Solar Energetic Particle and the Heliospheric Current Sheet

The effect of the heliospheric current sheet (HCS) on the propagation of solar energetic particles (SEPs) remains poorly known. In this study we address this question by surveying energetic (∼2.0–9.6 MeV nucleon–1) helium data acquired by the energetic particle acceleration, composition, and transport (EPACT) sensor on board the Wind spacecraft. A superposed epoch analysis of 319 HCS crossings made by Wind reveals a sharp drop in the SEP fluxes at the HCS for the low-energy channels and little change across the HCS for the high-energy channels. To help understand the statistical result, we studied a total of 15 SEP flux dropout (a decrease of ∼50% or more) events that coincided with the crossing of the HCS. One of the common features of these SEP events is that they were initiated in the western hemisphere but far away from the longitude of HCS crossings, suggesting that the source of SEPs was well connected initially but was cut off later after Wind moved to the opposite hemisphere (e.g., HCS crossing). Further analysis of the events suggests that the percentage of flux dropouts decreases with increasing energy. It is suggested that a strong scattering of MeV helium may have occurred as the particle gyroradius is comparable to the thickness of the current sheet. This study clearly provides solid evidence for the HCS as a barrier to suppressing SEP flux of MeV energies from the onset hemisphere to the other.


Introduction
Solar energetic particles (SEPs) are sudden increases in the flux of charged particles with energies ranging from tens of keV to GeV.Studies of SEPs and particle acceleration constitute a major branch of space physics.They also play an important role in space weather, as SEPs can pose a potential threat to spacecraft electronics and the health of unprotected astronauts.In general, there are two types (sources) of SEP events (see, e.g., Tsurutani et al. 2009): short-timescale (impulsive) events are accelerated by processes in the solar corona associated with solar flares (e.g., Pallavicini et al. 1977) and long-timescale (gradual) events are accelerated at shocks upstream of coronal mass ejections (CMEs; e.g., Kahler et al. 1978Kahler et al. , 1984;;Tsurutani & Lin 1985) and corotation interaction regions (Tsurutani et al. 1982).
Propagation of SEPs in the heliosphere is a subject of continuing research.Past studies (e.g., Cane et al. 1988) have depicted a magnetic connectivity model to explain the longitudinal structures of SEP.In the heliosphere, the average interplanetary magnetic field (IMF) bends in the Parker (Archimedean) spiral orientation (Parker 1958).Thus large and prompt SEP events should occur when the SEP sources, e.g., flares and CME-driven shocks, are in the west solar disk ranging between ∼30°and 90°from the Sun-Earth line.A later study, which used heavy ion SEP measurements from three spacecraft, suggests a distribution with ∼43°wide centered at ∼22°west of the flare site (Cohen et al. 2017).On the other hand, an east solar disk SEP source generally results in weak and delayed SEP fluxes.While such a model provides a general understanding of SEP flux variations relative to the source longitude, there remain large variations in the SEP longitudinal spread (Cohen et al. 2017) and SEP profiles (see Kahler et al. 1996).
In addition to the Parker spiral field, other solar wind structures may have significant effects on the propagation of SEPs in the heliosphere.For example, it is well known that the IMF is structured into hemispheres of either inward or outward polarity separated by relatively sharp boundaries, known as the heliospheric current sheet (HCS; e.g., Smith 2001).The HCS is one of the largest persistent solar wind structures in the heliosphere (Richardson et al. 2016).Owing to the tilted dipole field from the solar rotation axis and the outflowing solar wind, the HCS appears to be wavy in nature.This can result in HCS crossings and IMF polarity changes in near-Earth spacecraft data (see Figure 1(a)).In addition, the HCS is oriented along the Parker spiral field on average at 1 au (e.g., Liou & Wu 2021).Thus interactions of the HCS with outgoing solar transient events, such as CMEs, are likely, especially when most CMEs take place at low latitudes (Majumdar et al. 2023).When an observer is located at a different magnetic hemisphere from the source of SEPs, i.e., separated by the HCS, reduced or no SEP flux can result if the HCS can inhibit crossings of SEPs.However, such a speculation has not been proved, as results from previous studies are generally mixed (e.g., Kallenrode 1993;Kahler et al. 1996).For context, Figure 1(b) shows an example of two consecutive SEP events measured at the Wind spacecraft on 2000 September 12-19.Both SEP events were associated with a CME and its driven shock that arrived ∼2-3 days later.Notice that both CME events were western events taking place near the Sun-Earth line (S19W06 on September 12 and N14W07 on September 16).In both events, Wind encountered the HCS before the shock arrival.However, the SEP flux across the HCS shows opposite changes: a small but gradual decrease in the first HCS crossing and a large but fast increase in the second HCS crossing.
