Multispacecraft Energetic Particle Enhancements Associated with a Single Corotating Interaction Region

The radial evolution of particles accelerated at corotating interaction regions (CIRs) is not fully understood, particularly the distance range over which this particle acceleration occurs and how the energy spectra are modulated by transport through the inner heliosphere. Here, we present observations of energetic proton enhancements associated with a CIR observed by Parker Solar Probe on 2021 April 25 during the inbound leg of its orbit near ∼46 R s (∼0.21 au). The CIR is identified at additional spacecraft (Solar Terrestrial Relations Observatory, STEREO-A; Solar Orbiter, SolO; and Advanced Composition Explorer, ACE) using a corotation time delay estimation, and energetic proton spectra from each spacecraft are compared. We find that (1) energetic protons are observed near 46 R s streaming sunward ahead of the CIR; (2) the CIR persists for at least one solar rotation and the corresponding energetic proton enhancements are observed at STEREO-A, SolO, and ACE; and (3) the proton energy spectrum is steeper near the Sun and hardens near 1 au. This observation presents the closest in situ energetic particle observation of a CIR to the Sun ever recorded. Results presented here suggest that particles can be accelerated by CIR structures within 1 au and these particles can penetrate very deep into the inner heliosphere.


Introduction
Stream interaction regions (SIRs) form as a result of fast solar wind emanating from low-latitude portions of coronal holes overtaking slow solar wind emanating from mid-latitude coronal streamer belts (e.g., Gosling et al. 1995;Borovsky & Denton 2010;Richardson 2018;Cohen et al. 2020).The interplanetary magnetic field is frozen-in to and co-moves with the solar wind plasma, which prevents the fast solar wind plasma from mixing with the slow solar plasma at the interface.This results in a region of compressed plasma, characterized by enhanced ram pressure, thermal pressure, and magnetic pressure (e.g., Gosling et al. 1995;Borovsky & Denton 2010).These compression regions, or SIRs, can persist for multiple solar rotations, at which point they are referred to as corotating interaction regions (CIRs; e.g., Gosling et al. 1981).Observations of CIRs have shown that a pair of forward and reverse waves bound the compression region and that these waves can strengthen with increasing heliocentric distance into shocks (e.g., Barnes & Simpson 1976;McDonald et al. 1976;Gosling et al. 1993Gosling et al. , 1995;;Desai et al. 1997Desai et al. , 1999;;Cohen et al. 2020).
In the local plasma frame of reference, particles can be accelerated at both the forward and reverse shocks bounding a CIR by diffusive shock acceleration mechanisms (e.g., Reames et al. 1997;Lee 2005;Desai & Giacalone 2016).Early on, particle acceleration at CIRs was thought to occur at distant CIRs located several astronomical units beyond Earth's orbit by statistical processes (e.g., Gloeckler et al. 1979;Fisk & Lee 1980).Thus, the source of CIR-associated energetic particles observed near 1 au is typically associated with the reverse shock of distant CIRs.The early models of Gloeckler et al. (1979) and Fisk & Lee (1980) predicted that ions observed at Earth with energies less than 0.5 MeV n -1 would exhibit a rollover in their energy spectrum at lower energies, and that these ions may not be observed at all depending on the location of the acceleration location relative to Earth.This low-energy rollover is believed to occur due to significant energy loss via adiabatic deceleration (Fisk & Lee 1980).However, more recent 1 au observations have shown that energetic ions accelerated by CIR shocks