Analyses of ∼0.05–2 MeV Ions Associated with the 2022 February 16 Energetic Storm Particle Event Observed by Parker Solar Probe

We present analyses of 0.05–2 MeV ions from the 2022 February 16 energetic storm particle event observed by Parker Solar Probe's (PSP) IS⊙IS/EPI-Lo instrument at 0.35 au from the Sun. This event was characterized by an enhancement in ion fluxes from a quiet background, increasing gradually with time with a nearly flat spectrum, rising sharply near the arrival of the coronal mass ejection (CME)–driven shock, becoming nearly a power-law spectrum, then decaying exponentially afterward, with a rate that was independent of energy. From the observed fluxes, we determine diffusion coefficients, finding that far upstream of the shock the diffusion coefficients are nearly independent of energy, with a value of 1020 cm2 s−1. Near the shock, the diffusion coefficients are more than 1 order of magnitude smaller and increase nearly linearly with energy. We also determine the source of energetic particles, by comparing ratios of the intensities at the shock to estimates of the quiet-time intensity to predictions from diffusive shock acceleration theory. We conclude that the source of energetic ions is mostly the solar wind for this event. We also present potential interpretations of the near-exponential decay of the intensity behind the shock. One possibility we suggest is that the shock was overexpanding when it crossed PSP and the energetic particle intensity decreased behind the shock to fill the expanding volume. Overexpanding CMEs could well be more common closer to the Sun, and this is an example of such a case.


Introduction
Solar energetic particles (SEPs) are high-energy charged nuclei associated with processes occurring at the Sun.The term SEP is a broad categorization.They can be related to solar flares, even small ones, transient disturbances in the solar wind plasma, and interactions between high-speed and low-speed solar wind flows leading to corotating interaction regions.The SEP events of the highest intensity are well correlated with the occurrence of coronal mass ejections (CMEs; Gosling 1993).At energies below a few MeV nuc −1 , the arrival of a CMEdriven shock at the spacecraft can be accompanied by ion intensity increases (see Giacalone 2012), and these are given the term "energetic storm particle" (ESP) events (Bryant et al. 1962).A common characteristic of ESP events is that the particle intensity increases abruptly from the background several hours (even up to a day or so) before the arrival of the shock, and then increases gradually until 15-30 minutes prior to the arrival of the shock itself, where the intensities rise again very abruptly (see Reames 1999;Giacalone 2012, and references therein).Sometimes, during the gradual-rise phase of ESP events, the fluxes of energetic ions are very nearly the same and rise at the same rate (Lario et al. 2018).These produce very nearly flat energy spectra.This phenomenon is not presently well understood, but it may be related to the way in which particles escape from near the shock, where they are confined by turbulent magnetic fields (Perri et al. 2023), adiabatic cooling (Prinsloo et al. 2019), or perhaps a balance between the injection rate (at very low energies) at the shock and their escape upstream (Lario et al. 2018).
ESP events are excellent targets for studying the physics of particle acceleration and transport.For instance, the occurrence of these events provides a unique opportunity to directly determine transport coefficients (e.g., Gloeckler et al. 1985;Beeck & Sanderson 1989;Tan et al. 1989;Giacalone 2012).In addition, these events are generally associated with very high particle intensities, providing excellent counting statistics.This permits an event-based analysis on determining the source of the material being accelerated by the shock by comparing the distribution function at very low energies, including the thermal particles, just prior to and after the crossing of the shock.This was discussed by Guo et al. (2021), who analyzed the DOY 118, 2001 ESP event (see Lario et al. 2019) seen by the Advanced Composition Explorer; they concluded the highenergy protons must have originated as solar wind protons that were accelerated directly at the shock.
Parker Solar Probe (PSP), launched in 2018 (Fox et al. 2016), has a highly elliptical in-the-ecliptic orbit allowing for a sampling of the solar wind, magnetic field, and energetic particles over a range of heliocentric distances from ∼0.02 to ∼0.7 au.It has observed a number of CME-related SEP events (e.g., McComas et al. 2019;Giacalone et al. 2020;Cohen et al. 2021;Giacalone et al. 2021;Lario et al. 2021;Raouafi et al. 2023) at a variety of heliocentric distances.In this paper, we present analyses of another ESP event recently observed by PSP that occurred on 2022 February 16.This event displayed a quasi-flat energy spectrum upstream of the shock.In addition to the evolution of the energy spectrum across the shock, we also use observations from the EPI-Lo instrument (McComas et al. 2016;Hill et al. 2017), which is part of the Integrated Science Investigation of the Sun (ISeIS) (McComas et al. 2016), to determine transport coefficients of the energetic ions.This event was also characterized by a near-exponential decay in the particle intensities behind the shock with the same rate of decrease over a wide range of energies.We describe a few scenarios that may lead to such behavior.We also discuss the source of the accelerated particles for this event, presenting an analysis based on comparing the ratio of the peak intensity at a given energy at the time of the shock passage to an upper bound on the background intensity at the same energy obtained via the prediction of diffusive shock acceleration theory.This event was associated with a significant increase in the intensity of energetic ions, to permit such an analysis.

Observations
In this study, we analyze 1 minute resolution PSP/ISeIS/ EPI-Lo ion intensities (see McComas et al. 2016;Hill et al. 2017).We use both the ChanP (protons) and ChanC (He and O ions) data products in this study.We also use 1 s resolution magnetic field measurements from the FIELDS instrument (Bale et al. 2016) for contextual information, such as the timing of the passage of the shock, the arrival of the interplanetary coronal mass ejection (ICME), and the general nature of the direction of the magnetic field for this event.Additional contextual solar-wind velocity vector and ion number density data from the SWEAP instrument (Kasper et al. 2016) are also used.
Figure 1 shows an overview of the ESP event that occurred on 2022 February 16.The top panel shows the magnetic field vector magnitude and RTN coordinates, while the bottom two panels show ∼0.05-5MeV proton intensities.The middle panel shows time-intensity profiles at some selected energies, as indicated at the right, while the bottom panel shows all of the energies, with the intensity represented with the color scale.At this time, PSP was located about 0.35 au from the Sun.The solar eruption associated with the origin of this event has been analyzed by Mierla et al. (2022).Although it is not shown in this paper, analysis of STEREO-A (STA) Cor 2 images reveals that a CME appeared in the instrument's field of view at 22:23:30UT on 2022 February 15.The central bright part of the CME was seen to be moving northward relative to the ecliptic plane, at a latitude of some ∼45°.The CME had a relatively large latitudinal extent.Based on the relative locations of PSP and STEREO-A during this time, it is clear the CME was moving toward PSP.The magnetic field shown in the top panel of Figure 1 reveals that PSP observed a large-scale magnetic flux rope, suggesting that PSP was indeed crossed by the CME.In Section 4, we discuss the results from an ENLIL numerical simulation of this event, including a CME from the so-called "cone model," which required an initial speed of about 2500 km s −1 in order for the model to give a time of arrival consistent with that observed.As we discuss in the next section, we find that the shock associated with this CME was moving considerably slower than this, suggesting the shock had slowed considerably between the Sun and PSP.The SEP event itself is qualitatively similar to ESP events seen previously, in that there is a gradual increase in the particle flux prior to the arrival of the CME, which rises rapidly and peaks at the passage of the CME-driven shock, followed by a quasi-constant or gradual decay in flux in the CME-sheath region, then followed by a significant depletion within the flux rope itself (indicated by the dashed line labeled ICME in Figure 1).The timing of the CME appearance in the STA-Cor2 image, the shock arrival, and the ICME flux-rope arrival are indicated with vertical dashed lines in the figure.
Figure 1 also indicates two noteworthy periods.One is the gradual increase in particle intensity prior to the shock arrival, for which the intensity is nearly the same at all energies shown.This corresponds to a "flat spectra" period.This phenomenon has been seen in some SEP events observed by near-Earth spacecraft (Lario et al. 2018).To our knowledge, this is the first such observation by PSP reported to date, and it may represent the closest such observation to the Sun to date.We also identify a period of time after the shock arrival in which the intensity of energetic protons decreases with essentially the same rate at all energies.This represents a dispersionless decay in particle intensity.We discuss this further in Section 3.3.