The effects of the HCS on the propagation of SEPs were first mentioned by Roelof & Krimigis (1973).They mapped 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.0.3 MeV proton intensities from Mariner 5 to the chromosphere, where neutral lines can be identified with H α synoptic charts, to show some cases where sudden changes in proton fluxes can occur when the magnetic footpoint of an observer crosses the coronal neutral line.Kallenrode (1993) compared SEP flux measurements from two longitudinally separated spacecraft (Helios 1 and Helios 2) for 39 SEP events and found that coronal neutral line crossings can have significant effects on the onset and flux profiles, although SEP particles can be observed on both sides of the neutral line.Note that these studies indicate that large variability exists in the SEP flux changes (either increases or decreases).Shea et al. (1995) reported that the majority of proton (primarily ground-level enhancement) events they studied occurred when both the flares and the Earth were in the same hemisphere.On the other hand, Kahler et al. (1996) examined statistically the onset times, rise times, and peak fluxes of 134 large SEP events and concluded that the streamer structure (the coronal base of HCS) has no detectable effect on the development of the shock and CME driver.
The presence of an HCS may affect the time-intensity profile of "gradual" SEP events at a distant but magnetically wellconnected observer in two ways.First, when the HCS interacts with a shock, it may alter the shock structure and change the magnetic connectivity.Some theoretical works suggested that shocks can be deformed at the HCS (e.g., Steinolfson & Mullan 1980;Uralova & Uralov 1994), thus affecting the generation of SEPs.Using global magnetohydrodynamic simulations, Wu et al. (2016) demonstrated that the interaction of a shock with the HCS can result in a reduction of the shock strength (Mach number), thus reducing the generation of SEPs.Second, SEPs are confined by the HCS.Energetic particles propagating in the interplanetary space are guided by the largescale interplanetary magnetic field.Scattering by small-scale magnetic field irregularities can occur when the scale of the irregularities is comparable to the particle's gyroradius, and perpendicular transport can arise when scattering occurs.For example, Tsurutani et al. (1999) showed magnetic field decreases (MDs), which is a common feature associated with the HCS, can cause displacements of particle guiding center, thus resulting in cross-field diffusion.A cross-field diffuse rate for 100 keV-2 MeV protons due to MDs was estimated to be ∼0.1 Bohm diffusion rate (Costa et al. 2013).Anomalous cross-field diffusion of charged particles can also occur by cyclotron-resonant scattering and has been used to explain the low-latitude boundary layer (Tsurutani & Thorne 1982).
From the dynamic point of view, charged particle trajectories near a current sheet are stochastic (e.g., Chen 1992;Kaufmann et al. 1993;Artemyev et al. 2015).Büchner & Zelenyi (1989) proposed a simple adiabaticity parameter: κ = (R/ρ) 1/2 , where R is the minimum radius of curvature of the magnetic field and ρ is the maximum particle gyroradius at the field reversal, to describe particle trajectories in a magnetotail-like field reversal (i.e., the current sheet with a normal field component).Test particle simulation in an analytical HCS setup suggests that drift along the HCS can facilitate the spreading of energetic protons longitudinally and at the same time limit their HCS crossings (Battarbee et al. 2017(Battarbee et al. , 2018)).These studies seem to support the idea that the presence of the HCS can have more or less effects on SEP propagation.
Here we address the question if and to what extent the HCS affects the propagation of SEPs.We will perform a statistical study to demonstrate the overall SEP flux change across the HCS.Then we look for events of sharp dropouts in SEP fluxes that coincide with the HCS.We then study these events' common features to picture a possible scenario.In Section 2 we describe the SEP data and survey results, followed by the discussion and conclusions.

