far-upstream (06:40 UT). These spectra highlight a marked
absence of flux near 1 MeV, followed by a significant flux
increase toward 10MeV, forming what can be described as a
spectral rollover at low energies. The significant absence of
low-energy particles away from the shock may be due to the
fact that only high-energy particles diffuse farther from the
shock. Approaching the shock, however, the spectrum evolves
into a single power law with a spectral index of E−1 beyond
∼250 keV. Below approximately 250 keV, the spectral index
becomes steeper, approaching E−2. However, we refrain from
interpreting this finding, as it is potentially erroneous to
perform a spectral fit over a range that does not extend across at
least an order of magnitude.
Figure 2(F) presents the Fourier power spectra for B∥ and B⊥
during a 33 minute interval upstream (06:40–07:13 UT) and
compares it to the preevent background (01:30–02:07 UT). For a
detailed description of the spectral analysis, please refer to
Appendix E.2. Generally, upstream power for both B∥ and B⊥
exceeds preevent levels by more than an order of magnitude at
frequencies above the resonance frequency for particles of
energy ∼1MeV ( fres
1 MeV). Below this frequency, we observe
little difference between the upstream and preevent power of B⊥.
In contrast, there is an increase in B∥ relative to the preevent
power above fres
5 MeV. However, it is important to note that
frequencies at or below 10−2 Hz are subject to significant
uncertainties due to various factors, as detailed in Appendix E.2.
Zooming into the shock ramp, we note an uptick in both the
amplitude and intensity of these fluctuations. In Figures 2(G) and
(H), we show the energetic protons and magnetic field
fluctuations within a 2 minute window (07:12–07:14 UT) around
the ramp. Here, we detect an intense proton population with
energies between 100 and ∼250 keV, which correspond to the
energy range where the spectra become steeper in Figure 2(E).
This occurs concurrently with high-intensity, large-amplitude
δB⊥/B… 0.5 fluctuations. These fluctuations are estimated at
τ= 5 s, corresponding to resonant frequencies above 0.2 Hz,
which match those of protons in the hundreds of keV range. The
δB∥/B also shows an increase as we approach the ramp,
especially after 07:13 UT. These observations concur with prior
studies on the challenges of particle confinement at quasi-parallel
shocks leading to an extensive wave foreshock (Kennel et al.
1986). It also supports theoretical predictions that wave power
declines with increasing distance from the shock owing to the
reduced particle fluxes (Bell 1978; Vainio & Laitinen 2007).
Finally, the continuous detection of ions with energies less
than 100 keV to 10MeV near the shock is noteworthy.
Figure 2(C) highlights data from the W3 detector of EPI-Lo,
but all EPI-Lo detectors registered ions above 1MeV for about
90 minutes before the shock arrival. In contrast, „300 keV
protons were primarily observed near the shock transition. It is
likely that these are either reflected or gyrating ions, as
previously suggested by Kennel (1981), and thus deviate from
the E−1 law below ∼250 keV. Distinguishing between the two
components would require higher-cadence particle measure-
ments. However, if we assume near-specular reflection to be
active, the energy of the ions would primarily peak at twice the
speed (4 times the energy) of the upstream bulk flow (in the
shock rest frame), as most of the ions are reflected only once
(Gedalin 2016). Considering the quasi-parallel geometry of the
shock, these ions can diffuse ahead of the shock and participate
in DSA, thereby gaining significantly higher energies. An E−1
scaling law supports this process occurring in a lossless
manner, meaning that the protons (ions) are confined in the
vicinity of the shock without being lost. Conversely, this could
also suggest that they are replenished at the same rate as they
are lost, underscoring the efficiency of the shock in particle
acceleration.
2.4. Structure of the Quasi-parallel Shock Transition
In contrast to the infinitesimal boundary between two flows
marking a shock in MHD, the shock transition is where
processes crucial for regulating the distribution of kinetic
energy occur, such as dispersion, dissipation, and nonlinear
steepening (Krasnoselskikh 1985; Krasnoselskikh et al. 2002).
In Figure 3, we present a comprehensive analysis of the shock
transition, with further details available in Appendix F.
Figure 3(A) illustrates the magnetic field components and
magnitude over a 1.75 s interval (07:13:10.25–07:13:12.00),
complemented by Figure 3(B), which depicts the electric field.
Figures 3(C) and (D) depict the dynamic spectra of magnetic
and electric field perturbations, respectively, derived from the
Morlet wavelet transform. These panels emphasize the shock
ramp and its associated precursor wave train, notably within the
20–30 Hz frequency range (indicated by arrows), which is
higher than the ion gyrofrequency (ωci∼ 1.4 Hz). The wave
train observed here consists of circularly polarized waves, as
seen in Figure 3(G), the plane containing the intermediate and
maximum variance axes. Consequently, they also exhibit high
planarity in the plane containing the maximum and minimum
variance axes as shown in Figure 3(H). Such characteristics
indicate that these are electromagnetic whistler mode waves,
which are occasionally observed ahead of the shock ramp and
are associated with fundamental shock processes (Sundkvist
et al. 2012). These waves are right-hand circularly polarized in
the spacecraft frame and occur between the ion and electron
gyrofrequencies (ωci< ω< ωce). As the wavenumber (k)
increases and they approach ωce, these waves can also increase
in amplitude and may steepen.
The wave normal angle (WNA), depicted in Figure 3(E) (θkB,
the angle between the wave normal and the background
magnetic field direction), indicates that both the precursors and
the ramp are quasi-perpendicular to the magnetic field. Their
oblique propagation is an essential factor to be a standing wave
in the shock frame. Figure 3(F) illustrates the radial component
of the Poynting flux, estimated in the spacecraft frame,
indicating an anti-sunward propagation direction of the observed
wave activity near the shock. The technical material related to
the analysis of the precursor whistler waves can be found in
Appendix F.2. From this analysis, the estimated phase speed
(vph) is approximately 400 km s
−1. Given that θkB is approxi-
mately 75°, the radial component is calculated to be around
2600± 200 km s−1. This analysis of the precursor whistler wave
train lends credibility to the estimated shock speed.
More importantly, we demonstrate that the ramp and
precursors display a quasi-perpendicular geometry. This
finding is in line with theoretical predictions (Gedalin 1998;
Gedalin et al. 2015), which suggest that a quasi-parallel shock
becomes oblique, even quasi-perpendicular, due to the increase
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in transversal magnetic field amplitude in the ramp-overshoot
region. However, prior to our study, observational support for
this was limited (Balikhin et al. 2023). We have clearly
demonstrated that the enhancement of the transversal magnetic
field at the ramp overshoot leads to a quasi-perpendicular
geometry. The degree of enhancement is particularly note-
worthy given that the shock develops in a low plasma-β
environment, where large ramp-overshoot structures have
previously not even been observed in either oblique or quasi-
perpendicular obstacle shocks (Russell et al. 1982).