exhibit a power law at lower energies down to 0.03 MeV n -1 , which suggests that either (1) the energy loss due to adiabatic deceleration was overestimated by Fisk & Lee (1980), or (2) the source of these ions was closer to 1 au (e.g., Mason et al. 1997;Mason 2008Mason , 2012)).Furthermore, Ebert et al. (2012aEbert et al. ( , 2012b) ) found evidence of locally accelerated helium ions near the trailing edge of the CIR at 1 au, which occurred regardless of whether or not a reverse shock was observed locally and suggests an extended source for CIR-associated energetic particles near 1 au.In a survey of 50 CIR events, Bučik et al. (2009) concluded that 40% of the events showed signs of energetic particles accelerated locally at 1 au, while the remaining events showed signs of energetic particles accelerated from beyond 1 au.These observations suggests that CIRs can efficiently accelerate particles as close as 1 au and that the energy loss due to adiabatic deceleration may have been overestimated.
To date, there have been very few observations of CIRs within 1 au.Desai et al. (2020) analyzed energetic helium spectra from six CIRs observed by Parker Solar Probe (PSP) between ∼0.35 and 0.85 au.The closest of these CIR events (∼0.35 au) was also analyzed by Joyce et al. (2021).These studies show evidence of energetic ions with a power-law spectrum well within 1 au, which is inconsistent with remotely accelerated CIR particles undergoing transport effects within 1 au.Desai et al. (2020) suggested that the rarefaction region following a CIR could facilitate easier transport into the inner heliosphere and reduce the amount of adiabatic deceleration.In another study by Allen et al. (2020), PSP observations of SIRs Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
within 1 au were associated with isolated ion enhancements between 30 and 586 keV.These observations were interpreted as suprathermal ions undergoing local acceleration at the stream interface by non-shock-related processes (e.g., Schwadron et al. 1996;Giacalone et al. 2002;Ebert et al. 2012a;Chen et al. 2015;Filwett et al. 2017Filwett et al. , 2019)).Furthermore, this accelerated ion component was posited to be confined near the acceleration region within ∼0.5 au, at which point the accelerated ion component begins to broaden into the fast solar wind stream.Thus, it appears that particles are capable of being accelerated by SIRs and CIRs well within 1 au and regardless of whether a forward/reverse shock pair exists.These recent discoveries conflict with current models that assume particle acceleration by CIR shocks beyond 1 au and invoke transport effects to explain particle enhancements observed within 1 au.In order to resolve this discrepancy, additional in situ observations of CIR-associated particle enhancements within 1 au are needed.
We report on multispacecraft observations of energetic proton enhancements with energies 0.05-0.20 MeV associated with a single CIR first observed on 2021 April 25.We emphasize the energetic proton enhancement observed by PSP at ∼46 solar radii (R S ; ∼0.21 au), which is the closest-ever in situ observation of energetic proton enhancements associated with a CIR.This CIR is also identified at the Advanced Composition Explorer (ACE), Solar Terrestrial Relations Observatory (STEREO), and Solar Orbiter (SolO) spacecraft (SC), each of which also observe associated proton enhancements.The paper is organized as follows.Section 2 describes the SC and data products used, Section 3 describes the CIR identification at each SC, Section 4 discusses the resulting proton spectra observed by each SC, and Sections 5 and 6 provide a discussion of these results and a summary of the results, respectively.