Energy Spectra
Figure 2 shows the energy spectrum for this event for three different time periods as indicated in the legend at the lower left of the image (in units of decimal day of year 2002), using the ChanP data product.The highest energy at which the ESP event produced an increase appears to be about 2 MeV, because the three spectra match at energies above this.The dashed lines are representative power laws with two different spectral indices, as indicated.The spectrum shown with the blue lines and symbols is that just at the peak of the ESP event and slightly downstream of the shock.For the energy range ∼0.2-1 MeV, the spectrum is close to a power law with a spectral index of about −1.6.At energies below about 100 keV, the spectrum turns upward and is somewhat steeper.The cause of this is not presently understood.At energies above about 1 MeV, the spectrum steepens slightly to another power law with a spectral index closer to −2.The harder power law is likely the result of the acceleration of particles at the shock.In the theory of diffusive shock acceleration, a power-law spectrum is predicted for the shock and downstream region with a spectral index that depends only on the plasma density jump at the shock.A differential intensity spectrum with a power-law dependence on energy with a −1.6 index corresponds to a density jump of about 2.4.Later, we will show the plasma density for this event.It is difficult to determine a precise value of the density jump, due to significant variations in the density upstream of the shock, but a value of 2.4 is generally consistent with the observations.The plasma density variation across the shock is discussed later in Section 4.
The spectrum shown with the black symbols and solid lines corresponds to the period identified in Figure 1 as the flat spectra period.We see that this spectrum below ∼1 MeV is not perfectly flat, but it is certainly flatter than during the rise phase at the shock (red symbols and connecting solid lines) and at the shock and downstream (blue).It is also noteworthy that the spectrum very near but upstream of the shock (red circles and lines) has two separate power laws: a harder one for energies below ∼1 MeV, and steeper above this energy.

Determination of Diffusion Coefficients
By inspection of Figure 1(b), during the period of time associated with the nearly flat energy spectrum, the particle intensities rise very slowly with time.The fluxes are enhanced well above the background by at least 1 order of magnitude or more, but it is also clear that there are considerable fluctuations about an average value, presumably caused by poor statistics.Closer to the shock, starting just after 6:00 UT on DOY 47, the fluxes rise quite dramatically.The timescales of the intensity increases during these two time periods can be used to estimate diffusion coefficients, assuming the transport is diffusive and that their increase in intensity is the result of the approaching the shock, which is where the intensity reaches a maximum.The change from a gradual increase in the particle intensity to a rapid one suggests the diffusion coefficient is a function of distance from the shock, being larger far upstream from the shock and smaller closer to it.We note that the intensity increase of energetic ions upstream of shocks has been used in previous studies to estimate the diffusion coefficient or mean free path of the particles (e.g., Beeck & Sanderson 1989;Tan et al. 1989;Giacalone 2012;Wijsen et al. 2022).
We select two separate time periods upstream of the shock to perform our analysis of the diffusion coefficient.The first is a ∼3.6 hr period from 2:30UT to 6:00UT on DOY 47.We refer to this region as "far upstream of the shock."The second region is from 7:11UT to 7:26UT on DOY 47, a period of about 15 minutes.We average the data over a few energy bins in order to improve statistics.The time-intensity profiles are shown in Figure 3.For the interval far upstream of the shock, we show four energy ranges, as indicated in the figure caption (see also Table 1), in four separate panels.For the interval closer to the shock, we show all four energies on the same right-panel plot.The black lines in each of these figures are the least-squares fit to the data.Table 1 gives the exponential rise time, Δt, associated with each of these fits, as well as each correlation coefficient, R C .We do not show a profile for 75 keV protons far upstream of the shock, and for the cases near the shock, we do not show a profile for 750 keV protons.The reason is that we only show the results for the case of the largest correlation coefficients in the least-squares analyses, which, as it turns out, is R C > 0.47.The energies are 75 keV (cyan), 133 keV (red), 237 keV (green), 421 keV (blue), and 750 keV (violet).The black lines in all panels represent the least-squares fit to the data, with the exponential rise time and correlation coefficient shown in Table 1.
The exponential rise time of the particle fluxes is related to the diffusion coefficient according to (Equation (7) of) Giacalone (2012): where W 1 is the component of the plasma velocity normal to the shock, in the shock rest frame, and V sh is the speed of the shock in the spacecraft frame.Assuming the shock is moving radially away from the Sun, then W 1 = V sh − U 1 , where U 1 is the radial component of the solar wind speed in the spacecraft frame.Estimating these quantities requires plasma data, which is shown a bit later, in Figure 7.It turns out that the plasma velocity and density vary considerably during this period, making it difficult to arrive at a good estimate of either.For W 1 , we averaged the radial component of the observed solar-wind velocity from the time period 4:48UT to 7:12UT on DOY 47, giving a value W 1 = 532 km s −1 .The shock speed was estimated by assuming mass continuity across the shock.
Using the observations of the plasma number density and radial speed for the four points prior to and after the shock crossing, we estimate the shock speed to be 800 km s −1 .We use this value for our estimate of κ based on Equation (1).The results are given in Table 1.As we discuss below, there is some evidence that the shock was decelerating at the time it crossed PSP, complicating the estimate of the shock speed.We also suggest a bit later that the shock may be consistent with that of a blast wave.If this is the case, our approach of using just the few data points in the vicinity of the shock seems to us to be the most reasonable.This is discussed further in Section 5.The diffusion coefficient, κ, in this case is the component of the diffusion tensor along the radial direction, which we assumed was the direction of the unit-normal to the shock front.Judging from Figure 1, the magnetic field is nearly radial during this period (the radial component of the field is close to the magnitude throughout most of the interval), such that this diffusion coefficient is close to that along the magnetic field, or the so-called parallel diffusion coefficient.The parallel mean free path is related to this according to λ ∥ = 3κ/v, where v is the particle speed.λ ∥ is given in the far right column in Table 1.
For comparison, have also used another method to determine diffusion coefficients using the observed magnetic field and quasi-linear theory (e.g., Jokipii 1966;Giacalone & Jokipii 1999).In this case, the spatial diffusion coefficient parallel to the mean magnetic field is determined from the pitch-angle diffusion coefficient that depends on the turbulent component of the magnetic field.For this case, we use Equations (12) and (13) of Li et al. (2022) and consider the n component of the magnetic field, which is transverse to the mean field direction.We consider the same time intervals as discussed above, which determine the longest temporal scale of the power spectrum.In both cases, we use a 9 Hz (0.11 s) resolution magnetic field, which determines the smallest temporal scale.As discussed in Li et al. (2022), a minimum pitch cosine is needed for the required integration to relate the pitch-angle and spatial diffusion coefficients.This is because the observed magnetic power spectrum falls off sharply at high frequencies, due to the dissipation of turbulence, and this has an important effect on the scattering of particles near a pitch angle of 90°.In our case, we use a value of 0.05 for the minimum pitch cosine.The results of this calculation are discussed below.
The estimated diffusion coefficients are shown graphically in Figure 4, with the black open-circle symbols representing the values far upstream of the shock, and the red open-circle symbols representing the values closer to the shock.The solid lines in this figure are least-squares fits to these data.For the case of the far-upstream values, the diffusion coefficients are approximately independent of energy.For the near-upstream values, we find that the data are consistent with κ rr ∝ E 0.9 .The dashed lines in this figure are the results from the calculation using the quasi-linear theory, as discussed in the preceding paragraph, with the colors corresponding to the same time intervals-far from the shock, or near the shock-for the data symbols and solid lines.For the interval near the shock, the estimates of κ from the two different methods are generally consistent; however, far from the shock, the estimate based on Note.E min and E max define the energy range, and E is the logarithmic middle of the energy range.Δt is the exponential rise time associated with the intensity increase, determined by a least-squares fit to the data shown in Figure 3.The unit of Δt represents hours for the case far upstream of the shock, but minutes in the near-upstream time period.R C refers to the correlation coefficient of the least-squares fit.The final column is the diffusion coefficient determined from Equation (1) using W 1 = 532 km s −1 and V sh = 800 km s −1 , respectively.and near the shock (red), as estimated from the rise-time analysis and tabulated in Table 1.The solid lines are least-squares fits to these data.The dashed lines are estimates based on quasi-linear theory using the measured power spectrum of magnetic field fluctuations for each of these time intervals.See the main text for more details.
the quasi-linear theory is considerably smaller than that based on the exponential decay of the particle intensities.The two methods also do not give the same energy dependence.In fact, previous work has noted a similar discrepancy between predictions from quasi-linear theory using the observed magnetic field power spectrum and a separate compilation of diffusion coefficients determined from other methods (Palmer 1982;Bieber et al. 1994).It is worth noting that diffusion coefficients and mean free paths determined from the exponential rise of the energetic-particle intensity near interplanetary shocks (e.g., Beeck & Sanderson 1989;Tan et al. 1989;Giacalone 2012;Wijsen et al. 2022) are smaller than those of the so-called Palmer consensus (Palmer 1982), and in this particular case, they also agree reasonably well with the predictions of quasi-linear theory.
The change in the energy dependence of the diffusion coefficient, estimated using our first method discussed above, is noteworthy-but not easy to interpret.The diffusion of charged particles is the result of scattering by magnetic irregularities (e.g., Jokipii 1966); thus, we might expect that there is a change in the behavior of the magnetic field far from the shock and near the shock.It is generally predicted that close to the shock, the higher intensity of energetic particles leads to the excitation of magnetic fluctuations, which help trap the particles near the shock (e.g., Bell 1978;Lee 1983).Such self-excited waves are sometimes, but not always (or even often), seen at interplanetary shocks.In this case, it is noteworthy that our estimates of the diffusion coefficients from quasi-linear theory are larger far from the shock than near the shock, suggesting enhanced magnetic fluctuations near the shock.Later, we will show the magnetic field over a somewhat shorter time interval near the shock (Figure 7(a)).By inspection of this figure, it does seem that the magnetic field changes behavior close to the shock, which may account for the change in magnitude and energy dependence of the diffusion coefficient.It is puzzling, however, that the diffusion coefficient far from the shock is independent of energy.Far from the shock, the magnetic field is that of the ambient solar wind and is presumably unaffected by the low intensity of the energetic particles.Based on estimates of energetic-particle diffusion coefficients from quasi-linear theory using the well-observed power spectrum of interplanetary magnetic field fluctuations (e.g., Bieber et al. 1994;Giacalone & Jokipii 1999), the diffusion coefficient should be a function of energy.The discrepancy with our present analysis suggests that we do not understand well the energy dependence of the diffusion coefficient in interplanetary space (see also Palmer 1982).