The EPACT Instrument Data
To study variations of SEP flux across the HCS, the in situ particle measurements acquired by the Energetic Particle Acceleration, Composition, and Transport investigation (EPACT; Von Rosenvinge et al. 1995) on board the Wind spacecraft will be used.EPACT consists of eight different particle telescopes.For the present study, 5 m and 1 h data of helium (He) SEP (at seven energies 2.00-9.64MeV nucleon -1 ) from the Low-Energy Matrix Telescope (LEMT) are used.

Statistical Analysis
We perform a simple statistical analysis to determine if the HCS has an influence on the SEP flux observed at 1 au.
Figure 1.(a) Schematic drawing of the heliospheric current sheet (HCS) illustrating its "wavy" structure (adapted from Smith et al. 1978).(b) Two solar energetic particle (∼2.0-9.6 MeV helium) events observed at the Wind spacecraft on 2000 September 12-19.The CME onset is marked with a green vertical dashed line, whereas the HCS/shock crossing at Wind is marked with a red/blue dashed line.
Figure 2 shows the SEP fluxes around the HCS averaged from 319 HCS crossings at the Wind spacecraft.These events were selected from a list of 1115 HCS events identified with the Wind data from 1995 to 2020 (Liou & Wu 2021) using the criterion that the SEP flux (2 MeV He) must be greater than 10 −3 (cm 2 s sr MeV nucleon -1 ) −1 for more than 2 days.The statistical tool we use is the superposed epoch analysis.The SEP flux data around (±48 hr) the HCS crossing times are normalized and resampled into hourly bins.After that, we compute the mean (red circles), the standard deviation of the mean (error bars), and the median (blue traces) for each and every bin, and the result is shown in Figure 2 for (a) 2.00-2.40MeV and (b) 7.4-9.64MeV He channels.While such an analysis is rudimentary, the large number of HCS events would smooth out any uneven temporal and spatial distribution of SEP events.
As shown in Figure 2(a) there is a clear sudden flux drop (∼8%) at the zero epoch for the 2.00-2.40MeV channel.The drop is statistically meaningful as it is larger than the error bar and as it also appears in the median values.Note that the flux dropout seems to be more significant but gradual in the median values.Note that the epoch time can be translated to the west (negative epoch time) and east (positive epoch time) longitude respective to the HCS.Therefore, this SEP flux drop at HCS suggests that SEP fluxes are statistically larger westward of the HCS and smaller eastward of the HCS.Because of the Parker spiral of the IMF, western events are well connected and have a greater chance to reach the observer than eastern events.It could also mean that the HCS acts as a barrier for the SEPs.For a such large number of HCS crossings, we tend to believe the latter scenario (or both), as there is a large gradient in SEP fluxes at the HCS.Furthermore, such a SEP flux drop at HCS does not appear in the 7.40-9.64MeV He channel.This indicates that the HCS does not (or less) affect higher energy He.
To test the statistical significance of the flux dropouts at the HCS, two methods are performed.First, we test if the jump is solely by chance.This is done by randomly selecting a number of samples and repeating the superposed epoch analysis.This will yield a new sample mean for flux changes at the HCS.If this process is repeated many times, the sample mean will be normally distributed (the central limit theorem).To reduce bias toward large SEP events, SEP fluxes are normalized to the peak flux of each event.Here we select 160 events randomly from the 319 HCS events and perform the superposed analysis.After 10,000 iterations, the distribution of the flux change (in percentage) at the HCS is obtained and plotted in Figure 3.For the 2.00-2.40MeV channel, the calculated population mean (μ) is −11.1% and the standard deviation (σ) is 5.0%.The "2σ rule" suggests that 95% of the time, the true mean will fall into the confidence interval [−21.1%,−1.1%], meaning that a flux decrease at the HCS occurs 95% of the time.For the 7.40-9.64MeV He, the distribution is also Gaussian and is roughly symmetric around zero (μ = 1.6% and σ = 7.6%), meaning that the mean flux change is roughly evenly distributed around zero 95% of the time.