Multispacecraft Data Sources
We use solar wind and magnetic field observations to identify the same CIR at each SC and corresponding energetic proton energy spectra.The SC, instruments, and data products used in this study are described in Table 1.shows the solar speed, (e) shows the magnetic field magnitude, and (f) shows the magnetic field components in radial-tangential-normal (RTN) coordinates, along with the magnitude in black.The blue shaded region indicates the beginning of the compression region and region of associated H enhancements, characterized by an increase in solar wind speed from ∼250 to ∼400 km s −1 and an increase in magnetic field strength.The magnetic field enhancement remains high after the solar wind speed increases, indicating that this compression region is not yet well formed.This compression region was observed near ∼46 solar radii and thus is the closest-ever in situ observation of particle enhancements associated with a compression region.Within the shaded region, the H pitch-angle distribution in the solar wind frame (panel (c)) is distributed across pitch angles <90°.During this same time, the radial component of the magnetic field (blue curve in panel (f)) is negative, indicating that the field is pointing sunward.Thus, these protons observed in coincidence with the compression region are moving predominantly sunward.Furthermore, the enhancements are localized to the compression region and observed over a very narrow range of energies near ∼0.1 MeV.

Corotation Time Delay
In order to identify the CIR observed by PSP at other SC, we estimate the expected time delay between PSP and these SC )is the time delay between observations at PSP and an additional SC located at a longitude of j SC and radial distance r SC .j PSP is the longitude of PSP at the time of the PSP observation, and r PSP is the radial location of PSP.Ω Sun is the rotation rate of the Sun at the equator, and V SW is the solar wind speed of the fast wind observed at PSP ∼380 km s −1 .For each (j SC , r SC ) coordinate pair, a time of arrival is calculated as which represents the predicted time that the CIR would arrive at the specific longitude and radial location given by (j SC , r SC ).
The time at which the SC was at the location given by (j SC , r SC ) is referred to a t sc .This results in two time curves that are functions of heliographic position: one corresponding to the SC location along its orbit (i.e., t sc (j SC , r SC )) and the other corresponding to the predicted location of the CIR along the SC orbit (i.e., t arrival (j SC , r SC )).The intersection of these two curves provides the location, (j obs,SC , r obs,SC ), and time, t obs,SC , at which the SC is expected to observe the CIR.This is illustrated in Figure 2, which shows a schematic of the longitude of a particular SC (black) and the predicted longitude of the CIR at the radial location of the SC's orbit (red) as functions of time.Mathematically speaking, this is given by Equation (3) was applied using orbital data for each of the three SC: SolO, STEREO-A, and ACE. Figure 3 (left) shows the magnetic field (blue/red) and solar wind speed (black) from each SC, which have been time shifted by their respective value of t obs,SC (indicated by the vertical dashed line).The magnetic field strength is color-coded by the sign of the radial magnetic component (red for negative B r and blue for positive B r ).Note that in the first panel, the velocity data is from the Wind/Solar Wind Experiment (SWE) instrument and the magnetic field is from the ACE/Magnetic Fields Experiment instrument.This is because solar wind plasma data from ACE were not available for the desired time period.The observations are ordered downward Based on the observations shown in Figure 3 (left), the simple corotation time delay estimation does a strikingly good job at lining up the features of the CIR for SolO and STEREO-A.For the ACE observations, the estimated time delay appears to be off by ∼1 day with respect to the speed increase.In each panel, the peak in magnetic field strength occurs near the middle of the solar wind speed increase, which is consistent with results from a superposed epoch analysis of CIRs at 1 au performed by Borovsky & Denton (2010).Furthermore, for  PSP, SolO, and STEREO-A, the magnetic polarity appears to switch from positive to negative prior to the observed jump in velocity.At SolO, the solar wind speed shows two sharp increases in speed to the right of the vertical dashed line, which may indicate the formation of a forward/reverse shock pair.However, the magnetic field compression at SolO occurs well before these velocity features, and the density profile does not match what is expected for a forward/reverse shock pair (see Figure 4).Thus, it is unclear whether these are indeed shocks.Lastly, at STEREO-A, the CIR shows a gradual increase in velocity, which lags the magnetic field increase by a few hours.This may be indicative of time variations in the compression wave as it reacts to the interplanetary environment, resulting in multiple compressions and expansions of the CIR as it corotates.However, a full investigation of this phenomenon is beyond the scope of this paper.

Multispacecraft Plasma and Proton Observations
Solar wind plasma parameters and proton fluxes observed by each SC during the time of the respective CIR observation are shown in Figure 4. From the top, the panels show the magnetic field strength (color-coded by the sign of the radial component), solar wind speed, proton density, and proton temperature.The figure corresponding to ACE shows density, velocity, and temperature from the Wind/SWE instrument due to unavailable data at ACE during the time of the observation.The last panel in each group of panels shows hourly averaged proton fluxes at different energies measured by the respective instrument indicated in the top left corner of each panel.Since EPI-Lo also covers suprathermal energies (<0.1 MeV), its fluxes are Compton-Getting corrected following the methods in, e.g., Zirnstein et al. (2021), and then rebinned into logarithmic energy bins with 2 spacing in order to improve statistics.The gray shaded regions indicate averaging intervals used to compute proton spectra.Note that the STEREO-A flux is determined to be heavily influenced by solar energetic particles (SEPs) from a coronal mass ejection (CME) that occurred just before the CIR was observed at STEREO-A (discussed below).Thus, we do not present H spectra from STEREO-A in this paper, and no averaging interval is identified.These intervals were chosen based on the solar wind speed to capture the region during which the speed was increasing.At SolO, the proton enhancement persists well beyond the time of the peak in the solar wind speed.In contrast, the enhancements at ACE and PSP are relatively confined to the increasing period of the solar wind speed.These differences may be due to an additional SEP component resulting from independent solar events that occur near the time of the CIR observation at each SC, which is discussed below.