Determination of the Source of Accelerated Particles
Inspection of Figure 1 reveals that this SEP event is characterized by a large increase in ∼0.05-2 MeV proton intensities from a very low background.For instance, at 79.1 keV, the lowest energy shown in the middle panel of this figure, the peak intensity at the shock is more than 3 orders of magnitude larger than the intensity just after the event onset, and more than 4 orders of magnitude larger than the background fluxes between 18:00UT DOY 46 to 0:00 UT DOY 47.These particles must come from an abundant source.The most likely candidate is the solar wind, as we show below.
It has been suggested that preexisting suprathermal particles are an important source of SEP events, even those associated with fast CME-driven shocks.For instance, Mason et al. (2006) noted a significant enhancement of 3He in large CME-related events, despite the fact that 3He has a comparatively low abundance in the solar wind.These authors concluded that preexisting high-energy 3He, which is often seen associated with small solar flares, is reaccelerated at CME-driven shocks, accounting for their observations.In addition, the standard theory of diffusive shock acceleration (DSA) only predicts that particles are accelerated from some lower energy, but does not address either the value of this low energy or the source of the particles.In fact, the theory is based on the assumption the pitch-angle distribution is isotropic, and an analysis of this assumption at low energies (see Giacalone 2003;Guo et al. 2021) suggests that the theory is only applicable at energies much larger than the energy of a proton moving at the speed of the shock.For this event, the shock speed was estimated in the previous section to be about 800 km s −1 , corresponding to a proton energy of about 3.4 keV.DSA theory can be applied to a preexisting suprathermal particle distribution whose energies are considerably larger than a few keV, as was done by Guo et al. (2021) (see Section 3.3 of their paper).For the case of an initial source spectrum with a corresponding phase-space density f ST (p), having a power-law dependence on momentum p, with a spectral index of δ, application of DSA theory gives the following for the phase-space density at and downstream of the shock: where α = 3r/(r − 1), r is the plasma density jump across the shock, and p 0 is the "injection" momentum, which can be related to the injection energy, E 0 .As noted above, DSA theory is only strictly applicable for values of E 0 very much larger than a few keV.f ST (p 0 ) is the value of the phase-space distribution function for the preexisting population of particles at the momentum p 0 .This equation was derived in Guo et al. (2021) starting with an equation derived by Neergaard-Parker & Zank (2012).
In the limit α < δ, then at high values of p, the distribution is dominated by the first term, which is the standard result of DSA, in that acceleration proceeds from a low-energy source leading to a power-law spectrum with a spectral index that depends only on the shock density compression ratio.In the limit δ < α, the distribution at the shock is dominated by the second term, which has the same spectrum as the source-but boosted in intensity by the factor α/(α − δ).If this limit applies, as it might for weak interplanetary shocks, we would expect the distribution of high-energy particles at the shock to have a spectrum that is similar to, but slightly higher in intensity than, that of the preexisting distribution, which may explain the observations of Desai et al. (2004).
For the 2022 February 16 event analyzed in this paper, we find that the spectrum at the shock has a power-law dependence on energy with a spectral index of about 1.6 (see Section 2.1).This corresponds to a power-law dependence of the phase-space density on momentum with an index of ∼5.2.This is close to the quiet-time spectrum suggested by Fisk & Gloeckler (2006).Thus, it is reasonable to consider the special case that the downstream spectrum and preexisting quiet-time spectrum have the same spectral index.Taking α = δ, it is straightforward to show This can readily be converted to differential intensity, giving where J ST is differential intensity spectrum of the preexisting particles and γ is the power-law index associated with the energy spectrum (γ = α/2 − 1).
To illustrate the application of this to determine whether the source of particles is a preexisting suprathermal distribution, we consider the flux of protons with an energy of 174 keV.This choice is rather arbitrary, but it is illustrative.This energy is considerably higher than the lower limit of applicability of DSA theory, which is well above the 3.4 keV value noted above.The flux of 174 keV protons is shown by plus symbols in the top panel of Figure 5, along with three dashed lines.The blue dashed lines in this figure refer to an approximate upper limit on the value of the "quiet-time" flux at the energy of 174 keV.The actual value of the quiet-time flux at this energy must be lower than this, at least during the nearly one-day time period preceding the CME-related SEP event.We denote this as J ST (174 keV).The red dashed line in this figure shows the prediction of J sh , based on Equation (3), for the case in which the injection energy E 0 = 2 keV.We used γ = 1.6, which corresponds to the downstream spectral index as discussed in Section 2.1.The red dashed line is very much below the observed peak at the shock, which is represented as a black dashed line.In fact, the difference is about 2 orders of magnitude.Because this line is so much lower than the observed flux at the shock, this analysis effectively rules out a preexisting high-energy population of protons, reaccelerated at the shock, as the source of particles for this event.Larger values of E 0 lead to even lower values of the predicted J sh (174keV).Smaller values of E 0 will give somewhat larger values of the predicted flux at the shock; however, on the one hand, even values of a few eV give a predicted flux still far below what is observed, while on the other hand, as noted above, such small values are already below those for which DSA theory is applicable.
The middle and bottom panels in Figure 5 are the same analysis repeated for helium and oxygen ions (using the ChanC data product), using approximately the same energy per nucleon for the observed fluxes, and the initial energies (E 0 ) in the analysis described for the protons.For example, for the For helium, the range of total kinetic energy is 637-723 keV, and for oxygen, it is 2.38-2.73MeV.See the main text for more details.case of helium, the range of total energies, shown as black symbols, is from 637-723 keV, with a logarithmic middle energy of 678 keV, corresponding to 170 keV nuc −1 .The blue dashed lines in these two panels are upper bounds on the preexisting tail, and they are the values at the one-count level.If there is a preexisting population of particles, its intensity is below these blue dashed lines.We repeat the same steps as we performed for the protons.From the middle panel, we see that the red dashed line, for the case of E 0 = 8 keV (2 keV nuc −1 ), which represents the expected value of the flux at the shock of shock-accelerated preexisting particles, is well below the observed value shown in black.Thus, the source of helium ions in this event must come from a source other than a preexisting high-energy tail, reaccelerated at the shock.The bottom panel shows the same analysis for oxygen ions, with an energy per nucleon similar to those of the protons and helium.This test is not as conclusive as those for the other two species, given the rather limited statistics, but it is still suggestive that the source of oxygen for this event is also not a reaccelerated preexisting suprathermal distribution of particles.
The most likely source is the solar wind, which has a density that far exceeds that of the energetic protons.It has been shown in self-consistent plasma simulations of particle acceleration at shocks, such as the well-known hybrid simulation, that thermal plasma can be readily accelerated to high energies, for both quasi-parallel and quasi-perpendicular shocks (see Ellison & Eichler 1984;Scholer 1990;Giacalone et al. 1992;Giacalone 2005).The injection process is related to the kinetic dissipation that maintains the collisionless shock.So-called "supercritical shocks," with Alfvén Mach numbers larger than about 2.7 (e.g., Kennel et al. 1985), such as the event studied here, are known to require additional dissipation beyond that provided by resistivity between the electrons and ions in the shock layer (e.g., Leroy et al. 1981;Winske 1985).It has been found that a fraction of the thermal ions incident on the shock are specularly reflected at the shock ramp and return back upstream, where they gyrate around the magnetic field, return to the shock, and advect downstream of it.These ions are suprathermal in the frame moving with the upstream plasma.This process has been observed well at Earth's bow shock (e.g., Gosling et al. 1981).A fraction of these ions can be reflected again at the shock and are further energized, forming the high-energy tail on the distribution, as seen in the hybrid simulations referenced above.It is generally found that the energy flux contained in the highenergy tail can be as much as 10-20% of the dynamic energy flux incident on the shock (Giacalone et al. 1997).
In the bottom panel of Figure 6, we show the dynamic solarwind energy flux, (1/2)m p nV 3 , as black circle symbols, and the enthalpy flux of 79-1600 keV ions, 5/2P ep V, as violet circle symbols, as a function of time for this event.P ep is the partial pressure of the energetic ions, obtained from the observed energy spectrum (over the same energy range of 79-1600 keV), which is shown in the top panel in violet symbols.In these expressions, V is the component of the solar wind speed in the radial direction as measured in the shock frame, given by V sh − U r , where U r is the measured spacecraft-frame radial solar wind speed, which was obtained from the SWEAP instrument.We assumed V sh = 800 km s −1 for this analysis.We note that U r exceeds the estimated shock speed behind the shock, leading to a negative value of the dynamic energy flux downstream of the shock, and we did not plot these values, because our vertical axis uses a logarithmic scale.Also shown in the top panel of this figure are the spacecraft-frame dynamic energy pressure, nm U p r 2 , as black circles, and the magnetic pressure, determined from the observed magnitude of the field obtained from the FIELDS instrument, as red circles.
The two dashed lines shown in the bottom panel of Figure 6 indicate the values of the two plotted quantities at the shock.The ratio of the energetic-particle enthalpy flux (violet) to the dynamic solar-wind energy flux (black) is about 3.5/17 ≈ 0.2.This suggests that the shock converts about 20% of the incoming ramming energy flux into energetic particles, thereby providing an estimate of the acceleration efficiency.This is similar to that estimated in CME events by Mewaldt et al. (2005).We note that this estimate is very sensitive to the value of the shock speed.
We conclude from the above that the source of energetic protons in this event is the solar wind.It is clear that the source is not a preexisting suprathermal seed population.The solar wind has enough energy to account for the observed intensity of energetic ions, and there is a reasonable explanation of the physics of this process based on the results of previous selfconsistent plasma kinetic simulations.
It is also important to emphasize that, while we have suggested that the acceleration of solar-wind protons at the shock is related to the shock dissipation process, this is not necessarily true for minor ions.Minor ions have a negligible contribution to the energy budget of the plasma, field, and energetic particles.Thus, the injection of these ions into the shock acceleration process could well be different from that of the protons.