Since the above analysis is based on the normalized flux, it does not provide information about the actual flux changes at the HCS.To address this, we plot the normalized histogram (e.g., occurrence frequency) of the actual flux changes at the HCS.As shown in Figure 4, for the 2.00-2.40MeV channel, the occurrence frequency of the flux change is biased toward negative values (e.g., flux decreases).It is estimated that ∼32% of the events show little (within ±10%) flux changes, ∼21% of the events show a more than 10% flux increase, and ∼46% of the events show a flux decrease more than 10%.For the 7.40-9.64MeV He, we found that ∼28% of the events fall within ±10% of changes, ∼32% of the events show more than 10% flux increase, and ∼39% of the events show a flux decrease of more than 10%.Therefore, based on the above analysis, we conclude that changes in the He flux at the HCS can occur in the majority of cases, and the changes tend to be negative (about 2 in 3) for the lower-energy channel (2.00-2.40MeV) and such a trend decreases significantly (∼20%) for the higher-energy channel (7.40-9.64MeV).

Case Study of SEP Dropout Events
The statistical study performed above clearly shows high variability of SEP fluxes and a tendency for a negative flux change (e.g., flux dropout) across the HCS.Here we will focus on events with large flux dropouts to provide more insight.We survey in situ particle measurements acquired by the Energetic Particle Acceleration, Composition, and Transport investigation (EPACT; Von Rosenvinge et al. 1995) on board the Wind spacecraft for SEP dropout events.EPACT consists of eight different particle telescopes.For this study, hourly data of helium (He) SEP (at seven energies 2.00-9.64MeV nucleon -1 ) from the LEMT are used.The requirements for an SEP dropout event are: (1) it must coincide with the HCS crossing at Wind and (2) at the dropout, the decrease in the flux of the first energy (2.0-2.4MeV) channel must be greater than ∼50% within 3 hr (e.g., three data point).Note that the present study focuses on "gradual" SEP events that last days, meaning that our SEP events are likely associated with CMEs.They are different from the flare-associated impulsive SEP "dropouts" (Mazur et al. 2000;Chollet & Giacalone 2008).With these criteria, we have identified 15 events from 1995 to 2008 and the result is summarized in Table 1.
Here we first select two dropout events to explain how we determine the events in detail.The event occurred on 2000 July 31 (see Figures 5(a)-(d)).The HCS crossings are identified using the pitch-angle distribution of superthermal electron flux and magnetic field azimuthal angle (j B ) observed by the three-    Figures 5(e)-(h) show a well-connected SEP event associated with a CME.The CME event erupted on October 16 at 7:27 UT and was preceded (6:40 UT) by an M-class (M2.5) solar flare at N03W90.The response of the SEP was "prompt" (within the 1 hr data resolution) and showed a sharp flux increase followed by a slow decrease lasting more than 6 days.This event resembles the Type-D event of Cane et al. (1988).The SEP dropout occurred on October 22 and, as shown in Figures 5(e)-(g), was accompanied by the HCS crossing at ∼9:42 UT.
The 15 events listed in Table 1 are identified as "gradual" (see Figure A1 in Appendix), even though a shock was not observed in most of the events.This is probably because the shock was too far in longitude away from Wind but was magnetically connected to Wind (see Table 1).Judging from the smoothness and duration (days) of the SEP events, it is reasonable to assume that they were associated with CMEs.The source (CMEs/flares) onset times and locations, when available, are provided in Table 1.The CME and flare information is based on the SOHO/LASCO CME catalog (Yashiro et al. 2004;Gopalswamy et al. 2009).Information about the CME-associated flares is based on the work of Gopalswamy et al. 2019.A total of four dropout events have an identified CME/flare source.Table 1 is also furnished with the longitude of the HCS relative to the CME/flare source (third column) for the events.It is estimated by the sum of the time difference between the HCS crossing and CME onset, with an assumption of a uniform rotation speed of 13°.25 day -1 , and the source longitude (west is positive and east is negative).As we can see, all of the events have the HCS far east (>50°) of the source.The fourth column in Table 1 shows the percentage drop for the first energy channel (2.0-2.4MeV).The potential drop is defined as 1-I 1 /I 0 , where I 0 and I 1 are 3 hr averages of the flux before and after the drop occurred, respectively.It indicates that all events are associated with more than 50% of drops.