Overlapping SEP Observations at STEREO-A and SolO
SolO.On 2021 May 4, at 06:20 UT, SolO RPW (Maksimovic et al. 2020) radio spectrogram shows a type III radio burst indicative of a small solar event occurring near the magnetic footprint of the SolO SC (within ∼25°of SolO footprint longitude).The SolO magnetic footprint was obtained using a magnetic connection tool3 (Rouillard et al. 2020).Furthermore, SOHO LASCO CME Catalog4 (Yashiro et al. 2004) reports a very faint CME with a speed of 183 km s −1 and angular width of 51°on 2021 May 4 at 07:00 UT.Such slow CMEs were not observed to be associated with CME-driven shock SEP events.The solar source was behind the east limb as viewed from the Earth so no GOES X-ray flare was observed.SoLO STIX observed X-ray flare with estimated GOES class M1.6 with peak at 06:17 UT.If accelerated in the flare, ions in the energy range 0.25-1 MeV n -1 need between 3 and 6 hr to travel to SoLO without scattering.Thus, the first SEPs should  arrive between ∼10 UT and 13 UT depending on energy.However, the onset of the ion enhancement on SolO is at ∼03 UT and is thus attributed to the CIR.While there are no clear signatures of SEPs observed at SolO during the time of the CIR observation, it is possible that SEPs generated by this small solar event are observed by SolO/Suprathermal Ion Spectrograph (SIS) in coincidence with CIR-associated particles.This may explain why the H spectrum at SolO is much flatter than those observed by PSP and ACE.This should be considered when comparing the proton spectrum observed by SolO to that observed by PSP.
STEREO-A.On 2021 May 7, near 20:00 UT, High Energy Telescope (HET) on STEREO-A observed onset of energetic protons at 24-41 MeV.The event was associated with a fast CME.SOHO LASCO CME Catalog reports a CME with a speed of 754 km s −1 and angular width of 76°on 2021 May 7 at 19:24 UT.The NOAA SWPC report type II radio burst (a signature of shock acceleration) at 19:02 UT, type III radio bursts at 19:24 UT, and M3.9 X-ray flare peaking at 19:04 UT.At this time, SolO HET, separated by ∼45°in longitude from STEREO-A, observed the same SEP event with proton intensity enhancement in 27-75 MeV.Thus, this SEP event was widespread, and it seems likely that the particles detected by the Suprathermal Ion Telescope on board STEREO-A during the passage of the CIR are SEPs from the CME rather than CIR particles.Nevertheless, we included the STEREO-A observations in this paper to show that the CIR persisted for at least a solar rotation and was clearly observed by multiple SC.