The Decay Rate of Particle Intensity behind the Shock
The bottom panel (e) of Figure 7 shows fluxes of 79.1 keV to 1.66 MeV protons over a 9.6 hr period approximately centered on the arrival time of the shock, indicated with the vertical dashed line.The color coding of the ion fluxes is the same as that in Figure 1.The other panels show the plasma density (top, panel (a)); radial component of the solar-wind velocity vector (panel (b)); t-and n-components of the plasma velocity, in red and green, respectively (panel (c)); and the magnetic field vector and magnitude (panel (d)), with the same color coding as that shown in the top panel of Figure 1.
The energetic-proton fluxes peak at the shock and then decay downstream, all at very nearly the same rate at all energies.The prediction of steady-state diffusive shock acceleration (DSA) theory for a planar shock is that the fluxes should be constant downstream.Thus, the observed behavior is not consistent with Figure 7. From the top panel, plasma number density, radial component of the solar-wind velocity, t-and n-components of the solar-wind velocity (red and green, respectively), magnetic field vector magnitude (black) and components (r, in blue, t in red, and n in green), and fluxes of 79.1 keV to 1.66 MeV energetic protons over a 9 hr period nearly centered at the shock crossing time, indicated with the vertical dashed line.The color code for the magnetic field and proton fluxes is the same as that shown in Figure 1.
the prediction of the standard solution of DSA theory.This behavior has been noted previously in large ESP events (Reames et al. 1997;Daibog et al. 2000), and it might be an example of the so-called "reservoir" phenomenon (e.g., Dalla et al. 2002;Reames 2023, and references therein).In most of the events studied previously, the intensity decay occurs over a considerably longer timescale than is seen in the 2022 February 16 event, and typically at higher energies than in this event.Moreover, this phenomenon is certainly not always observed; there are other observations of ESP events, especially in the energy range we are interested in this event, which reveal nearly constant fluxes behind the shock (see Giacalone 2012, and Figure 1(a) of Lario et al. 2018).The more rapid decay in the event studied here might be due to the fact that PSP is much closer to the Sun than 1 au.If this is an example of the reservoir phenomenon, it is reasonable to expect the decay rate to be related to the rate at which the volume of the reservoir is increasing, and because it is closer to the Sun, the volume likely expands more rapidly, leading to a higher rate of decay.Another possibility is that the decay is caused by diffusive transport away from the source.Because the observed decay rate is nearly the same at all energies, it suggests that, if this were the case, the diffusion coefficient must be independent of energy.This would lead to a very interesting scenario, given the results presented in Section 3.1, where the diffusion coefficient is independent of energy everywhere except for very near the shock.
It is also noteworthy, however, that the plasma density (top panel, (a)) also decreases approximately exponentially from the shock into the downstream region over roughly the same time period as the energetic-proton fluxes.This suggests that the decay in energetic particles might be related to the decay in plasma density.On the one hand, as we showed in the previous section, the source of the accelerated particles is the solar wind; therefore, it seems entirely reasonable that the energetic particles and solar wind density are correlated.However, this is not as simple as it might otherwise seem, because the energetic particles are more mobile than the solar wind and it is not immediately clear why they would have the same spatiotemporal behavior as the plasma.On the other hand, as we discuss in Section 5, the decay in the plasma density is consistent with that expected from an overexpanding CME.In this case, the overexpansion leads to the energetic particles filling an increasing volume, leading to their decrease as well.This is discussed further below.
Another possibility is that the near-exponential decay is caused by adiabatic cooling of the energetic particles in the expanding solar wind behind the shock.Energy change in charged particles occurs when the particles encounter compressions or rarefactions in the plasma.Acceleration occurs at compressions, such as shocks, but rarefactions cause energy loss.The Parker transport equation (also known as the cosmicray transport equation) includes the energy term, which is proportional to the divergence of the plasma velocity (e.g., Parker 1965).If we assume that this is the dominant term downstream of the shock, we find where f is the phase-space distribution function, U is the plasma velocity vector, and p is the particle momentum.Assuming the distribution is a power law, consistent with the blue curve shown in Figure 2, it is readily found that this leads to where δ is the power-law index for the phase-space distribution function as a function of momentum.That is, f ∝ p δ , and because the differential intensity is p 2 f, we find that δ = 2 (1 + α), where α is the power-law index associated with the flux versus energy, as shown in Figure 2.For this case, we find α = 1.6, giving δ = 5.2.
By fitting the particle fluxes from the shock arrival time into the downstream region (later in time), we find that the e-folding timescale τ e ≈ 2 hr.Thus, from Equation (5), we have ∇ • U ≈ 0.29 hr −1 .If assume that the plasma velocity is radial and nearly constant behind the shock (it clearly is not, as seen in Figure 7(b), but this is addressed below), then ∇ • U = 2U r /r, where r is heliocentric distance.PSP was located at r = 0.35 au at this time.With these assumptions, we find that a value of U r ≈ 2000 km s −1 is required in order to account for the observed exponential decay, assuming it is caused strictly by adiabatic cooling in a uniform, radially expanding plasma.This value is considerably larger than the observed radial plasma speed shown in Figure 7(b).Alternatively, it is also instructive to consider that this cooling might be the result of a gradient in a direction other than radial.The middle panel (c) in Figure 7 shows the t and n components of the plasma flow for this event.One can clearly see a significant nonradial flow after the passage of the shock.We note that, aside from the change in flow direction at the shock, there is another change in the flow direction at about DOY 47.43, which we know to be real because inspection of velocity distributions (not shown here) during this time period reveal that the solar wind was within the instruments field of view.If the divergence in the plasma velocity was dominated by the nonradial terms-for example, the t direction-then we would have ∇ • U ≈ ΔU t /L t , where ΔU t is the change in U t over the length scale of variation in the t direction, represented by L t .An upper limit on L t would be perhaps half of the lateral extent of the CME, which is on the order of the heliocentric distance of PSP, 0.35 au, times half the CMEs angular extent.Based on a simulation of events discussed below, the angular extent appears to be on the order of, at most, 90°, and half of this is 45°.This gives L t ∼ 0.27 au.Thus, setting the divergence of 0.29 hr −1 equal to ΔU t /L t , we obtain ΔU t ∼ 3250 km s −1 .Judging from the red symbols in the middle panel of Figure 7(c), the t component of the plasma speed does change slowly downstream, but the change is more than 1 order of magnitude smaller than this estimate.Thus, adiabatic cooling of energetic particles from the contribution to the plasma divergence arising from variations in the nonradial components of the plasma speed downstream of the CME shock cannot account for the observed exponential decay.
Adiabatic cooling may contribute to the decay in particle intensity behind the shock; however, based on the simple assumptions used above, it seems unlikely.We also do not favor the interpretation that this is caused by diffusive escape.This is likely related to previous examples of invariant spectra observed during the decay phase of large ESP events seen previously (e.g., Reames et al. 1997;Daibog et al. 2000;Dalla et al. 2002;Reames 2023).Yet, the behaviors of the plasma density and velocity behind the shock are somewhat unusual, and as we discuss below, they suggest that the shock is undergoing a rather rapid change at the time it crossed PSP.In fact, as suggested by global modeling of the inner heliosphere at the time of the CME eruption, from the well-known ENLIL model (e.g., Odstrcil 2003), discussed below, PSP was very close to a large plasma compression associated with a corotating interaction region.This can be seen in Figure 8.We suggest below that this interaction led to the rapid, but probably short-lived, deceleration of the CME shock at about the same time it crossed PSP.Although this does not necessarily lead to a more rapid adiabatic cooling of the high-energy particles that estimated above, it likely caused the reduction in plasma density behind the shock.Since the source of energetic protons is the solar wind, as we discussed in the preceding section, it seems reasonable that their fluxes are related to the plasma density.
As we shall now discuss, we suggest that the deceleration of the shock was caused by its interaction with a localized enhancement in plasma density, possibly related to a corotating interaction region.As the shock interacted with this density enhancement, it is reasonable to infer that the flux of source particles was initially increased, but then, as the shock overtook the structure, the plasma density, and associated source particle flux, declined like the plasma density.