As indicated in Table 1, most of the HCS are far east of the source location.If the HCS has little effect on the propagation of SEPs, the presence of HCS relative to the CME/flare source location should play little role in the reduction of the SEP flux.Here we use the source surface map to provide more insight.Figure 6(a) shows the source surface map for CR #1965 (event b).The map is derived from the photospheric magnetic field observed at the Mount Wilson Observatory (MWO) using the potential field source surface (PFSS) model (Altschuler & Newkirk 1969;Schatten et al. 1969) with the source surface height at 2.5 Rs.Notice that the Carrington map has the longitude starting from the left and the time from the right.The neutral line (B r = 0) is derived and plotted as solid lines in Figure 6.The CME onset time for this event was at 10:54 UT on 2000 July 27, corresponding to 136°. 1 in the Carrington map shown in Figure 5(a).Note that this is the Earth's location at 1 au.Since the source is 64°west of the Earth, the source longitude in the source surface map is ∼200°.1 (marked as an open star).
SEPs are charged particles and are guided by IMF.To estimate the Earth's conjugate point on the source surface, we will use a simplified Parker's spiral field model.The difference in longitude, Δj, between the Earth at 1 au and at the source surface can be approximated by Δj = Ω × r 0 (r sc /r 0 -1)/v sw , w h e r e Ω ( =2.972 × 10 -6 rad s −1 ) is the Sun's angular velocity, r sc is the radial distance of spacecraft from the Sun, r 0 ( =2.5 R s ) is the source surface from the center of the Sun, and v sw is the speed of solar wind measured at the spacecraft.Here we use the average solar wind bulk speed 1 hr prior to the CME onset (v sw = 348 km s −1 ).This results in ∼68°.6 in the longitudinal difference from the Earth's longitude (136°.1).The Earth's location after mapping at the source surface is marked as an open circle in Figure 6(a).We use the same method to map the Earth to the source surface at the HCS crossing (using v sw = 402 km s −1 and Δj = 59°.3), and the result is marked as a closed circle in Figure 6(a).This mapping suggests that the Earth was in the toward sector (B r < 0), the same sector as the CME, at the CME onset but in the away sector (B r >0) after the HCS crossing.Comparing with the in situ magnetic field measurements shown in Figure 2, our analysis suggests this is a perfect match between the neutral line crossing and the observed HCS crossing at 1 au.Note that the Parker spiral model assumes no change in the latitude and thus applies to the near equator region.We believe such an effect can be ignored for the present case.Right after the HCS crossing and the Wind spacecraft moved to an opposite sector, SEP dropouts occurred.
Figure 6(b) shows the source surface map for the October 22 event (event c).The source surface map suggests that the CME source and Wind were in opposite hemispheres, separated by ∼50°in longitude; however, the SEP data shown in Figure 3 shows little delay in onset time.This suggests that the CMEdriven shock was longitudinally wide enough and quickly expanded into the toward sector from the away sector after the eruption.This is highly likely because the typical longitudinal width of CME is ∼50° (Yashiro et al. 2004).Cross-field transport of the SEPs generated at the shock in the toward sector can populate a large area of the toward sector at low latitudes.After the current sheet crossing, the Earth was in the away sector, and SEP dropouts occurred, suggesting that SEPs were blocked by the HCS.

Discussion
We have studied the effect of the HCS on SEP (helium) fluxes using superposed epoch analysis on 319 HCS crossings observed by the Wind spacecraft.Unlike some previous studies, which have been focused on the onset time and maximum intensity of SEP events (e.g., Kallenrode 1993; here we focus on SEP flux changes at the HCS.Our statistical analysis indicates that a sudden drop in the low-energy (2.00-2.40MeV) SEP flux occurs at the HCS, and the sudden drop is statistically significant at a 5% significance level.It is found that the decrease (>10%) in the low-energy SEP flux occurred in the majority of the events and is not due to a few events with very large decreases.Note that we have made no attempt to identify the SEP type because the HCS does not distinguish the particle source.Kallenrode (1993) also suggested no difference between impulse and gradual events in her statistical study.
To provide insight, we selected 15 SEP events with large flux dropouts (>50% decrease) at the HCS and studied their properties in detail.Although Wind did not observe a shock in these SEP events, the time intensity of these SEP events was gradual and long lasting (more than a day).Thus we would assume that these SEP events were associated with a CME source in the western hemisphere, where a good magnetic connection usually occurs due to the large-scale Parker spiral field configuration (e.g., Cane et al. 1988).Indeed, an immediate increase in the SEP flux was observed in many of these events (see Figure A1 in Appendix).Note that we have focused on SEP dropout events associated with a simultaneous HCS crossing only.Sometimes the HCS is accompanied by a prompt SEP intensity increase or no change at all.These events are associated with a CME initiated near the neutral sheet.A CME-driven shock can easily penetrate the HCS and form a continuous shock across the HCS (e.g., Wu et al. 2016).A near-Earth observer can observe the SEPs without significant delay irrespective of the hemispheric location of the observer and source of CME relative to the HCS.