3. Discussion
Strong CSWs, spanning a wide range of Mach numbers in the
heliosphere, have been extensively studied to enhance our
understanding of particle acceleration in astrophysical shocks,
such as those in SNRs. However, in contrast to SNR shocks,
even the strongest heliospheric shocks (planetary bow shocks)
are ineffective accelerators of relativistic particles (Hoppe &
Russell 1982). This inefficiency is largely attributed to their
smaller size and the weak magnetization of the ambient medium,
resulting in inadequate particle confinement (Terasawa 2011).
Conversely, IP traveling shocks are significantly larger but rarely
as strong as planetary bow shocks. Remote observations have
occasionally identified CME-driven shocks possessing strengths
comparable to planetary bow shocks and speeds similar to some
SNR shocks (Yurchyshyn et al. 2005). Particle acceleration by
these shocks is anticipated to be highly efficient (Afanasiev et al.
2018). Measurements from PSP enable us to investigate these
shocks in situ, unprecedentedly close to the Sun. This proximity
significantly narrows the gap between our understanding of
heliospheric shocks and SNRs, allowing for an in-depth study of
efficient acceleration mechanisms.
In this study, we have presented extraordinary observations
of a strong (MA∼ 9.1± 1.35), fast (vsh∼ 2800± 300 km s
−1),
and near-parallel (θBn∼ 8° ± 4°) traveling IP shock. This
shock, one of the fastest IP traveling shocks observed in situ to
date, exhibits a magnetic structure that aligns with theoretical
models. Figure 4(A) illustrates the clear rotation of the
transverse magnetic field components at the shock transition
not obscured by nonlinear structures formed in the foreshock.
This alignment with theoretical predictions is essential for
making reasonable comparisons with SNR shocks.
As expected from such a prominent shock, it proved to be an
efficient accelerator of particles. A notable observation is the local
acceleration of electrons across a wide range of energies by such a
near-parallel shock, often disregarded as potential accelerators of
energetic electrons. Typically, in the MHD context of a near-
parallel shock, the magnetic field amplification is minimal and
smooth, lacking fine structures, which means the electrons are
barely affected by it. Electron acceleration presents a significant
challenge due to the substantial scale difference from ions, as
highlighted by the mass ratio. In the case of quasi-perpendicular
shocks, electron acceleration is believed to primarily occur via
simple adiabatic reflection (in low-β plasma) due to the large
magnetic gradient. However, only a small number of particles
participate due to the steep energy requirements for injection
(Jebaraj et al. 2023). Conversely, in quasi-parallel shocks, where
there is no single large magnetic gradient, electron acceleration
may require the presence of high-frequency oblique wave activity.
These waves can induce either adiabatic, nonadiabatic, or both
types of behavior in electrons, thereby energizing them
(Gedalin 2020). The presence of such waves is illustrated in the
schematic of the shock transition presented in Figure 4(B).
The schematic, based on the magnetic field data in Figure 4(C),
details various spatial scales and directions for clarity. It
demonstrates that at scales where the shock transition is considered
a simple MHD discontinuity, it is quasi-parallel. At smaller scales,
within the shock’s transition region, we identify whistler precursors
and the ramp-overshoot structure. This area is marked by quasi-
perpendicular electromagnetic waves, instrumental in the injection,
trapping, and eventual acceleration of electrons to relativistic
energies. Such processes have been supported by numerical
Figure 3. Analysis of the waves at the shock transition. Panels (A) and (B) show the magnetic and electric field components. The duration of the precursor whistlers
(between 07:13:11.10 and 07:13:11.45) is annotated on top. Panel (A) also indicates the approximate spatial scale of the upstream in units of λi estimated in the plasma
frame. Panels (C) and (D) show the Morlet wavelet spectrum of the magnetic and electric fields. The θkB angle between the wavevector k and the magnetic field B is
shown in panel (E). In panel (F), we show the Poynting flux estimated in the spacecraft frame Ssc. Finally, the hodographs of precursor whistler waves in the maximum
vs. intermediate variance plane and the maximum vs. minimum variance planes are presented in panels (G) and (H), respectively. In both panels, the blue arrow
denotes the mean field B0.
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The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
simulations (Riquelme & Spitkovsky 2011). Once electrons attain
sufficient energy and their Larmor radii increase adequately, they
can interact with ion-driven waves. Thus, accurately quantifying
these distinct spatial scales is critical, as it influences the
redistribution of flow kinetic energy into processes like electron
heating and acceleration (Balikhin et al. 1993; Schwartz et al.
2011).
Finally, we have demonstrated for the first time that the
quasi-perpendicular ramp-overshoot region reflects ions,
whereas the quasi-parallel upstream region allows their escape.
The latter inability of the quasi-parallel shock to effectively
confine particles at the ramp results in the generation of ion-
scale waves in the upstream region. These phenomena
collectively create a continuous process at the shock transition,
essential for particle injection and sustained acceleration,
resulting in an uninterrupted ion population. We have observed
this continual presence of ions with energies ranging from less
than 100 keV to 10MeV. We found the concurrent occurrence
of >1MeV streaming ions and intense transverse waves up to
90 minutes prior to shock arrival, suggesting active DSA. This
is supported by the low-energy rollover observed in the
upstream energy spectra, which is unstable, leading to the
growth of ion-driven instabilities. Conversely, the confinement
of low-energy ions near the shock leads to a consistent E−1
energy spectrum, in line with DSA predictions (with no losses)
for a shock with rgas= 4.
In this study, we used in situ evidence to demonstrate that a
strong quasi-parallel shock can self-consistently accelerate both
ions and electrons from the background medium to high
energies. Such as self-consistent mechanism is enabled by the
amplification of both the magnitude of the mean magnetic field
and the level of multiscale fluctuations relative to it. This is
compelling even from an elementary prediction that a shock
must either be very large or highly magnetized to effectively
confine high-energy particles (Hillas 1984; Terasawa 2011).
Our findings naturally lead to the conclusion that strong shocks
close to the Sun are highly effective at particle confinement by
virtue of being highly magnetized. This makes them compar-
able to much larger shocks with lesser magnetization. These
conditions are somewhat analogous to the most efficient PeV
cosmic-ray acceleration scenarios proposed, where a young
SNR rapidly expands in a dense and highly magnetized
medium (Vieu et al. 2022). These rare observations were made
possible by the pioneering capabilities of the PSP and its
unprecedented proximity to the Sun. If the physics of cosmic
shocks, like those in SNR blast waves, adhere to the
fundamental principles of CSWs, then understanding the
evolution of the shock transition is crucial for facilitating the
acceleration of charged particles.
Acknowledgments
Author contributions—The study was initiated by I.C.J.
and conceptualized together with O.V.A., V.V.K., and M.G.
The methodologies for data analysis were provided by I.C.J.,
O.V.A., V.V.K., L.V., M.G., and E.P. Data analysis was
performed by I.C.J., O.V.A., L.V., M.G., K.E.C., E.P., and
A.K. The ISeIS data were processed by J.G.M., L.V., C.M.S.C.,
N.D., and A.K. The SPAN-i data were prepared by J.V. and
analyzed by I.C.J., O.V.A., L.V., and K.E.C. The results were
interpreted by I.C.J., O.V.A., V.V.K., M.G., and R.V. The data
were visualized by I.C.J., O.V.A., L.V., and K.E.C. I.C.J. wrote
the manuscript and prepared the final draft. The final draft was
prepared taking into account extensive comments from O.V.A.,
V.V.K., M.G., M.B., N.D., R.V., E.K.J., and S.D.B. All authors
have agreed to the results presented in the manuscript.
