Superposed Epoch Analysis of Galactic Cosmic Rays and Solar Wind based on ACE Observations During Two Recent Solar Minima

Based on galactic cosmic ray (GCR) and plasma observations from the ACE spacecraft, in this work, we analyze the relation between the GCR counts and the solar wind parameters during two recent two solar minima (for the years 2007.0–2009.0, and 2016.5–2018.5) by means of the superposed epoch analysis (SEA) method. The results indicate that GCRs are strongly modulated by the co-rotating interaction regions (CIRs) in the solar wind, and that the occurrences of stream interfaces (SIs) between fast and slow solar wind are correlated with a depression in GCR counts. The so-called “snow plow” effect of GCR variation prior to SI crossing appears during the first solar minimum, and the GCR counts decrease after the crossing, corresponding to a sudden drop in the diffusion coefficient at the SIs. The gradient of GCR counts shows that the transport efficiency of GCRs is low (high), relative to slow (fast) solar wind. However, during the second solar minimum, we see a completely opposite scenario; the “snow plow” effect is not observed, and GCR transport becomes faster in slow solar wind, and slower in fast solar wind. In addition, heliospheric current-sheet crossings also correlate with GCR counts. Particles drift along the current sheet, then accumulate in a pileup structure, where diffusion and drift effects may be balanced. It is found that the drift effect rivals the diffusion and convection on the GCR transport at 1 au during the two solar minima.


Introduction
Galactic cosmic rays (GCRs) comprise high-energy charged particles (mainly protons) originating from outside the heliosphere. They are generally thought to be accelerated by shocks associated with supernova explosions (Ackermann et al. 2013). Voyager 1 has been measuring the near-constant GCR flux since the heliopause crossing in 2012 August (Cummings et al. 2016), and its observations confirm the theoretical expectation that heliopause is the modulation boundary for GCRs (Jokipii 2001;Guo & Florinski 2014;Kota & Jokipii 2014). Upon entering the heliosphere, less energetic GCRs are "modulated" by the heliospheric magnetic field. GCRs with a rigidity less than approximately 10 GV are deflected in the inner heliosphere, because their gyroradii are smaller than the size of typical solar wind structures (Schlickeiser 2002). GCRs are scattered by the magnetic irregularities (turbulences) present in the outwardly expanding solar wind, and are, as a result, "swept" away from the Sun. As a result of all these effects, the GCR flux decreases inward, starting from the heliopause (Parker 1965;Jokipii & Kopriva 1979;Potgieter 1998;Florinski & Pogorelov 2009). Gradient and curvature drifts are the significant mechanisms assisting the global transport of GCRs along the heliospheric current sheet (HCS) at low latitude, and their escape at high latitude for the period qA < 0, in the heliosphere (Jokipii & Kopriva 1979;Kota & Jokipii 1983;Webber et al. 1990;Potgieter 1993;Cane et al. 1999), where q is the particle charge, and A is the polarity of the radial component of the heliospheric magnetic field (HMF) in the Northern hemisphere. This drift pattern is inverted where qA > 0. The polarity of the HMF changes every 22 yr, and the solar activity has a period of 11 yr. These cycles affect the drift and diffusive transport of GCRs in the heliosphere, respectively, and cause long-term variations in their intensities (Jokipii & Thomas 1981;Kota & Jokipii 1991). In the inner heliosphere, the 27 day solar rotation causes shortterm variations in solar wind properties and GCR counts (Simpson 1954;Richardson 2004;Alania et al. 2011). According to some observations, long-term GCR variations might be produced by an accumulation of a large number of short-term transient events in the outer heliosphere (Burlaga et al. 1984;Potgieter & Le Roux 1994). Moreover, GCRs gain or lose energy when they travel through compression and rarefaction regions, respectively. Some examples of this phenomenon include acceleration due to termination shock, or interplanetary traveling shocks (Sarris & Van Allen 1974;Langner & Potgieter 2004).