Spectral Analysis Results
For each SC (ACE, PSP, and SolO), we identified an averaging time interval by eye (represented by shaded regions in Figure 4).The time interval at PSP was chosen based on the flux enhancements and pitch-angle distribution shown in Figure 1 to isolate the observed sunward-streaming proton population.This period corresponds to the time during which the solar wind speed is increasing, which often corresponds to the peak intensity of the ion enhancements (e.g., Bučik et al. 2009).To be consistent with the PSP time interval, the time intervals for ACE and SolO were chosen to capture the ramp in velocity throughout the compression region, and these intervals end when the solar wind speed reaches its peak.Note, the resulting spectra do not change significantly if the averaging time intervals are slightly shortened/lengthened.For each identified time interval, the proton fluxes from each instrument are time averaged and plotted as a function of energy.In Figure 5(a), the purple spectrum is the omnidirectional average flux from EPI-Lo, the blue spectrum corresponds to the average of flux from SIS-a and SIS-b (i.e., sunward-and anti-sunwardmoving particles), and the green spectrum is the ACE/ULEIS fluxes corresponding to anti-sunward-moving particles along the nominal Parker field line direction only.The gray dashed lines in Figure 5(a) are weighted linear fits to each spectrum in log-log space from which the spectral slope is inferred (shown in the bottom left corner of Figure 5(a)).The spectrum at PSP is much steeper than the ACE spectrum, which is in turn steeper than SolO spectra.The flatter spectra observed by SolO may be due to the contribution of SEPs from an independent solar event that occurred around the time of the SolO observation discussed in the previous section.The fact that PSP observes sunward-moving protons suggests that some of these protons are accelerated by the CIR farther out from the SC.If these protons were accelerated beyond 1 au, then we would expect the PSP spectrum to be similar to the ACE spectrum with a depletion of particles at lower energy due to transport effects as the particles traveled from ACE orbit (1 au) to PSP.However, the steepness of the observed spectrum from PSP does not support this hypothesis.The localized nature of the proton enhancements observed by PSP in the absence of a shock agrees with the previous observations by Allen et al. (2020), which is suggestive of localized acceleration processes.Thus, perhaps the observed proton enhancement at PSP is due to a combination of particles accelerated locally within the compression region, and particles accelerated beyond the location of PSP that are streaming back toward the Sun.The unit vectors (in RTN coordinates) of the EPI-Lo apertures, which define the direction of the travel of particles measured by each aperture, were used to identify particles traveling in a direction within 60°of the sunward (−R) and anti-sunward directions (+R).The fluxes from the identified sunward/antisunward apertures are averaged together and then time averaged, resulting in the sunward/anti-sunward spectra shown in Figure 5(b).The PSP sunward-moving proton spectrum is larger in magnitude by a factor ∼2 than the anti-sunward spectrum, and both spectra appear to roll over near 0.1 MeV.However, this is difficult to confirm due to the scarcity of spectral points above and below this energy.Note that this rollover is not observed in the omnidirectional distribution (Figure 5(a)) due to the inclusion of particles moving in the transverse direction relative to the +R direction.This also explains why there is one less data point near 0.22 MeV in the anti-sunward/sunward spectra shown in Figure 5(b).For SolO, the sunward spectrum corresponds to SIS-b, and the antisunward spectrum corresponds to SIS-a, and the spectra are very similar, which indicates that the particles are isotropic in the plasma frame.Note, the shift in energy bins between the two spectra results from the applied Compton-Getting correction.These observations show evidence that particles can be efficiently accelerated at CIRs near and within 1 au and that these particles are capable of penetrating deep into the inner heliosphere as far as 46 R S for this event.