Funding information—The Parker Solar Probe spacecraft
was designed and built and is now operated by the Johns
Hopkins Applied Physics Laboratory as part of NASAʼs Living
with a Star (LWS) program (contract NNN06AA01C). Support
from the LWS management and technical team has played a
critical role in the success of the Parker Solar Probe mission.
The authors express their gratitude to all the instrument teams
for their work in processing and publishing the publicly
available data from the Parker Solar Probe. All the data used in
this study are from the Parker Solar Probe spacecraft. The data
used in this study are available at the NASA Space Physics
Data Facility (SPDF), https://spdf.gsfc.nasa.gov. This research
Figure 4. Transition region of the quasi-parallel shock. Panel (A) displays the time evolution (depicted by the colors blue to red) of the transversal magnetic field
components. The dotted line through the middle represents the mean field, B0. Panel (B) illustrates a 2D schematic of the shock transition in the plasma frame. The
spatial scales are in λi (represented with 50λi × 50λi squares) and are estimated for the upstream and downstream separated at the edge of the quasi-parallel shock
(Q∥). The gray scale represents the change in B across the shock. The direction of B and the shock normal are also marked by arrows. The dark stripes in the middle
represent the quasi-perpendicular structure at the ramp and the whistler precursors. Panel (C) presents the magnetic field magnitude upon which the schematic is based.
7
The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
was supported by the International Space Science Institute
(ISSI) in Bern through ISSI International Team project
No. 575, “Collisionless Shock as a Self-Regulatory System.”
I.C.J., N.D., and L.V. are grateful for support by the Academy
of Finland (SHOCKSEE, grant No. 346902) and the European
Unionʼs Horizon 2020 research and innovation program under
grant agreement No. 101004159 (SERPENTINE). O.V.A. was
partially supported by NSF grant No. 1914670, NASAʼs Living
with a Star (LWS) program (contract 80NSSC20K0218), and
NASA grant contracts 80NNSC19K0848, 80NSSC22K0433,
and 80NSSC22K0522. O.V.A. and V.V.K. were supported by
NASA grants 80NSSC20K0697 and 80NSSC21K1770. V.V.K.
also acknowledges financial support from CNES through grants
“Parker Solar Probe” and “Solar Orbiter.” L.V. acknowledges the
financial support of the University of Turku Graduate School. E.P.
acknowledges support from NASA’s Parker Solar Probe Guest
Investigators (PSP-GI; grant No. 80NSSC22K0349) program.
N.W. acknowledges support from the Research Foundation—
Flanders (FWO-Vlaanderen, fellowship No. 1184319N). A.K.
acknowledges financial support from NASA NNN06AA01C
(SO-SIS Phase-E, PSP EPI-Lo) contract. J.L.V. acknowledges
support from NASA PSP-GI grant 80NSSC23K0208. The
FIELDS experiment was developed and is operated under NASA
contract NNN06AA01C.
Appendix A
Experimental Details
A.1. Electromagnetic Fields (FIELDS)
Our study primarily utilizes full electromagnetic fields
measured by the FIELDS instrument suite on board the PSP
spacecraft (Bale et al. 2016). The electric field measurements are
made using the electric fields instrument consisting of two pairs
of dipole electric field antennas oriented in the TN plane and
extending beyond the PSP heat shield and a fifth antenna located
behind the heat shield on the instrument boom; the location of
antenna V5 in the wake of PSP means the R component is
susceptible to detrimental interference by the wake electric field
and cannot be reliably interpreted (Bale et al. 2016). Two three-
component flux-gate magnetometers measure the magnetic field
from DC to approximately 60Hz during aphelion and up to 293
vector measurements per second during 2–4 days around
perihelion. The latter is used in the present study.
Additionally, we incorporate high-frequency electric field
measurements from both the high-frequency and low-fre-
quency receivers of the Radio Frequency Spectrometer (RFS;
Pulupa et al. 2017). The RFS includes four electric antennas
and measures over a wide frequency range, spanning from
1 kHz to 20 MHz at a 3.5 s cadence during the science phase. A
particularly relevant application of these measurements in our
study is in determining the electron plasma frequency, ωpe.
A.2. Solar Wind Electrons, Alphas, and Protons
Considering that shock waves manifest as discontinuities in
both electromagnetic fields and plasma, our study employed the
Solar Wind Electrons, Alphas, and Protons instrument suite
(Kasper et al. 2016), specifically using the ion electrostatic
analyzer referred to as SPAN-i (Livi et al. 2022). SPAN-i
measures the 3D velocity distributions of solar wind ions with an
additional time-of-flight component to distinguish between
protons and heavier ion species. For this event, we used the L3
sf00 data product corresponding to uncontaminated protons at a
3.5 s cadence in the energy range 20 eV to∼20 keV. However, it
is important to note a limitation: due to the placement of the
instrument on the ram side of PSP, its field of view (FOV) is
obstructed by the thermal protection system, which means only
partial plasma moments are available. Significant deflections in
the solar wind flow (characterized by the angle between the
magnetic field vector B and the plasma flow velocity vector v,
denoted as θBv), with respect to the spacecraft frame, may result
in parts of the bulk distribution being undetected by the
instrument. When the proton velocity distribution function
(VDF) sufficiently departs from the FOV of SPAN-i, the
temperature measurement is largely overestimated, since the
instrument will only capture the wings of the distribution.
An example of this deflection is evident at 05:30 UT in
Figure 1(B), where the VDF remains unrecorded, as deflections
in the +T direction are most susceptible to measurement
reliability. Additionally, during the shock-crossing period, the
proton VDF not only sufficiently deflected from the FOV but
also exceeded the energy range of SPAN-i. Consequently, the
downstream plasma measurements become entirely artificial
and fail to reflect the actual conditions. Regarding the
temperature at the time of the shock’s arrival, the proton
VDF’s tails are exceptionally broad, resulting in an anom-
alously high measured temperature. During the period of time
when the upstream velocity was obtained, however, the VDF
was sufficiently in the FOV, as verified by plotting the VDFs
from the L2 sf00 data product and confirming that the majority
of the bulk flow is unobstructed (not shown). However, parts of
the VDF other than the core may be unaccounted for when
estimating the number density, resulting in discrepancies.
A.3. Integrated Science Investigation of the Sun
To analyze the energetic particle populations, in particular
electrons and protons, we used the Integrated Science
Investigation of the Sun (ISeIS) instrument suite (McComas
et al. 2016). It measures energetic particles from ∼20 keV to
over 100MeV nuc–1 with two energetic particle instruments
(EPIs), EPI-Lo (Hill et al. 2017) and EPI-Hi (Wiedenbeck et al.