CIRs are formed by the process whereby slow solar wind streams are overtaken by faster streams from higher latitudes (Sarabhai 1963). They represent the most common structures in nearby interplanetary space (∼1-5 au from the Sun) (Gosling et al. 1972;Siscoe 1972). CIRs are known to cause short-term variation in GCR fluxes, via changes in the solar wind speed (affecting GCR convection and energy changes), magnetic irregularities (diffusive effects), and the magnetic field magnitude (variations of drifts and diffusion). However, which phenomenon dominates flux variability is still a matter of debate (Richardson 2004). Diffusion perpendicular to the magnetic field is one of the factors responsible for GCR variations in the inner heliosphere (Kota & Jokipii 1995).
Observations have shown that the solar wind speed in CIRs correlates well with particle intensities, highlighting the importance of convection effects (Leske et al. 2013). Specifically, the stream interfaces (SIs) between fast and slow solar wind streams and the leading edge (fast wave or shock) in CIRs always correspond to depressions in GCR intensities. Our previous simulations have demonstrated that GCR diffusion near SIs is far more important than the drift effects associated with the HCS during a time of solar minimum (Guo & Florinski 2016). A recent superposed epoch analysis (SEA) revealed that the perpendicular diffusion coefficient is highly correlated with cosmic ray intensities, indicating that diffusion effects play a crucial role in recurrent GCR modulation (Ghanbari et al. 2019). However, others have argued that GCR variations might be associated with HCS crossings (Badruddin & Vadav 1985;El-Borie 2001). Interestingly, the latter is also supported by SEA (Thomas et al. 2014). Groundbased observations of GCRs from the global muon detector network also point to the importance of drift effects in relation to variations in particle intensity (Okazaki et al. 2008). This disagreement regarding the physical mechanism causing GCR variation in the inner heliosphere must be addressed with further observational data analysis. In this paper, we contribute to this topic, and the question of a relationship between solar wind properties and GCR counts in general, based on ACE observations.

Data and Method
ACE (Advanced Composition Explorer) is a spacecraft that has been in orbit at Lagrangian point L1 for more than 30 yr, since its launch in 1997 (Stone et al. 1998). In this paper, we utilize Level 2 data with 1 hr resolution from three ACE instruments: the solar wind density, bulk speed, and temperature from SWEPAM, magnetic field data from MAG and cosmic ray information from the Cosmic Ray Isotope Spectrometer (CRIS). Two time intervals were selected for our data analysis, the first being from the years 2007.0 to 2009.0, and the second from 2016.5 to 2018.5, roughly corresponding to the solar minima at the beginning and end of the 24th solar cycle, respectively. During the solar minimum, most of the fast solar wind streams originate from the solar surface at high latitudes, while slow streams appear at low latitudes (McComas et al. 2008). In some cases, fast solar wind can also be traced back to coronal holes at low latitudes (Abramenko et al. 2010). Eruptive solar wind events, such as interplanetary coronal mass ejections (ICMEs) are less frequently observed during these periods; as such, most solar wind events are expected to be CIR-related.
Stream interfaces are identified by sudden increases in solar wind speed, and maxima of total (thermal plus magnetic) pressure (Jian et al. 2006). Proton density and temperature are simultaneously enhanced during SI crossings. Table 1 lists the crossing time of SIs during the two intervals, comprising 82 and 75 events, respectively. The HCS or magnetic sector boundaries (SBs) are identified by the abrupt change in magnetic longitude (Jian et al. 2015). There are 79 events in the first interval, and 79 events in the second interval ( Table 2). For individual sector crossings, it is difficult to estimate effects on GCR variation if the time of the HCS event is too close to that of an SI. To exclude such situations, we simply remove those HCS events occurring within one day of an adjacent SI. The filtered HCS events are shown in bold type in Table 2, which includes 35 and 42 events for the two intervals, respectively.