Evidence of a Locally Decelerating Shock
Consider the behavior of the radial component of the solarwind velocity shown in Figure 8.There is a jump in the speed at the shock, as expected, but then the speed increases approximately linearly from about DOY 47.31 to DOY 47.36 before becoming approximately constant afterward.In an idealized interplanetary shock that is in steady state in the frame moving with the shock, mass conservation across the shock can be used to determine the shock speed.For a forward shock, if U 1 and U 2 are the observed solar wind speeds (normal to the shock, assumed to be radial), upstream and downstream of the shock, respectively, and n 1 and n 2 are the plasma densities upstream and downstream, then the shock speed is given by V sh = (U 2 r − U 1 )/(r − 1), where r = n 2 /n 1 .For the ideal case, if we assume the shock is "strong," in that the value of the plasma density jump is nearly 4, which is approximately consistent with that observed very near the shock, then the shock speed is about (4/3)U 2 .Thus, the behavior of the observed (approximately) linear increase in U r immediately downstream of the shock shown in Figure 8 could be interpreted as the shock speed decreasing linearly.That is, if we take U 2 to be the observed speed after DOY 47.36, we obtain a shock speed of about 1000 km s −1 , which is larger than we have used in the analysis discussion in the previous sections, which is based on the properties of the shock seen locally at PSP.This suggests the shock was decelerating when it crossed PSP.Moreover, the decrease in density behind the shock would be expected if the shock crossed a larger density enhancement and then overtook it, and such an interaction would also likely cause the shock to slow down.
Figure 8 shows two images obtained from an ENLIL numerical simulation run,12 including a CME represented by the so-called "cone model," performed as a run-on-request from the Community Coordinated Modeling Center (CCMC).The two images are snapshots at the times given in the figure caption.The CME parameters used for this run-on request were lat = 30, lon = −158, rad = 51, and vel = 2554, and the CME was initiated on 22:09 UT on 2022 February 15.The images show plasma density times r 2 , with the color code shown in the figure legends, in the equatorial plane.Also shown in these images are the positions of four spacecraft, as indicated above each image, as well as magnetic field lines that connect each spacecraft to the source surface at the center of the image.The left image in Figure 8 shows the solar wind conditions just prior to the eruption of the CME and reveals a density enhancement associated with a corotating interaction region that is about to overtake PSP (the green square).The image at the right shows the time after the CME has launched and is just about to cross PSP.We see that the CME is also interacting with the preexisting density enhancement at about the same time it crosses PSP.This is consistent with our suggestion above that the CME shock was decelerating locally as it crossed PSP.
The ENLIL simulation also provides plasma and field parameters at PSP as a function of time.In Figure 9, we show the results from this model run with the magnetic field field strength in black, plasma density in red, and radial plasma velocity in blue.The model run provides a reasonable estimate of the arrival time of the shock, and the plasma density is qualitatively similar to the observed; however, the radial component of the flow velocity and the field strength time profiles do not agree with the observations after the passage of the shock.For instance, the ENLIL-model flow speed declines after the shock crossing, which is not consistent with that observed.This is perhaps not surprising, given that this CME was on the back side of the Sun relative to the Earth, and the inner boundary conditions used in the model are not well constrained during this time period.Although these particular simulations do not demonstrate that the shock was locally decelerating, we show in the next section that such behavior is to be expected when a shock passes over a preexisting density enhancement.