2017). EPI-Lo is a time-of-flight mass spectrometer with 80
separate apertures to provide a ∼2π wide FOV. We use a few
different data products from EPI-Lo, namely, the ChanP (triple
coincidence protons), ChanR (high time cadence triple
coincidence proton measurements), ChanT (time-of-flight-only
ion measurements), and ChanE (used primarily to measure
electrons) channels. EPI-Hi includes two low-energy telescopes
(LETs) measuring ions from ∼1 to 20MeV nuc–1: one double-
ended with a sunward facing aperture, LETA, and an anti-
sunward aperture, LETB, and a single-ended telescope, LETC,
pointing orthogonally to the LETA instrument axis. The higher
energies (>10MeV nuc–1) are captured in EPI-Hi by a double-
ended high-energy telescope (HET) with one side, HETA,
pointed sunward and the other, HETB, pointed anti-sunward.
The sunward and anti-sunward designations are based on the
assumption of the nominal magnetic field line.
Appendix B
Plasma Parameter Estimations
B.1. Estimation of the Downstream Flow Speed
The downstream distribution of the bulk plasma flow is
beyond the measurement capabilities of the SPAN-i instrument
for E15, which corresponds to approximately 20 keV or
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2000 km s−1. Consequently, it was not feasible to directly
obtain plasma parameters such as density and velocity at the
moment of the shock crossing, parameters that are crucial for
understanding the shock wave’s characteristics.
To gauge the extent to which the downstream bulk flow was
shifted, we utilized data from the EPI-Lo ChanT, which
extends down to 30 keV. This is illustrated in Figure 1(D) of
the main text, where part of the distribution is observable at
30 keV. This observation strengthens the assertion that the bulk
flow’s kinetic energy exceeded SPAN-i’s measurement range
and was not merely deflected away from its sensor. However, it
is a complex task to match a thermal distribution across two
different instruments. Therefore, we infer that the center of the
distribution lies somewhere between 20 and 30 keV. Since
these measurements represent the kinetic energy (Eke) of the
bulk flow, we estimated the downstream velocity (vd) using the
formula =v E m2d ke p , where mp denotes the proton mass.
This calculation yields a downstream velocity of approximately
2200± 200 km s−1. The±200 km s−1 uncertainty is due to the
large energy bin width (20–30 keV) that was considered.
Comparatively, the upstream bulk flow velocity (vu), measured
by the spacecraft, was around 410± 40 km s−1 in the 2 minute
interval preceding the shock’s arrival. While it is possible to get
an approximation for the magnitude, vd, of the downstream
flow vector, it is not possible to obtain the direction of the flow.
B.2. Estimation of Electron Density
To verify the plasma density measurements from SPAN-i,
we employed the electron plasma frequency measured by the
FIELDS/RFS electric field antennas as a proxy. Under usual
conditions, the RFS antennas determine electron density from
quasi-thermal noise (Liu et al. 2023). However, this approach
was not feasible during the observed period because the Debye
length (λDe) was larger than the effective length of the antennas
(Moncuquet et al. 2020). In such cases, electrostatic waves, and
especially electron beam-driven Langmuir waves typically
resonating near the electron plasma frequency (ωpe), can be
used. In cases where electron sound waves are present, a result
of electron cyclotron instabilities, the frequency can be
downshifted to approximately 30%–60% of ωpe (i.e.,
0.4−0.7ωpe; Lobzin et al. 2005). Therefore, the highest-
frequency waves detected in our observations are presumed
to be Langmuir waves.
When observed with a dipole antenna pair like the FIELDS/
RFS (namely, V1− V2 and V3− V4), electrostatic waves should
exhibit high phase coherence (Krasnoselskikh et al. 2011). We
constructed a phase coherence spectrum to identify such
coherent signals both upstream and downstream of the shock.
Coherence can be estimated as
g = * * *
* *
X X X X
X X X X
.2 0 1 0 1
0 0 1 1
( ˜ ˜ )( ˜ ˜ )
( ˜ ˜ )( ˜ ˜ )
In the above equations, *X X0 0˜ ˜ is the autospectrum from the
(channel 0) V12= V1− V2 dipole, and *X X1 1˜ ˜ is the autospec-
trum from the (channel 1) V34= V3− V4 dipole. *X X0 1˜ ˜ is the
cross-spectrum between the two channels.
The top panel of Figure 5 displays this coherence spectrum,
clearly distinguishing upstream electrostatic waves near the
Figure 5. In situ arrival of the shock as observed through high-frequency electric field data from the FIELDS/RFS. The top panel displays the coherence spectra,
while the middle panel presents the normalized linear polarization, Stokes Q/I. The estimated upstream and downstream plasma frequencies (ωpe) are indicated by
horizontal black lines, with arrows highlighting the observed electrostatic waves. The bottom panel juxtaposes the estimated electron density (ne)—with the range of
uncertainty depicted as a red shaded area—against the ion density measured by SPAN-i.
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The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
60± 10 kHz frequency channels. We focused exclusively on
highly coherent signals, enabling distinct identification of the
waves at the shock transition and the upstream. Nonstationary
processes and general noise typically exhibit near-zero phase
coherency. Intriguingly, two coherent downstream signals were
also detected, marked by arrows, at frequencies of
125± 10 kHz. A notable capability of the FIELDS/RFS
receivers is their measurement of full Stokes parameters,
providing robust verification of the wave types observed.
Langmuir waves, being highly field-aligned, are strongly
linearly polarized. Linear polarization is quantified by the
Stokes Q parameter normalized with the total intensity (Stokes
I), expressed as Q/I. Both Stokes Q and I are estimated as
= +* *I X X X X ,0 0 1 1˜ ˜ ˜ ˜
= -* *Q X X X X .0 0 1 1˜ ˜ ˜ ˜
The second panel of Figure 5 presents these strongly linearly
polarized electrostatic waves upstream, with the coherent
downstream signals also showing a relatively high degree of
linear polarization.
During the upstream interval from 07:06 to 07:12 UT, the
highest frequency recorded was 65± 10 kHz. This uncertainty
is due to the frequency channel’s 4.5% bandwidth and the
variation in the highest-frequency wave observed during this
period. For the downstream interval, we utilized the frequen-
cies of the two strongly coherent and linearly polarized signals,
125± 10 kHz.
To estimate the electron plasma density using Langmuir
waves, we can use the linear dispersion relation for Langmuir
waves in the spacecraft frame:
w w w q= + +
v k
kV
3
4
cos ,kBpe
th
2 2
pe
sw
where k is the wavenumber, =v k T m2 Bth e e represents the
electron thermal speed, and θkB is the angle between the solar
wind flow and the wavevector k. The equation includes a final
term accounting for the Doppler shift caused by the plasma
flow past the spacecraft. These two factors may cause ω to
deviate from ωpe: the increase in frequency due to the thermal
speed and the Doppler shift. It is noteworthy to mention that
the Doppler shift may be both positive and negative and
accounts for the largest contribution to the observed frequency.