The CRIS instrument provides GCR fluxes or counts of He and heavier ions up to Z ; 30 in energy intervals, from ∼50 to ∼500 MeV/n (Stone et al. 1998). Although proton measurements are available (Ghanbari et al. 2019), here, we focus only on heavy ions for which data can be obtained from the public database (http://www.srl.caltech.edu/ACE/ASC/). Given that heavy ions have low abundance ( ∼ 1% of all cosmic ray particles), their counts are added together to represent the total GCR counts evaluated in this work. Figure 1 shows the temporal variations in solar wind and energetic particles from 2008.5 to 2008.6, including the magnetic field strength, magnetic longitude in RTN coordinates, total pressure, bulk solar wind speed, and GCR count rates. The red dashed lines mark the HCS crossings, and the green dashed lines are the crossings of SIs. In the fifth panel, GCR count rates, averaged over 24 hr and 30 days, are indicated by black and blue lines, respectively. The former represents short-term variations in the Table 1 Stream Interface Crossing Times During the Two Intervals Studied in this Paper counts, while the latter indicates the long-term trend. In this figure, three SI crossings are associated with depressions in GCR count rates, represented by a black line. The particles appear to accumulate near the HCS for the first two events, at 2008.5067 and 2008.5521. The different behaviors of GCR counts for SI and sector boundary crossings indicate the existence of the different physical mechanisms, which we will explore further in this work.
In order to investigate the roles of SI and HCS in GCR variation, the solar wind events shown in Tables 1 and 2 must be analyzed statistically. Here, we use the Superposed epoch analysis (SEA) method for SI and HCS crossing events during the two intervals. The zero epoch corresponds to the time of the SI or HCS crossing, with a total duration of eight days. All relevant events are added together, then divided by the number of events. This treatment removes some random noise, but the physical trend is expected to be retained. Long-term count rates serve as the mean trend that is then subtracted from the 12 hr count rate averages. The resulting variations in particle count rates with respect to either the SI or SB zero epoch are discussed in the next section.

Results
We first apply the SEA to the SI events listed in Table 1. The SEA procedure is as follows: (1) define the occurrence time of the SI (SB) crossing, as shown in the table, as a key time for each event, and extract the corresponding eight-day interval from the solar wind or GCR data, with the key time centered; (2) superpose all extracted data intervals by adding them together, with result then divided by the number of extracted intervals. This procedure will effectively remove noise, and extract physical variation from the data. Figure 2 shows the solar wind speed, the magnetic field strength, the GCR count rates, the bend-over length, the turbulence ratio, and the estimated radial and azimuthal components of the diffusion tensor, κ rr and κ ff . The black and blue curves correspond to the profiles for the two intervals, respectively. The vertical dashed red line marks the epoch time of the SI, across which the solar wind speed increases from ∼350 to ∼540 km s −1 . The solar wind is highly compressed in an SI, with a peak in magnetic field strength measuring, on average, twice the field strength of the neighboring solar wind.
A Monte Carlo approach is utilized to find the significance of any variation in the superposed epoch result. In this test, identical analyses to those above are repeated, using the SEA method, but for 100 randomly selected zero epoch times during the first interval, rather than the actual SI crossing times. In Figure 2, the calculated Monte Carlo mean is indicated by dotted-dashed orange lines. The two dotted orange curves  represent the boundaries containing 90% of the random epoch time means, with the upper and lower curves corresponding to 5% and 95% confidence levels for the generated variations. Given that the SEA trends fall well outside the random fluctuation range, we conclude that the observed SI crossings are highly significant. The bend-over length and the turbulence ratio are estimated based on the spectrum of the magnetic field (Ghanbari et al. 2019); no Monte Carlo treatment is applied either in these plots, or to the diffusion coefficients, for the sake of simplicity.