An important finding of this study is that the elevated He SEP flux persists until the crossing of the HCS.There are two implications from this finding: (1) Effective cross-field transport of the He SEPs took place in these events, and (2) the HCS can, at least partially, "block" He SEPs in the energy range of ∼2-7 MeV.Motion of energetic particles in the heliosphere is often described by the transport theory, in which particles are not only guided by the heliospheric magnetic field, but also experience convection, diffusion, drift, and adiabatic cooling.There are several reports about SEPs being observed by longitudinally separated multiple spacecraft (e.g., Reames et al. 1996Reames et al. , 1997;;Dresing et al. 2012), meaning that the SEPs can extend much further in longitude than shocks.The efficiency of particle transverse transport has been a subject of debate and is not easily explained by the focused transport equation originally developed by Roelof (1969).The crossfield diffusion coefficients obtained from the magnetic turbulence spectrum in the quasi-linear theory (Jokipii 1966) were later found to be too small to explain the observed large perpendicular diffusion.A number of models, e.g., cross-field diffusion caused by MDs (Tsurutani et al. 1999;Tsurutani & Lakhina 2004), nonlinear guiding center (Matthaeus et al. 2003), stochastic differential equation method (Zhang et al. 2009), and drift-induced transport (Marsh et al. 2013) among others, have been proposed to address the observed large perpendicular diffusion.More recently, Battarbee et al. (2017Battarbee et al. ( , 2018) ) used test particle simulations of 1-800 MeV proton in a flat or a wavy HCS and suggested that current sheet drifts can transport SEPs to a greater longitudinal area.However, it is not known if the current sheet drifts are effective for lower-energy SEPs.
The role of the HCS plays in the propagation of SEPs is still poorly known.Evidently, the SEP flux dropout events that we have identified to occur simultaneously with an HCS crossing strongly suggest that the HCS can form a barrier to the propagation of SEPs in the heliosphere, at least for those 2-7.4MeV He SEPs.The appearance of the SEP flux cutoffs and the HCS crossings simultaneously is not likely to happen by accident because the chance for these events to be coincident would be very small.
The present finding strongly suggests that the observed SEPs must have gone through large-angle scattering, with a large fraction of SEPs reflecting off of the current sheet they encounter.Figure 7 shows the percentage of flux drop with respect to particle energies.Although there is a large variation in the energy flux from event to event, a decreasing trend with the increase of energy can be seen.Assuming the flux decreases linearly with energy, we fit the average values with a straight line using the least squares regression: Y = (82.8±4.7)-(2.98±1.15) X, with the Pearson correlation coefficient r = −0.95.Assuming Helium SEPs are fully ionized, the gyroradius of ∼2-8 MeV Helium in a B = 5 nT magnetic field is in the range of ∼3 × 10 4 -6 × 10 4 km.This is comparable to the average thickness (w = 2.7±2.9 × 10 4 km) of these current sheets, with the adiabaticity parameter κ ∼ 0.7-1.At this range of κ, particles would fall into the chaotic motion category (Büchner & Zelenyi 1989;Kaufmann et al. 1993).
While the structure of HCS is different from the neutral sheet in the magnetotail, the dynamical behavior of particles in the magnetotail current sheet may, to some extent, still be applicable to the HCS.The HCS is not always a tangential discontinuity (TD), where the normal field is zero or very small compared to the total magnetic field just outside of the HCS (e.g., Lepping & Behannon 1986).Observations of the HCS at 1 au indicate that there is a considerable (∼1/3) number of HCS measured exhibits nonzero normal field, the feature of a rotational discontinuity (RD; Lepping et al. 1996).Kaufmann et al. (1993) traced particles after they are injected into a onedimensional current sheet.They found that as κ approaches 1 a large number of particles can be totally reflected by the current sheet for some values of κ (κ < 2), which corresponds to the number of oscillations a particle makes.Note that in the one-  1.The filled circles are the average value and the error bars represent the standard deviation of the sample mean.While the percentage of flux drop varies from event to event, the general trend is that the drop decreases with increasing particle energy.
dimensional current sheet configuration the κ parameter is proportional to the ratio of the normal to the ambient magnetic field (Büchner & Zelenyi 1989).Therefore, the exact value of κ for the HCS is probably different.It is reasonable to argue that SEP particles with certain energies cannot go through the HCS due to chaotic motion.