The range of k was estimated by Graham et al. (2021), who
found 0.11„ kλDe„ 0.25 for typical parameters found in the
solar wind. For instance, they considered an electron temper-
ature Te∼ 15± 5 eV, similar to the values obtained by Liu
et al. (2023) using the PSP measurements, Te∼ 20± 5 eV. The
Doppler shift accounts for a solar wind speed Vsw∼ 400 km
s–1, which is similar to the vu= Vsw measured upstream of the
shock. Graham et al. (2021) also considered linearly polarized
Langmuir waves, which are field-aligned. By using these
parameters in the linear dispersion relation, we estimated the
Langmuir wave frequency to range from 0.95ωpe to 1.15ωpe.
As expected, the variation in ω is largely attributable to the
Doppler effect. It is worth noting that this estimation might
change when considering a more accurate but complex
dispersion relation, such as the quasi-electrostatic slow
extraordinary mode wave presented in Larosa et al. (2022).
The longitudinal component of the wave, indicated by the ratio
w
w
ce
2
pe
2 , becomes prominent when k is on the order of this ratio.
However, for the conditions presented here, where
~ww - -10 103 2ce
2
pe
2 – assuming ω≈ ωpe, its effect is minimal.
The ωpe is of particular interest, as it is directly related to the
electron plasma density (ne), which is given by the formula
w =

n e
m
,pe
e
2
0 e
where e is the elementary charge, ò0 is the vacuum permittivity,
and me is the electron mass. The ne can be estimated by
rearranging the formula for ωpe:
w= n m
e
.e
pe
2
0 e
2
Given the range of ω with respect to ωpe, we can directly
estimate a range of values for ωpe. We estimate that the ωpe
corresponding to ω= 65± 10 kHz is ωpe= 61.5± 10 kHz, and
for ω∼ 125± 10 kHz, we estimate ωpe= 121± 12 kHz. Next,
by applying the measured values of ωpe, we can estimate ne.
The upstream density using ωpe= 61.5± 10 kHz results in an
estimated average electron plasma density of 46.5± 15 cm−3.
However, data from SPAN-i, as shown in the last panel of
Figure 5, indicate an average proton density of approximately
22 cm−3, which is a factor of 2 smaller than our estimate, while
ωpe= 121± 12 kHz corresponds to an average electron density
of 184± 35 cm−3. We may consider the SPAN-i measurement
of number density to be a lower limit in our estimations.
Appendix C
Shock Parameter Estimations
C.1. Shock Normal
Identifying the shock wave’s normal direction necessitates
pinpointing its transition. To achieve this, we implemented a
moving average technique with a 30 s sliding window to filter
out high-frequency signals and isolate the magnetic gradient.
We observed an increase in the mean field 30 s prior to the
transition, indicated by the principal shock jump at 07:13 UT.
For the estimation of the normal, we employed two methods:
MVA (Sonnerup & Scheible 1998) and the MCT (Colburn &
Sonett 1966). Due to uncertainties and the absence of necessary
plasma measurements such as velocity, we could not apply
other methods such as velocity coplanarity and mixed-mode
techniques. To ensure robustness, all available methods are
often applied when estimating the shock normal (Paschmann &
Schwartz 2000).
For the MVA technique, applied when a spacecraft
encounters a transition layer like a shock front, the relevant
equations are
å l=
n
mn n m m
=
M n n .
1
3
Here, Mμν equals 〈BμBν〉− 〈Bμ〉〈Bν〉, and nMVAˆ aligns with
the smallest eigenvalue, lmin. We assess reliability using the
ratios l lint max and Bn/B, with l l  2int max and Bn/B„ 0.3
indicating a well-defined shock normal.
We selected the time window for MVA to span from 07:03
to 07:23 UT, i.e., centered on the shock ramp at 07:13 UT.
Within this interval, the eigenvalue ratio between the
intermediate and minimum variance directions, l lint min, was
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The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
approximately 7.5, suggesting a good distinction—the three
eigenvalues are l = 8298max , λint= 3070, and l = 408min .
The normal, indicated by the direction of the minimum
variance eigenvector, was determined to be [0.976, −0.052,
−0.216] in the inertial RTN coordinate system. However, the
magnetic field ratio Bn/B≈ 0.66 suggested that the normal
direction was not well defined, even after accounting for the
high-frequency components of the field fluctuations. For a
well-defined normal direction, it is expected that Bn/B< 0.1.
However, in the case of quasi-parallel shocks, where Bn is on
the order of B, the ratio of eigenvalues (l lint min) serves as a
far better indicator of quality (Paschmann & Schwartz 2000).
To corroborate these findings, we applied the MCT, the only
other feasible method using solely magnetic field data. The
MCT calculates the shock normal nMCTˆ , assuming that Bu, Bd,
and nˆ are coplanar:
=  - ´ ´- ´ ´n
B B B B
B B B B
.MCT
d u d u
d u d u
ˆ ( ) ( )
∣∣( ) ( )∣∣
We set the upstream and downstream windows for this
analysis from 07:04 to 07:12 UT and from 07:15 to 07:23 UT,
respectively. The choice of the interval is motivated by
previous statistical studies of in situ shocks (Kilpua et al.
2015). The estimated shock normal nˆ was found to be [0.995,
−0.101, −0.026] in the RTN coordinate system. Despite the
limitations of both methods, their yielding of similar results
lends credibility to the estimated shock normal.
C.2. Shock Geometry
We can determine the shock angle, θ, which is the angle
between the shock normal nˆ and the upstream magnetic field
Bu, using the following definition:
⎜ ⎟
⎛
⎝
⎞
⎠
q = B
B
n
n
arccos .Bn
u
u
· ˆ
∣∣ ∣∣ ∣∣ ˆ∣∣
Our calculations yielded shock angles of approximately
q ~ 12 . 5BnMVA for the MVA method and q ~ 3 . 9BnMCT for the
MCT method. Hence, both methods suggest that the shock was
quasi-parallel.
C.3. Shock Speed
The shock was measured in situ at a distance of
approximately 0.23 au, roughly 3 hr and 55 minutes following
the solar eruption. The FIELDS/RFS measurements presented
in Figure 6, the only remote-sensing observation in this period,
served as the basis for estimating the transit speed. The solar
eruption is marked by the dispersionless signal in the FIELDS/
RFS receiver when the probe was at 0.24 au. This timing
suggests a ballistic speed for the eruption-driven shock of
approximately 2450 km s−1. While this offers a basic first-order
estimate of the expected speed of the piston (CME), it does not
provide an accurate measure of the local shock speed.