Discussion
It is well understood that CIR structures are capable of accelerating particles to MeV energies via diffusive shock acceleration processes (Barnes & Simpson 1976;Fisk & Lee 1980;Lee & Fisk 1982).Typical models of particle acceleration at CIRs (e.g., Fisk & Lee 1980) predict that accelerated particles undergo adiabatic deceleration as they propagate back upstream toward the Sun from their acceleration site, which modulates the particle spectrum as a function of radial distance.Furthermore, as these accelerated particles propagate upstream against the solar wind, the diffusion coefficient is smaller for lower-energy particles, which causes the low-energy particle intensity to fall off faster than the highenergy particle intensity and results in a low-energy rollover in the observed particle spectrum (e.g., Mason et al. 1999).However, this simple picture of CIR-associated energetic particles conflicts with recent studies within 1 au, which found evidence of local acceleration at the stream interface by nonshock related processes (e.g., Schwadron et al. 1996;Giacalone et al. 2002;Ebert et al. 2012a;Chen et al. 2015;Filwett et al. 2017Filwett et al. , 2019)).These studies posited that near the Sun (within ∼0.5 au), the accelerated ion component is thought to be confined to the acceleration site.The CIR observed by PSP in this paper was not accompanied by a shock, yet a clear proton enhancement was observed associated with the rise in velocity.The differential intensity of these protons exhibited a pure power-law energy distribution and is anisotropic in the plasma frame with a strong sunward-streaming component.The pitchangle distribution of these protons is distributed across pitch angles <90°, which is likely indicative of pitch-angle scattering effects.This observation agrees with the studies mentioned above and provides evidence of local acceleration by nonshock-related processes occurring at distances beyond the PSP radial location but likely within 0.5 au.Cohen et al. (2020) analyzed energetic proton observations of CIRs made by PSP within 0.65 au.They found that the proton spectra corresponded to power laws with indices ranging from −4.3 to −6.5.However, in their study, all observations exhibited particle isotropy, which was taken as evidence for the lack of local acceleration processes.In our study, the PSP spectral index is −5.3, and the distribution is anisotropic with a strong sunward-moving component, which is indicative of local acceleration processes.Once the CIR reaches the SolO SC, the energetic protons are nearly isotropic, which agrees more with what was found in the Cohen et al. (2020) work.We suggest that these differences are due to the radial evolution of the CIR from its observation at PSP (close to the Sun) to SolO (near 1 au).At PSP, the CIR does not appear to be well formed, and thus, it may be that the energetic protons observed result from initial stages of local acceleration processes.By the time the CIR structure reaches SolO (near 0.91 au), the compression has strengthened, and the acceleration has become more efficient, resulting in the isotropic distribution that is observed by SolO.This also would explain the harder spectra that are observed at ACE and SolO compared to PSP.As the CIR evolves radially, the acceleration becomes more efficient and has a longer time to act on the particles.Thus, these results suggest that ion acceleration within CIR structures can occur very close to the Sun, and this acceleration evolves in time as the CIR evolves radially outward.Lastly, note that although the ACE and SolO spectra have similar spectral indices, they differ significantly in magnitude, which likely reflects time variations in the particle source since these observations were made ∼18 days apart.

Summary
We present the closest-ever in situ observation to the Sun of energetic particle enhancements associated with a CIR by PSP (∼46 R s ; 0.21 au).This CIR persisted for at least a solar rotation and was observed by ACE, SolO, and STEREO-A.We used a corotation-based time delay equation to estimate the time at which the CIR was observed by other SC and confirmed these observations using magnetic field and solar wind data.Energetic proton spectra averaged over the time period corresponding to the CIR solar wind speed increase were compared among SC.The protons observed by PSP were sunward moving in the plasma frame, and the omnidirectional spectrum showed no sign of a low-energy rollover, which indicates that some of these particles may have been accelerated locally and well within 1 au.Although the sunward and anti-sunward spectra may show signs of a low-energy rollover near 0.1 MeV, this is difficult to confirm due to the scarcity of spectral points above and below this energy.In contrast, the proton spectra from ACE and SolO are flatter with similar spectral indices, and the SolO spectrum is isotropic in the solar wind frame.These results suggest that particles can be efficiently accelerated by CIR structures well within 1 au and that these particles can penetrate into the inner heliosphere close to the Sun.