It is worth mentioning two recent studies of SEPs that may be relevant to the present work.Battarbee et al. (2017) used full test particle simulations to study SEP (1-800 MeV) transport near a flat HCS in the heliosphere with the Parker spiral field.Later they performed test particle simulations using a wavy HCS inferred from the source surface neutral line (Battarbee et al. 2018).While the two studies focus on cross-field transport of high-energy (mainly cosmic rays) SEPs, their results suggest that particles whose trajectories intersect the neutral sheet will experience current sheet drift.Because the drift is energy dependent, the effect is stronger for higher energy particles.In other words, highenergy protons (>100 MeV) may undergo the Speiser orbit due to a large value of the κ parameter.For low-energy SEPs, such as those in the present study, the current sheet drift is probably not as important as their studies suggested.
While our statistical analysis indicates that the majority of HCS crossings are associated with a decrease in the SEP flux, there is a large minority of events that are associated with an increase or a little change in the SEP flux.This high variability of SEP fluxes across the HCS is in general consistent with the conclusions made from previous studies (Roelof & Krimigis 1973;Kallenrode 1993).In particular, Kallenrode (1993) analyzed two spacecraft (Helio-1 and Helio-2) data and found that SEP particles can be observed on both sides of the HCS.Although her work concluded that sector boundaries have a clear influence on the intensities and timescales of SEP events, the influence on the intensities seems to be less clear.
Although we did not address events with little or positive flux changes, we wish to propose a possible explanation for such events.When a moving CME encounters the HCS, large deflections of the HCS can occur due to the large inertia of the CME.On the other hand, the appearance of HCS has little effect on the CME propagation, and this has been demonstrated in global magnetohydrodynamic (MHD) simulations (e.g., Odstrcil et al. 1996;Wu et al. 2016).In particular, Wu et al. (2016) studied the evolution of the 2013 March 15 CME event using time-dependent, global three-dimensional MHD simulation.A pressure pulse was used to simulate the nonfluxrope CME and to drive a fast-mode shock in front of the CME.They demonstrated that when the shock encountered the HCS, the shock strength (Mach number) weakens at the current sheet due to a larger fast-mode wave speed there.Immediately after the HCS crossing, the shock strength increases again.Clearly the shock strength in the opposite hemisphere depends on the local solar wind parameters upstream of the shock.Since SEPs are accelerated at the shock, SEP fluxes in the opposite hemisphere will depend on the shock strength in that hemisphere.This means that an increase in the shock strength is expected to enhance SEP intensity.On the other hand, a decrease in the shock strength is expected to reduce SEP intensity.This scenario can occur when the source of CME is not too far in longitude from the current sheet crossing (e.g., the two SEP events shown in Figure 1(b)).The angular width of CME varies significantly in the range of ∼40°-120° (Wood et al. 2017).Therefore, a large percentage of CME events that occur within ∼80°on average from the longitude of the HCS crossing will have a good chance of colliding with the HCS during their outbound passage.The Parker spiral nature of the IMF and HCS further complicates the situation.Owing to a lack of observations, the scenario proposed above cannot be easily proved nor disproved.Perhaps, global MHD simulation with a realistic setup of the CME may help provide a better understanding of the CME/shock propagation and interaction with the HCS.In our future work, we intend to perform realistic CME simulations similar to that of Wu et al. (2016) to provide insight into shock-HCS interaction.

Conclusions
We have performed superposed epoch analysis of the He (2.00-2.40 and 7.40-9.64MeV) and SEP data acquired by EPACT on board the Wind spacecraft, with the zero epoch being the time of HCS crossings by the Wind spacecraft.Based on 319 coincident SEP events, it was found that the SEP fluxes show a sudden drop at the HCS in the majority of the events for the lowenergy (high-energy) channel.A detailed study of 15 events of large SEP dropouts found that these events cannot be random, as such a flux dropout depends on the energy of SEPs.This is also supported by a superposed epoch analysis.Therefore, we conclude that this study presented clear evidence of the blocking effect of the HCS on the propagation of helium SEPs in the MeV energy range.Although more work needs to be done to provide more theoretical understanding, any successful SEP model needs to be able to predict the present finding.