Based on the standard quasi-linear theory (QLT) for magnetostatic slab turbulence (Zank et al. 1998;Giacalone & Jokipii 1999), the parallel diffusion coefficient near-stream interfaces were deduced on the basis of the observations of magnetic field fluctuations, 〈δB 2 〉/B 2 , where 〈δB 2 〉 is the mean square of the magnetic fluctuations, and B is the average magnetic field strength. Here, we use the same approach, with the following expression: where l b is the bend-over length, marking the transition between the energy-containing range and the power-law inertial region of the turbulent power spectrum (e.g., Giacalone & Jokipii 1999), and approximately equal to the characteristic size of large-scale eddies in the solar wind (Zank et al. 1996); Ω and v are the particle gyrofrenquency and speed, respectively, and 2 is the amplitude of the slab turbulence. The intensity of the slab component is assumed to be 20% of the total 〈δB 2 〉, with the two-dimensional component, d á ñ B 2D 2 , making up the remainder (Bieber et al. 1996). For the two intervals, the two parameters, l b and 〈δB 2 〉/B 2 , can be found in panels D and E of Figure 2, respectively. The bend-over length increases noticeably after the SI crossing, being larger in the fast wind than in the slow wind for both intervals. These results are similar to those found in previous research (Ghanbari et al. 2019), and agree with the values elsewhere in the literature (e.g., Matthaeus et al. 2005). The turbulence ratio of 〈δB 2 〉/B 2 represents the level of magnetic field fluctuation, and is greatly enhanced, from ∼ 0.8 − 1.0 to ∼ 1.3 − 1.6, during SIs, due to the velocity shear between the two streams. It is expected that the parallel diffusion will be reduced in SIs with such a highturbulence background.
The diffusion perpendicular to the magnetic field is more complicated and less well understood, but is usually assumed to be positively correlated with turbulence strength. Here, we use the nonlinear guiding center (NLGC) model (Matthaeus et al. 2003;Zank et al. 2004;Shalchi & Kourakis 2007), with the perpendicular diffusion coefficient for GCRs expressed as follows (Zhao et al. 2018): is a constant, in which ν = 5/6 yields a Kolmogoreov spectrum, λ P = 3κ P /v is the parallel mean-free path (MFP), 2 2 is the amplitude of the two-dimensional turbulence, and λ 2D is the corresponding 2D correlation length, being approximately equal to the correlation length, λ c , of the turbulence model (Breech et al. 2008). Here, the correlation length is related to the bend-over length such that λ c = 0.7925l b , in accordance with the power-spectrum model of magnetic turbulence (Giacalone & Jokipii 1999).
Panel F of Figure 2 shows the diffusion coefficients of 200 MeV/n oxygen ions, computed using the method described. Given that the spiral angle of the interplanetary magnetic field is ∼ 45°at a heliocentric distance of 1 au, the radial and azimuthal components of the diffusion tensor are similar, i.e., κ rr ; κ ff , so only one is shown here.
The diffusion coefficients for Interval 1 are larger than for Interval 2, since the magnetic field was weaker during the former (Panel B). At the point of SI crossing, both diffusion coefficients decrease to a low value of ∼ 3.0-3.5 × 10 21 cm 2 s −1 , which is approximately half of its pre-crossing value. The corresponding cosmic ray count rates drop dramatically across the SI, from 1-1.5% to −1%, relative to the mean. Note that the GCR count rates are also different for the two intervals. For interval 1, the GCR count rate begins to increase two days prior to the crossing, and reaches its maximum one day prior to the interface. After that, it drops rapidly, reaching its minimum value some 12 hr after the crossing, and remaining at a low level of about −1% for the next several days. Temporal GCR enhancements before SI crossings indicate that the structures act as barriers to particle propagation. This is known as the "snow plow" effect, which has been well documented in previous works (e.g., Thomas et al. 2014).
The count rates behave differently for Interval 2. They mostly remain constant ( ∼ 1%) until one day before SI, dropping to a minimum past the interface, and then recovering steadily to zero level by the end of the 8 day interval. The "snow plow" effect appears to be diminished for interval 2. This different behavior in terms of GCR counts during SI crossings could be the result of different physical mechanisms being responsible for the variations during the two intervals. According to panel F, the "snow plow" effect during Interval 1 may be interpreted as a sudden drop in the radial (azimuthal) diffusion coefficient, κ rr and (κ ff ), near the SI, which reduces the efficiency of effective transport of particles along the radial direction. For Interval 2, the obtained diffusion coefficients predict the presence of "snow plow" prior to SIs, which differs from the observed depletion in GCR counts roughly from day 0 to 2 near SIs. This discrepancy may be solved by considering the effect of combined transport, based on diffusion and drift during the two intervals.