Figure 1
Figure 1 shows an overview of the PSP observation of the CIR: (a) omnidirectional and hourly averaged H intensity from Energetic Particle Instrument (EPI-Lo) averaged over three different energy ranges; (b)-(c) show the H 1/v spectrogram and pitch-angle distribution in the solar wind reference frame, both derived from EPI-Lo data.Panel (d)shows the solar speed, (e) shows the magnetic field magnitude, and (f) shows the magnetic field components in radial-tangential-normal (RTN) coordinates, along with the magnitude in black.The blue shaded region indicates the beginning of the compression region and region of associated H enhancements, characterized by an increase in solar wind speed from ∼250 to ∼400 km s −1 and an increase in magnetic field strength.The magnetic field enhancement remains high after the solar wind speed increases, indicating that this compression region is not yet well formed.This compression region was observed near ∼46 solar radii and thus is the closest-ever in situ observation of particle enhancements associated with a compression region.Within the shaded region, the H pitch-angle distribution in the solar wind frame (panel (c)) is distributed across pitch angles <90°.During this same time, the radial component of the magnetic field (blue curve in panel (f)) is negative, indicating that the field is pointing sunward.Thus, these protons observed in coincidence with the compression region are moving predominantly sunward.Furthermore, the enhancements are localized to the compression region and observed over a very narrow range of energies near ∼0.1 MeV.
H + from the SIS: ∼0.2-2.0MeV Two telescopes pointed sunward (SIS-A) and antisunward (SIS-B) H + flux: ∼0.2-2.0MeV Single telescope pointed sunward along the nominal Parker spiral Mason et al. (1998) STEREO-A PLASTIC Solar wind velocity vector, density, and temperature Galvin et al. (2008) MAG Magnetic field vector Acuña et al. (2008) due to corotation using the formula from Richardson et al.
(a)-(d), based on the time of the CIR observation at each SC.This ordering is consistent with what would be expected based on the relative locations of each SC at the time of the PSP observation as shown in the orbital configuration plot Figure 3 (right).In this plot, the dashed colored lines represent the nominal Parker spiral magnetic field line, assuming a 380 km s −1 solar wind speed connecting to each SC, and the solid colored lines show the orbit trajectories of each SC over the time period 2021 April 15-2021 May 11, with the open circles representing the locations of each SC at the beginning of this time period.The filled symbols represent each SC location at the time of the PSP observation.

Figure 1 .
Figure 1.(a) Time series of EPI-Lo H fluxes averaged over three energy ranges.(b) 1/(ion speed) time spectrogram computed from EPI-Lo H energy flux.(c) Pitch angle of EPI-Lo H ions vs. time.(d) Magnitude of solar wind speed.(e) Magnitude of magnetic field.(i) Magnetic field components in RTN coordinates and field strength (black).The shaded region indicates the H enhancements and identifies the averaging interval used to compute H spectra.

Figure 2 .
Figure 2. Illustration of the time delay method used to identify the CIR at additional SC.The black line shows the longitude of an SC along its orbit as a function of time, and the red line shows the predicted longitude of the CIR at the radial location of the SCʼs orbit as a function of time.The intersection of these two lines provides the expected time at which the SC would observe the CIR.

Figure 3 .
Figure 3. (left) Time series magnetic field strength (red for −B r and blue for +B r ) and solar wind speed (black) observations from each SC ordered downward by the time of the observation (ACE, PSP, SolO, and STEREO-A).The data have been time aligned to the PSP observation time (black dashed line) using the estimated corotation delay time for each SC relative to the PSP observation.(right) Orbital configuration of the four SC in heliographic inertial coordinates.The symbols indicate each SC location at the time of the PSP observation, and the solid lines show the orbits for the time period 2021 April 15 to 2021 May 11.

Figure 4 .
Figure 4. Overview of plasma and magnetic field observations from each SC.From the top, the panels show the magnetic field strength (color-coded to the polarity of B r ), plasma speed, plasma density, and plasma temperature.The bottom panel in each group of panels shows H fluxes at different energies from each respective instrument indicated in that panel.The gray shaded region indicates the averaging interval for each SC used to compute H spectra.
Figure 5(b) shows protons moving sunward and antisunward, referring to the direction of travel of the observed particles in the solar wind frame (Compton-Getting corrected).

Figure 5 .
Figure 5. (a) Average H spectra from ACE, PSP, and SolO.These spectra have been averaged over all available look directions for each instrument and then time averaged over the respective intervals identified in Figure 4.The gray dashed lines are power-law fits to each spectrum, and the resulting spectral slope is shown in the bottom left corner.(b) Spectra from PSP and SolO representing protons moving sunward/anti-sunward.

Table 1
Description of the Instruments and Data Used in This Paper ISOIS/EPI-Lo Triple coincidence H + flux: ∼0.02-10 MeV n -1 Full sky coverage with 80 instrument apertures