Figure 2 .
Figure 2. Superposed differential flux derived from 319 HCS events for (a) 2.00-2.40MeV and (b) 7.40-9.64MeV helium observations from Wind.The average (red) and median values of the hourly flux are drawn centered around the HCS crossings.The error bars are one standard deviation of the mean.

Figure 3 .
Figure 3. Distribution (sample size N = 10,000) of the sample mean (normalized flux change at the HCS) from a randomly selected sample for (a) 2.00-2.40MeV He and (b) 7.40-9.64MeV He.The green curve in each panel indicates the Gaussian fit.

Figure 4 .
Figure 4. Distribution of the flux changes at the HCS for (a) 2.00-2.40MeV He and (b) 7.40-9.64MeV He.
dimensional plasma and energetic particle investigation (3DP;Lin et al. 1993) and the magnetic field investigation (MFI;Lepping et al. 1993), respectively, on board the Wind spacecraft.Figure5(a) shows the pitch-angle distribution of differential energy flux at ∼255 eV (channel 5) for superthermal strahl electrons.The HCS crossing can be clearly identified at 19:47 UT on July 31 when the pitch-angle of superthermal electrons changes from antiparallel to parallel to the IMF.Figure5(b) shows the IMF azimuthal angle, supplemented with the total (black dots) and x-and ycomponents (blue and red dots) of IMF in Figure5(c).The exact HCS crossing time can be identified by the magnetic field measurement (red vertical line).The IMF data can help determine the HCS crossing more precisely.Figure5(d)shows the differential flux of helium for the seven energy channels.The time-intensity profile of He SEP flux indicates this is a weak SEP event with an onset delay of ∼12 hr.The SEP dropout can be clearly identified as coinciding with the HCS crossing.

Figure 5 .
Figure 5. (Panels (a)-(d)) A sharp dropout event observed at Wind on 2000 July 31.Panels from top to bottom show (a) pitch-angle distribution of superthermal electrons from the Wind 3DP electron electrostatic analyzer, (b) the magnetic field azimuthal angle from the Magnetic Field Investigation, (d) the x-(blue dots) and y-component (red dots) of magnetic field and the magnetic intensity (black dots), and (d) helium differential flux (2.0-9.6 MeV nucleon -1 ; color coded) from the EPACT (Energetic Particle Acceleration, Composition, and Transport) measurements from 2000 July 25 to August 2.The flux dropout occurred at 19:47 UT on July 31, coinciding with the heliospheric current sheet (HCS) crossing at Wind (red vertical lines).Blue vertical lines indicate shock crossing at Wind.The standard RGB colors are used in panel (a) to indicate the intensity of superthermal flux with red being the high and blue being the low intensity.The energy range for each channel of EPACT is provided in (d) and color coded as inserts.(Panels (e)-(h)) The same format as Figure 4A but for the SEP dropout event on 2000 October 22.

Figure 6 .
Figure 6.Source surface maps for (a) CR1965 and (b) CR1968 derived from the magnetograms acquired at the Mount Wilson Observatory (MWO) showing the radial component of the magnetic field (color coded) at 2.5 R s .The neutral line (B r = 0; black trace) is plotted.In each panel, the star sign denotes the CME eruption site, whereas the open (close) circle denotes the projection of the Earth's location at the CME/flare onset (HCS crossing) time using the Parker spiral field.

Figure 7 .
Figure 7. Percentage drop of SEP averaged over the 15 events listed in Table1.The filled circles are the average value and the error bars represent the standard deviation of the sample mean.While the percentage of flux drop varies from event to event, the general trend is that the drop decreases with increasing particle energy.

Table 1
Sharp-intensity Drop Helium Solar Energetic Flux Events with Associated CME/Flare Onset Times and Source Locations and HCS Crossing Times HCS longitude relative to CME/flare source (assuming rotation speed of 13°. 25 day -1 ) at onset.