Results from a One-dimensional Hydrodynamic Simulation
To test the rather simplified physics argument given above, we have performed a one-dimensional spherically symmetric hydrodynamic numerical simulation of a fast forward shock wave overtaking a preexisting density structure.The details of this simulation are given in the Appendix.In this section, we just present the results and interpretation.It is important to emphasize that this numerical simulation is not a direct simulation of the 2022 February 16 CME.Rather, this is a proof of concept to support our suggestion that a shock will undergo a deceleration as it crosses a preexisting density enhancement, and that the resulting behavior of the density and flow speed are qualitatively similar to that observed for this event.The parameters used in the one-dimensional simulation, however, are not based on observed values during the time period of the CME event.
Shown in Figure 10 are simulated profiles of the plasma number density and solar wind speed (assumed to be radial) as a function of heliocentric distance at four different times, as indicated.The black curves are the profiles at 0.83 hr after the start of the simulation.The top panel shows the preexisting density enhancement at about 0.16 au.The fast disturbance is at about 0.1 au at this time and has already formed a forward/ reverse shock pair.This is expected in the ideal case modeled here, even close to the Sun, in which a high-speed radial flow overtakes a slow-peed radial flow, because this model is spherically symmetric.At 3.19 hr (red curves), the density enhancement is moved outward and has also formed a forward/reverse shock pair.The reverse shock is located about 0.175 au, while the fast forward shock associated with the disturbance is approaching it at about 0.15 au.At 5.56 hr (blue curves), the fast forward shock of the disturbance has overtaken the reverse shock caused by the initial density enhancement.The density profile at this time shows a large density jump at about 0.2 au, which is caused by the forward shock overtaking the density enhancement of the reverse shock.At about 7.92 hr (magenta curves), the fast forward shock, associated with the large disturbance (consider it the simulated CME), has overtaken the reverse shock completely, and it will later also overtake the forward shock seen at about 0.28 au.
Figure 11 shows the same profiles, but as functions of time as seen by three observers located at about 0.2 au, as indicated.These observers are located near the large density enhancement seen in the blue curve of the top panel of Figure 10.We note that there is a qualitative consistency between these time profiles and those observed for the PSP event described above, as can be judged by comparing the red curves of Figure 11 and the black circle symbols of Figures 7(a) and (b).There are certainly quantitative differences between the results of our simulation and those observed.For instance, the density decrease behind the shock is not obviously exponential, and it does not decrease by as large a factor as that observed.Moreover, the increase in the flow speed from near the shock to further downstream is not obviously linear.Furthermore, the timescales of the variations are considerably smaller in the simulations, compared to the observations.Regardless, the simulation is qualitatively consistent with the observations and with our suggestion that the CME-driven shock was decelerated by its interaction with a preexisting density enhancement.In this case, that structure was a corotating interaction region, as evidenced by Figure 8.
While we have provided evidence that the shock was decelerating locally as it crossed PSP, this does not obviously relate to the uniform decay of the energetic particles behind the shock, as discussed in Section 3.3.The cause of this remains unclear.In the next section, we discuss another possibility: that the shock seen locally at PSP was caused by an overexpanding CME, leading to a blast wave.In this scenario, the depletion of the SEPs behind the shock would be caused by the energetic particles filling an increasing volume.