Knowing the shock normal vector nˆ is essential for
estimating the local speed of the shock, a critical parameter
for analyzing different shock rest frames. We utilize the
upstream velocity (vu= 410± 40 km s
−1) and the downstream
velocity (vd= 2200± 200 km s
−1, along with the shock
normal and the expected density compression ratio of a strong
shock (rgas∼ 4), to calculate the shock speed. The caveat of not
having proper plasma measurements downstream is that it is
not possible to obtain the vector direction; therefore, only the
magnitude of vd is used. To estimate the density compression
ratio, we use the proxy measurements of density from the
FIELDS/RFS: nd= 184± 35 cm
−3 for downstream density
and nu= 46.5± 15 cm
−3 for upstream density. From these
values, we derive the density compression ratio rgas= nd/nu,
which approximates to 4, aligning with the characteristics of a
strong shock. We then use the conservation of mass flux across
the parallel shock to estimate the shock speed (vsh) as
= --
-
-v
v r v n
r1
,sh
d gas
1
u
gas
1
( ) · ˆ
yielding an estimated speed of vsh∼ 2800± 300 km s
−1, which
seems to align with the ballistic estimation. The direction of the
vector dot product is completely artificial, as only the
magnitude of the downstream flow (vd) is used in the
calculation. Then we estimate the Alfvénic Mach number
(MA) as the ratio of the upstream velocity component normal to
the shock (Vu) to the Alfvén speed (vA). The Alfvén speed is
calculated as m=v B n mA u 0 u p , where Bu is the upstream
magnetic field magnitude and nu is the upstream proton number
density. Here, we use the electron number density obtained
from proxies. We then compute = -V v n vu u sh· ˆ , which
results in Vu∼ 2400± 300 km s
−1. Consequently, for this
range of Vu, MA is estimated to be approximately 9.1± 1.35.
Figure 6. Dynamic radio spectra constructed from the FIELDS/RFS receivers. The solar flare onset and the in situ shock arrival are indicated on top of the panel.
11
The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
This estimation can be further validated using the proxies
established in Gedalin et al. (2021). We can estimate the value
of MA using the expression
= - - +B
B
M s2 1 1 1 .max
u
A
2 ( )
Here, =B 330max nT and Bu= 90± 5 nT are the overshoot
and the upstream magnetic field, respectively. The normalized
potential jump (s) is calculated as f=s m v2 NIF p u2, where fNIF
is the cross-shock electrostatic potential, mp is the proton mass,
and vu is the upstream velocity. The value for s= 0.15 is
selected as a reasonable adjustment of the median cross-shock
potential to the magnetic overshoot. This selection is justified
based on Dimmock et al. (2012), who demonstrate that for
MA∼ 9, s is approximately 0.25, and this value decreases with
decreasing θBn. Therefore, a value of s = 0.15 for a nearly
parallel shock is justified. Inserting these values into the
equation yields MA∼ 9, which closely aligns with the value
estimated from observations.
In a magnetized medium with β= 1, the critical Mach
number (Mc) for near-parallel shocks can be as low as ∼1.5
(Kennel et al. 1985). The ratio MA/Mc∼ 6.07± 0.9 clearly
indicates that the shock is significantly supercritical. However,
energetic particles and associated waves may lead to a change
in Mc (Laming 2022).
Appendix D
Energetic Particle Observations
During the event, and particularly at the arrival of the IP
shock, particle intensities increased dramatically. Due to these
high intensities, EPI-Hi transitioned to dynamic threshold
modes, which involve raising the energy thresholds on various
detector segments to limit the effective instrumental geometry
factor for incident protons, helium, and electrons. EPI-Lo,
which was less affected by the high intensities, was therefore
the primary observing instrument.
In response to these conditions, we utilized all available
observations from EPI-Lo. Initially, we employed EPI-Lo’s full
time-of-flight data (ChanT), as shown in Figure 1(D) of the
Letter, to demonstrate that the bulk flow reached energies
within EPI-Lo’s range. As ChanT only utilizes the particle time
of flight through the instrument, this channel cannot distinguish
ion species. While Figure 1(D) displays measurements from
only the sunward detector, we supplemented these data with
measurements from all wedges in Figure 7.
Furthermore, we used the energy resolution of EPI-Lo
ChanP and the temporal resolution of ChanR to analyze the
various proton populations at the shock. Measurements from
the sunward-pointing detector (W3) are presented in
Figure 2(C) of the main text. Complementary measurements
from all wedges, supporting the discussions in the main text,
are provided in Figures 8 and 9.
Figure 7. Ion energy fluxes measured by EPI-Lo ChanT, the full time-of-flight data. The vertical line indicates the moment of the in situ shock’s arrival. Gray shaded
areas in the graph represent intervals where data were not available.
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The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
Appendix E
Wave Analysis of the Upstream
E.1. Estimating Magnetic Field Fluctuations
The level of magnetic fluctuations is measured with δB/B, where
δB= |B− 〈B〉|= |δB| and B= 〈|B|〉. 〈B〉 and 〈|B|〉 are calculated
as running means of the magnetic field vector and magnitude,
respectively, centered around the time stamp. The length of the
averaging window τ is denoted in the plot, e.g., d t=B B 1 min( ) .
Fluctuations parallel and perpendicular to the mean field are
quantified with δB∥/B and δB⊥/B, where δB∥= |δB∥|=
|δB · 〈B〉/|〈B〉|| and d d d d= = +^ ^ ^ ^BB B B12 22∣ ∣ .
E.2. Fourier Analysis
In Figure 2(F), we present power spectral densities of the
magnetic field in the window 06:40–07:13 UT and in a
background window of 01:30–02:07. We note that different
Figure 8. Ion energy fluxes measured by EPI-Lo ChanP, the high energy resolution channel. The vertical line indicates the moment of the in situ shock’s arrival. Gray
shaded areas in the graph represent intervals where data were not available.
Figure 9. Ion energy fluxes measured by EPI-Lo ChanR, the high time resolution channel. The vertical line indicates the moment of the in situ shock’s arrival. Gray
shaded areas in the graph represent intervals where data were not available.
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The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
periods prior to the solar eruption yielded similar background
spectra. The background window was chosen to be before the
solar eruption at 03:16 UT. This choice is because of the
probe’s proximity to the Sun, meaning that the fastest particles
arrive almost instantaneously in its vicinity. To avoid any
potential modifications of the magnetic field influencing our
measurements, we selected the preevent background. Figure 10
shows the magnetic field observation during these periods. We
performed a Fourier transform (applying a Hann window) of
each magnetic field component BR, BT, and BN. The magnetic
field in both intervals is strongly dominated by BR. Therefore,
we show the BR power spectral density, which estimates the
power parallel to the background magnetic field, and the sum of
the BT and BN power spectral densities, which estimates the
total transverse power. The presented spectra have been
smoothed by averaging over adjacent frequencies.
There are two important considerations regarding the data
analysis conducted here. The first concerns the window sizes,
set at approximately 35 minutes, which correspond to a
maximum possible wave period of 2100 s (approximately
5× 10−4 Hz). A wave with a period of 300 s (approximately
3× 10−3 Hz) would be sampled around seven times. There-
fore, for frequencies below 10−2 Hz or wave periods shorter
than 100 s (sampled about 21 times), the statistical representa-
tion might not accurately reflect reality. The second considera-
tion pertains to the time series analysis itself, which represents
a random process—in this case, the magnetic field. The
estimations made here are under the assumption of ergodicity,
and long time averaging together with the azimuthal motion of
PSP may break this behavior. This limitation becomes more
significant when PSP is closer to the Sun, affecting the range of
wave periods from the same plasma that can be analyzed using
Fourier analysis.