Evidence of a Blast Wave
As noted previously, the decay of energetic particles behind the shock is similar to the decay of the plasma density behind the shock.This behavior would be expected if the shock were locally a blast wave since it is well known that such shocks are associated with a region of overpressure, followed by a significant decrease in the pressure (and density).A blast wave can result from a CME when its internal pressure is greater than that of the surrounding solar wind.Gosling et al. (1998) studied a few such cases observed by Ulysses.The CME in our case  was directed toward a higher latitude than where PSP was located (Mierla et al. 2022), yet PSP observed a rather strong shock at its location.The enhancement in density and change in flow speed were rather large, despite the fact that PSP was well south of the CME "nose." We might reasonably assume that the radius of the blast wave is on the order of the distance between PSP and the Sun, which was about 0.35 au.In the well-known Sedov blast wave solution, it is found that after the initial increase in the plasma density (or pressure) at the shock, the density decays over a scale that is about 10% of the shock radius (see Chapter 17 of Shu 1992).This gives a scale of the density variation for our case of about 0.035 au.Assuming the shock is moving 800 km s −1 , based on our previous estimate, it would take about 1.8 hr for such a scale to pass by PSP.This corresponds to about 0.07 of a day, and judging from Figure 7, this is consistent with the scale of the variation of the density and SEP intensity decays behind the shock.This rather simple estimate could be refined and even include the speed of the spacecraft.However, our estimate is sufficient to justify the principal conclusion, given that, at this time, PSP had a radial speed of less than 30 km s −1 , which is well below the ∼800 km s −1 speed of the shock.
Thus, we suggest that the SEP intensity increase behind the shock is the result of the SEPs filling an expanding volume associated with the propagation of a blast wave as it crossed PSP.We suggest that this is an example of an overexpanding CME, whose internal pressure is larger than that of the surrounding medium, and which has been seen previously at larger heliocentric distances (e.g., Gosling et al. 1998).In this case, the overexpansion can drive shocks, or compressions that steepen into shocks farther from the Sun.However, the case analyzed here is much closer to the Sun and may indicate that overexpanding CMEs, a very explosive phenomenon, are more common closer to the Sun than previously realized.This interpretation may also explain why the rate of decay in the particle intensities for this event is shorter than seen in previous ESP events, as we discussed in Section 3.3.

Summary and Conclusions
We have presented a number of analyses of the CME-related ESP event observed by PSP on 2022 February 16 when the spacecraft was 0.35 au from the Sun.This event was broadly characterized as a significant enhancement in the intensity of ∼0.05-5 MeV protons, which started with a slow and gradual increase after the onset of a CME as seen by the STEREO-A Cor2 coronagraph, peaking at the arrival of a shock, and then decayed significantly at the arrival of the ICME flux rope.There were counts detected for this event up to 80 MeV nuc −1 , although our focus in this study was the ESP phase of the event at lower energies.The event began approximately 1.5 hr after a clear signature of the CME was seen in the STA/Cor2 images.The shock, and associated peak in energetic particles, occurred about 9 hr after the CME eruption.The ICME arrival occurred about 8 hr after the arrival of the shock.
Shortly after the onset of the ESP event, the fluxes of protons from ∼0.079-1 MeV showed equal intensities lasting for 4-5 hr prior to the shock arrival.This represented a quasi-flat energy spectrum.While this feature has been noted in prior CME-related SEP events observed at 1 au (e.g., Lario et al. 2018), here we report this observation for PSP at 0.35 au.The fluxes during this period rose slightly with time until about 30-45 minutes prior to the shock, where the fluxes began to rise more abruptly and with a rate that depended on energy such that the fluxes "separated."The spectrum at the shock from ∼0.079-1 MeV had a power-law dependence on energy with a spectral slope of about −1.6.At higher energies, the spectrum was a bit steeper but also had a power-law dependence on energy.
We calculated diffusion coefficients by fitting the rate of increase of the proton fluxes both far from the shock, during the flat spectra period, and closer to the shock, to exponential functions, representing diffusive decay in the intensity of particles with distance from the shock upstream.We found that, far from the shock, the diffusion coefficient was independent of energy with a value of (0.87-1.5)×10 20 cm 2 s −1 .Because the magnetic field was nearly radially outward during this time, this represents the parallel diffusion coefficient.For the period closer to the shock, we found that the diffusion coefficient increased with energy such that κ rr ∝ E 0.9 , having a value of 3 × 10 18 cm 2 s −1 at the energy of 56.2 keV.
We also performed an analysis to determine the source of the energetic particles in this event, in particular whether they could be produced by the enhancement of a preexisting suprathermal population by reacceleration at the shock.We did this by invoking diffusive shock acceleration theory for the case of a source of preexisting particles having a high-energy power-law dependence on energy, and we determined the increase in intensity of the reaccelerated particles at the shock.We constrained the intensity of the preexisting high-energy particles by using the quiet-time intensity of particles with energies between 165 and 184 keV nuc −1 .We determined the intensity enhancement at the shock as expected from DSA theory and compared this to the observed increase for protons, helium, and oxygen.We found that the enhancement of the quiet-time tail cannot account for the peak flux at the shock for protons and helium, while the test was not conclusive for oxygen.In fact, the peak flux of protons at the shock was some 3 orders of magnitude larger than the (upper bound) of the flux of quiet-time protons.For helium, the observed flux at this energy was some 2.5 orders of magnitude above the one-count level, which was used because there were no counts of quiettime particles detected.For oxygen, the statistics were even more limited, and the peak at the shock was only a factor of 10 or so above the one-count level.The maximum enhancement, according to the theory, is only 1 order of magnitude or less.We further showed that the energy flux contained in the energetic particles at the time of the shock crossing was about 20% of the incoming dynamic energy flux of the solar wind.Thus, there is sufficient energy in the solar wind to draw from to produce the energetic protons.We noted that the 20% value is consistent with previous self-consistent numerical simulations.We conclude that the energetic protons in this ESP event are the result of the acceleration of solar wind protons directly at the shock front.Our results also suggest that helium is also accelerated directly from the solar wind.This may also be true of oxygen, but our analysis was unable to make a definitive statement on this, due to the limited statistics available.
This ESP event is also characterized by a near-exponential decrease in intensity of the particles immediately after the passage of the shock, lasting for about an hour.We considered whether adiabatic cooling, caused by the divergence in the solar-wind velocity vector downstream of the shock could account for this behavior.From the observations, we determined the e-folding decrease in the flux to be τ e ≈ 2 hr., which we assumed was the rate of cooling.We equated this time to that predicted from energetic-particle transport theory, which relates the cooling rate to the power-law spectral index of the SEP energy spectrum and the divergence of the plasma velocity.From this, we estimated that, to achieve the observed rate of flux decrease, the plasma would have to have a speed of 2000 km s −1 , which is far greater than that observed.Thus, this could not be caused by adiabatic cooling in a purely radial and constant shocked solar wind.We also considered whether variations in the nonradial directions might lead to a faster cooling rate, but this analysis was inconclusive.
We also noted that the observed solar-wind plasma density also decays behind the shock at a rate the same as that of the energetic particles.This suggests a close relationship between the two.As we have already concluded that the main source of energetic particles in this event is direct acceleration of thermal solar wind at the shock, it is perhaps not surprising that the time behavior of the two are related.The solar-wind velocity also had a time behavior that suggested the shock was undergoing, or had recently undergone, a deceleration.The global solar wind at this time, according to an ENLIL simulation, revealed that the CME occurred at a time where PSP was about to encounter a preexisting plasma compression associated with a corotating interaction region.Therefore, the CME crossed over this compression, which, we suggest, caused the CME shock to slow down.To verify this, we performed a simple onedimensional, spherically symmetric, hydrodynamic calculation of our own.We found that, if an observer were to be fortuitously positioned as a shock wave overtook a large density enhancement, it would observe a time evolution of the density and radial flow speed that is qualitatively consistent with that observed by PSP in the 2022 February 15 event.
Finally, we also considered the possibility that the time behavior of both the plasma density and the SEPs behind the shock could be understood in terms of the passage of a blast wave across PSP.It has been noted previously that CMEs are an explosion-like phenomenon and can expand rapidly into the preexisting medium and lead to the existence of blast waves (Gosling et al. 1998).STA/Cor2 images of the CME in the event showed that the CME was propagating at a higher latitude than where PSP was located, yet PSP still observed the shock.If the shock seen by PSP was similar to that of a blast wave, then the plasma density would decrease approximately exponentially behind the blast wave, in the shocked plasma.The same is true of the energetic particles.This is an attractive possibility, and as PSP was located at some 0.35 au from the Sun at this time, it may indicate that CME blast waves could be common close to the Sun.consider the following initial conditions: the flow speed is taken to be constant with a speed 550 km s −1 .The number density is taken to fall off as 1/r 2 , with a value of 5 cm −3 at 1 au, and the thermal pressure is also taken to fall of as 1/r 2 with a temperature of 1.9 MK at the inner boundary.The variation of the pressure was taken rather arbitrarily, but given that the thermal pressure is smaller than the plasma dynamic pressure, our choice of the pressure does not much affect the general conclusions of our study.
At t = 0, a Gaussian-shaped density enhancement with a width of 2.5 × 10 −3 au and peak value at r = 0.15 au is initiated.This enhancement evolves with time, forming forward and reverse shocks at either edge.This can be seen in Figure 9.At t = 0.5 hr, a large impulse is created by setting the inner boundary to have a speed of 10 8 cm s −1 .The speed at the inner boundary after the release of this impulsive "blob" slowly decays exponentially over a scale of about 60 hr, which is far greater than the maximum simulation time.The result of this inner boundary condition is a fast-moving compression that forms a forward/reverse shock pair, which both move outward relative to the Sun.This can also be seen in Figure 9.

Figure 1 .
Figure 1.Overview of observations of the SEP event observed by PSP on 2022 February 16.The top panel shows the magnetic field vector, with components represented by colors as indicated at the right of the panel.The middle panel shows the differential intensity of energetic protons, with energies indicated at the right of the panel.The bottom panel shows the differential intensity, represented as a color spectrogram, of all protons in our study with energy along the vertical axis.The vertical dashed lines represent the time of significant events.The one on the left is the time in which STEREO-A/Cor2 first observed the CME, the middle one represents the arrival of the shock, and the far right one is the onset of the magnetic flux rope associated with the ICME.

Figure 2 .
Figure 2. Energy spectra of energetic protons for this SEP event taken over three separate time intervals, as indicated in the legend at the lower left of the figure.The dashed lines are representative power-law distributions, presented as a guide.

Figure 3 .
Figure3.Differential intensity over selected intervals upstream of the shock: far from (left) and near the shock (right).The energies are 75 keV (cyan), 133 keV (red), 237 keV (green), 421 keV (blue), and 750 keV (violet).The black lines in all panels represent the least-squares fit to the data, with the exponential rise time and correlation coefficient shown in Table1.

Figure 4 .
Figure 4. Open-circle symbols are diffusion coefficients far upstream (black)and near the shock (red), as estimated from the rise-time analysis and tabulated in Table1.The solid lines are least-squares fits to these data.The dashed lines are estimates based on quasi-linear theory using the measured power spectrum of magnetic field fluctuations for each of these time intervals.See the main text for more details.

Figure 5 .
Figure5.Top: (black plus symbols) flux of 165-184 keV protons (logarithmic middle energy of 174 keV) for a 3 day period including the ESP event of 2022 February 16. (Blue dashed line) an approximate estimate of the upper bound on the preexisting flux of particles within this energy range, for a ∼1 day period prior to the initial increase.A red dashed line shows the estimate of the increase of particles at the shock resulting from the acceleration of the preexisting particles at the shock based on diffusive shock acceleration theory for an injection energy of 2 keV.A black dashed line indicates the value of the flux at the shock arrival.Middle and Bottom: same format as the top panel, but for the cases of helium (middle) and oxygen (bottom) ions with approximately the same energy per nucleon as the protons.For helium, the range of total kinetic energy is 637-723 keV, and for oxygen, it is 2.38-2.73MeV.See the main text for more details.

Figure 6 .
Figure 6.(Top panel) partial pressures of SEPs (violet symbols), dynamic pressure of solar wind (black symbols), and magnetic field pressure (red symbols).(Bottom panel) dynamic energy flux of the solar wind in the shock rest frame (black symbols), and the energetic-ion enthalpy flux (violet symbols).The dashed lines in the bottom panel show the values near the shock.See the main text for more details.

Figure 8 .
Figure 8. Results from the modeling of the solar wind in the inner heliosphere at about the time of the CME based on the ENLIL model (see the main text for details).Shown are two snapshots of the solar-wind density times r 2 in the ecliptic plane at two different times on 2022 February 16, as indicated above each image.The left image is for time = 00:00:26 UT, and the right image is for time = 00:06:24, when the CME was just about to cross over PSP, as indicated by the green square in each image.Also shown are the positions of five spacecraft, as indicated above each image.The dashed lines are magnetic field that connect from the spacecraft to the inner boundary of the model calculation, at about 0.1 au.

Figure 9 .
Figure 9. Magnetic field strength (black), plasma number density (red), and radial component of the solar wind speed (red) as a function of UT, DOY 47, 2022 from the ENLIL model of the 2022 February 16 CME at PSP.

Figure 10 .
Figure10.Fluid speed and density as a function of radial distance at four different times from a one-dimensional, spherically symmetric hydrodynamic simulation of a fast disturbance overtaking a preexisting density enhancement.The times associated with each curve are indicated in the legend in the upper panel.See the main text and the Appendix for more details.

Figure 11 .
Figure 11.Same as Figure 9, except that these are profiles as a function of time seen by three different radial distances (observation locations), as indicated by the legend in the bottom panel.See the main text for more details.

Table 1
The Top Part of This Panel Refers to the Time Interval 2:30 UT to 6:00 UT on DOY 47, Far Upstream of the Shock, while the Bottom Portion Is for the Interval 7:11 UT to 7:26 UT on DOY 47, Near Upstream of the Shock