E.3. Estimation of Characteristic Frequencies
In order to understand the effect of the upstream magnetic
fluctuations on the ions, we estimate the frequencies of Alfvén
waves that resonate with 1 and 5MeV protons. When
considering waves moving parallel to the background magnetic
field, wave–particle cyclotron resonance is governed by the
Doppler condition (Vainio 2000),
w - = W k v n ,
where ω is the resonant wave frequency, k∥ is the wavenumber,
v∥ is the particle speed along the magnetic field, Ω is the proton
cyclotron frequency, and n is an integer. We consider particles
with pitch-angle cosine μ= 1, and thus v∥= vμ= v, where v is
the speed of the particle. We take n= 1 corresponding to the
fundamental resonance and consider outward-propagating
Alfvén waves with the dispersion relation ω= k∥(vu+ vA) (in
the spacecraft frame), where vu is the solar wind speed and vA is
the Alfvén speed. Here, we ignore the motion of the spacecraft
and approximate that the solar wind flows along the magnetic
field. Finally, the resonant frequency becomes
w = ++ - W
v v
v v v
.u A
u A
Appendix F
Wave Analysis of the Shock Ramp
F.1. Morlet Wavelet Analysis
To determine the properties of the electromagnetic waves in
our observations, we applied a Morlet wavelet transform on the
time series of both magnetic and electric fields. Wavelets are
generally preferred for nonstationary signals such as whistlers;
therefore, it allows the estimation of power distribution as a
function of time and frequency. In short, it reveals the temporal
evolution of spectral parameters of wave activity. Here, we have
followed the same wavelet parameters and methodology as used
by Sundkvist et al. (2012) and Karbashewski et al. (2023).
F.2. Whistler Wave Analysis
An important aspect of any quasi-parallel shock is the
number of large-amplitude magnetic structures throughout the
magnetic gradient of the shock. It is widely understood that the
general structure of the quasi-parallel shock is highly
nonstationary and therefore time-dependent. At a shock
propagating at high speeds such as the one studied here, we
would require a close to 1 kHz resolution for both magnetic
fields and plasma properties to truly understand the evolution in
detail. In our observations, the FIELDS instrument suite was
the only one capable of capturing phenomena on the scale of
several ion inertial lengths (λi= c/ωpi). We performed a
spectral and phase wave analysis of the data, which revealed
several features in the vicinity of the shock. The large-
amplitude waves in the frequency range of 0.1–10 Hz are
located close to the ramp, both upstream and downstream. The
observed local peak of the electric field indicates the crossing
of the ramp at 07:13:11.45. The ion inertial length estimation is
based on electron density processing using the FIELDS plasma
wave measurement. In the upstream, we found the ne to be
∼46.5± 15 cm−3. Assuming that the plasma is quasi-neutral,
the ion density may not vary far from the electron density, and
Figure 10.Window selection for Fourier analysis. The pink shaded areas indicate the fast Fourier transform windows utilized for estimating the power spectral density
shown in Figure 2(F).
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The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
as such would correspond to an ion inertial length, λi∼
32.5± 3 km.
The distinct whistler precursor is observed in the upstream
region of the quasi-perpendicular ramp. Several wave periods
are seen at frequencies of around 30 Hz. The waves are right-
hand circularly polarized (Figure 3(H)) and have amplitudes up
to 35 nT. The WNAs (θkB) are derived by making use of the
singular value decomposition technique (Karbashewski et al.
2023). The WNA for the whistler wave was found to be around
73° ± 3° (Figure 3(E)). The oblique propagation is the essential
factor for the wave precursor to be a standing wave in the shock
frame.
The Poynting flux can only reliably be determined along the
Sun–spacecraft R-axis due to the unreliable R-component
electric field measurement. The Poynting flux in the spacecraft
frame is calculated using the complex Ew and Bw spectra:= -* *S Re E B E Bz wx wy wy wx( · · ) from Figures 3(C) and (D) and
subsequently mapped to a bisymmetric logarithmic scale
shown in Figure 3(F). The wave phase speed (vph) is estimated
using the flow speed and the WNA.
F.2.1. Schematic of the Shock Transition
The schematic in Figure 4(B) presents a 2D simplified
reconstruction of the shock structure based on the values and
direction of the magnetic field recorded by PSP during the
shock crossing presented in Figure 4(C). The changing velocity
of the plasma flow is reflected in the nonlinear (but isotropic in
each particular point of the schematic) spatial scales. The
physical scales are indicated by squares of 50λi× 50λi. The
color scheme represents the magnetic field magnitude.
ORCID iDs
Immanuel Christopher Jebaraj https://orcid.org/0000-0002-
0606-7172
Oleksiy Agapitov https://orcid.org/0000-0001-6427-1596
Vladimir Krasnoselskikh https://orcid.org/0000-0002-
6809-6219
Laura Vuorinen https://orcid.org/0000-0002-2238-109X
Michael Gedalin https://orcid.org/0000-0003-1236-4787
Kyung-Eun Choi https://orcid.org/0000-0003-2054-6011
Erika Palmerio https://orcid.org/0000-0001-6590-3479
Nicolas Wijsen https://orcid.org/0000-0001-6344-6956
Nina Dresing https://orcid.org/0000-0003-3903-4649
Christina Cohen https://orcid.org/0000-0002-0978-8127
Athanasios Kouloumvakos https://orcid.org/0000-0001-
6589-4509
Michael Balikhin https://orcid.org/0000-0002-8110-5626
Rami Vainio https://orcid.org/0000-0002-3298-2067
Emilia Kilpua https://orcid.org/0000-0002-4489-8073
Alexandr Afanasiev https://orcid.org/0000-0001-9325-6758
Jaye Verniero https://orcid.org/0000-0003-1138-652X
John Grant Mitchell https://orcid.org/0000-0003-4501-5452
Domenico Trotta https://orcid.org/0000-0002-0608-8897
Matthew Hill https://orcid.org/0000-0002-5674-4936
Nour Raouafi https://orcid.org/0000-0003-2409-3742
Stuart D. Bale https://orcid.org/0000-0002-1989-3596
References
Afanasiev, A., Vainio, R., Rouillard, A. P., et al. 2018, A&A, 614, A4
Agapitov, O. V., Krasnoselskikh, V., Balikhin, M., et al. 2023, ApJ, 952, 154
Axford, W. I., Leer, E., & Skadron, G. 1977, ICRC (Plovdiv) 11, 132
Bale, S. D., Goetz, K., Harvey, P. R., et al. 2016, SSRv, 204, 49
Balikhin, M., Gedalin, M., & Petrukovich, A. 1993, PhRvL, 70, 1259
Balikhin, M., Krasnoselʼskikh, V. V., Woolliscroft, L. J. C., & Gedalin, M.
1998, JGR, 103, 2029
Balikhin, M. A., Gedalin, M., Walker, S. N., Agapitov, O. V., & Zhang, T.
2023, ApJ, 959, 130
Bell, A. R. 1978, MNRAS, 182, 147
Blandford, R., & Eichler, D. 1987, PhR, 154, 1
Blandford, R. D., & Ostriker, J. P. 1978, ApJL, 221, L29
Burgess, D., Lucek, E. A., Scholer, M., et al. 2005, SSRv, 118, 205
Colburn, D. S., & Sonett, C. P. 1966, SSRv, 5, 439
Dimmock, A. P., Balikhin, M. A., Krasnoselskikh, V. V., et al. 2012, JGRA,
117, A02210
Dresing, N., Kouloumvakos, A., Vainio, R., & Rouillard, A. 2022, ApJL, 925, L21
Fox, N. J., Velli, M. C., Bale, S. D., et al. 2016, SSRv, 204, 7
Galeev, A. A. 1976, Physics of Solar Planetary Environments, 1 ed.
D. J. Williams (Washington, DC: AGU), 464
Gedalin, M. 1998, PhPl, 5, 127
Gedalin, M. 2016, JGRA, 121, 754
Gedalin, M. 2020, ApJ, 895, 59
Gedalin, M., Kushinsky, Y., & Balikhin, M. 2015, AnGeo, 33, 1011
Gedalin, M., Russell, C. T., & Dimmock, A. P. 2021, JGRA, 126, e29519
Giuffrida, R., Miceli, M., Caprioli, D., et al. 2022, NatCo, 13, 5098
Graham, D. B., Khotyaintsev, Y. V., Vaivads, A., et al. 2021, A&A, 656, A23
Helder, E. A., Vink, J., Bassa, C. G., et al. 2009, Sci, 325, 719
Helder, E. A., Vink, J., Bykov, A. M., et al. 2012, SSRv, 173, 369
Hill, M. E., Mitchell, D. G., Andrews, G. B., et al. 2017, JGRA, 122, 1513
Hillas, A. M. 1984, ARA&A, 22, 425
Hoppe, M. M., & Russell, C. T. 1982, Natur, 295, 41
Jebaraj, I. C., Dresing, N., Krasnoselskikh, V., et al. 2023, A&A, 680, L7
Karbashewski, S., Agapitov, O. V., Kim, H. Y., et al. 2023, ApJ, 947, 73
Kasper, J. C., Abiad, R., Austin, G., et al. 2016, SSRv, 204, 131
Kennel, C. F. 1981, JGR, 86, 4325
Kennel, C. F. 1988, JGR, 93, 8545
Kennel, C. F., Coroniti, F. V., Scarf, F. L., et al. 1986, JGR, 91, 11917
Kennel, C. F., Edmiston, J. P., & Hada, T. 1985, GMS, 34, 1
Kilpua, E. K. J., Lumme, E., Andreeova, K., Isavnin, A., & Koskinen, H. E. J.
2015, JGRA, 120, 4112
Krasnosselskikh, V., Balikhin, M., Gedalin, M., & Lembege, B. 1995, AdSpR,
15, 239
Krasnoselskikh, V., Balikhin, M., Walker, S. N., et al. 2013, SSRv, 178, 535
Krasnoselskikh, V. V. 1985, JETP, 62, 282
Krasnoselskikh, V. V., Dudok de Wit, T., & Bale, S. D. 2011, AnGeo, 29, 613
Krasnoselskikh, V. V., Lembège, B., Savoini, P., & Lobzin, V. V. 2002, PhPl,
9, 1192
Krymskii, G. F. 1977, DoSSR, 234, 1306
Laming, J. M. 2022, ApJ, 940, 98
Larosa, A., Dudok de Wit, T., Krasnoselskikh, V., et al. 2022, ApJ, 927, 95
Lembege, B., Giacalone, J., Scholer, M., et al. 2004, SSRv, 110, 161
Liu, M., Issautier, K., Moncuquet, M., et al. 2023, A&A, 674, A49
Livi, R., Larson, D. E., Kasper, J. C., et al. 2022, ApJ, 938, 138
Lobzin, V. V., Krasnoselskikh, V. V., Schwartz, S. J., et al. 2005, GeoRL, 32,
L18101
Malkov, M. A., & Drury, L. O. 2001, RPPh, 64, 429
Malkov, M. A., & Völk, H. J. 1998, AdSpR, 21, 551
Masters, A., Slavin, J. A., Dibraccio, G. A., et al. 2013a, JGRA, 118, 4381
Masters, A., Stawarz, L., Fujimoto, M., et al. 2013b, NatPh, 9, 164
McComas, D. J., Alexander, N., Angold, N., et al. 2016, SSRv, 204, 187
Moiseev, S. S., & Sagdeev, R. Z. 1963, JNuE, 5, 43
Moncuquet, M., Meyer-Vernet, N., Issautier, K., et al. 2020, ApJS, 246, 44
Paschmann, G., & Schwartz, S. J. 2000, in ESA Special Publication, Cluster-II
Workshop Multiscale/Multipoint Plasma Measurements, ed. R. A. Harris,
Vol. 449 (Paris: ESA), 99
Pulupa, M., Bale, S. D., Bonnell, J. W., et al. 2017, JGRA, 122, 2836
Quest, K. B. 1988, JGR, 93, 9649
Reames, D. V. 1999, SSRv, 90, 413
Riquelme, M. A., & Spitkovsky, A. 2011, ApJ, 733, 63
Russell, C. T., Hoppe, M. M., & Livesey, W. A. 1982, Natur, 296, 45
Russell, C. T., Mewaldt, R. A., Luhmann, J. G., et al. 2013, ApJ, 770, 38
Sagdeev, R. Z. 1966, RvPP, 4, 23
Sonnerup, B. U. Ö., & Scheible, M. 1998, ISSIR, 1, 185
Schwartz, S. J., Henley, E., Mitchell, J., & Krasnoselskikh, V. 2011, PhRvL,
107, 215002
Sundkvist, D., Krasnoselskikh, V., Bale, S. D., et al. 2012, PhRvL, 108,
025002
Talebpour Sheshvan, N., Dresing, N., Vainio, R., Afanasiev, A., &
Morosan, D. E. 2023, A&A, 674, A133
15
The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.
Terasawa, T. 2003, PThPS, 151, 95
Terasawa, T. 2011, in IAU Symp. 274, Advances in Plasma Astrophysics, ed.
A. Bonanno, E. de Gouveia Dal Pino, & A. G. Kosovichev (Cambridge:
Cambridge Univ. Press), 214
Vainio, R. 2000, ApJS, 131, 519
Vainio, R., & Laitinen, T. 2007, ApJ, 658, 622
Vieu, T., Reville, B., & Aharonian, F. 2022, MNRAS, 515, 2256
Vink, J. 2020, Physics and Evolution of Supernova Remnants (Berlin: Springer)
Vink, J., Prokhorov, D., Ferrazzoli, R., et al. 2022, ApJ, 938, 40
Wang, B. B., Zank, G. P., Zhao, L. L., & Adhikari, L. 2022, ApJ, 932, 65
Wiedenbeck, M. E., Angold, N. G., Birdwell, B., et al. 2017, ICRC (Busan),
301, 16
Yurchyshyn, V., Yashiro, S., Abramenko, V., Wang, H., & Gopalswamy, N.
2005, ApJ, 619, 599
16
The Astrophysical Journal Letters, 968:L8 (16pp), 2024 June 10 Jebaraj et al.