During Interval 1, the large and small GCR gradients appear in slow and fast solar winds, respectively, indicating that the effective GCR transport becomes much slower in regions of slow solar wind than in those of fast solar wind. The slowest transport occurs in the SI transition region, which is believed to be a tangential discontinuity, where the field lines are not allowed to cross (Crooker et al. 1999). In the case of possible non-axisymmetry turbulence near SIs, the particle transport across the SI will be retarded, due to the asymptotic (pitchangle-averaged) diffusion coefficient in the perpendicular direction along which transverse magnetic fluctuations are damped (Strauss et al. 2016). The GCR transport efficiency follows the pattern of "low-lowest-high" when transiting respectively from fast solar wind, to SI, to slow solar wind during the interval. In contrast to Interval 1, the pattern of GCR transport efficiency becomes "high-lowest-low" for Interval 2, where the GCR gradient decreases in slow wind, and increases in fast wind. This phenomenon cannot be explained if only the diffusion shown in Figure 2 is considered; the unknown drift effect needs to be taken into account in the effective GCR transport, as observed in previous works (e.g., Jokipii & Kopriva 1979). Future models of cosmic ray transport must account for these differences in transport coefficients during cycles of opposite polarity.
Next, we perform the same SEA, using sector boundaries as the zero epoch for every event listed in Table 2. Figure 3 shows the corresponding variations in solar wind speed, magnetic field strength, GCR count rates, bend-over length, turbulence ratio, and diffusion coefficients for the period±4 days around the zero epoch. In this figure, the vertical red dashed lines mark the zero epoch of HCS crossing. During solar minimum, the HCS is closely associated with the slow solar wind originating from low-latitude regions on the solar surface (Smith 2000). In practice, some SBs appear very close to SIs (see e.g., the HCS shown in Figure 1), and the solar wind speed exhibits an clear increase after the HCS crossing over several hours (Jian et al. 2019), indicating that the effect of the HCS on GCRs cannot be properly evaluated due to the influence of adjacent SIs. After HCS crossing, not only does the azimuthal component of the magnetic field reverse its direction, but the total field magnitude also shows an abrupt enhancement. In contrast to the SI crossing shown in Figure 2, the bend-over length does not change abruptly at the interface during the two intervals. However, the turbulence ratio reaches a peak of ∼3.0 for interval 1, and ∼2.0 for interval 2. These values are much larger than those shown in panel E of Figure 2, demonstrating that turbulence enhancement depends on the HCS, rather than the SIs. As a result, the diffusion coefficients are both depressed near the HCS for the two intervals, and the duration of the diffusion gaps are much narrower than those shown in Figure 2.
According to panel C, GCR count rates are also expected to decrease in response to the drop in the diffusion coefficients. The GCRs accumulate, owing to the "snow plow" effect, with a peak at ∼ − 1 day before the crossing. Compared with Figure 2, the cosmic ray peak in Figure 3 appears much closer to the crossing point, indicating the importance of drift effects in relation to GCR accumulation. The previous simulation indicated that one might expect a peak at the HCS for the A < 0 period, and a minimum for A > 0 (Kota & Jokipii 1983). However, this result is not observed. Subsequently, the particles drop to a significantly lower level during Interval 1, as compared with Interval 2, which one might expect to be consistent with the different behavior of the diffusion coefficients near the HCS. However, we do not see a significant difference between the two diffusion coefficient measurements, which may imply that some other mechanism, e.g., the drift effect, may play an important role as regards GCR counts. In these cases, we may conclude that the GCR variation is caused by the combined effect of diffusion near SIs, and drifts near the HCS.
In order to evaluate the effects of isolated HCS on GCR variation, we remove all events where an SI is present within one day of the sector boundary. We also remove pairs of current sheets that are too close to one another within ∼1.2 days. The remaining events are shown in bold in Table 2. Figure 4 shows the corresponding SEA results. Here, there is no jump in the solar wind speed, since these are associated with SIs. The HCS is embedded in the "valley" of the slow solar wind, as expected, based on the notion that the sheet originates from the low-latitude solar surface. The magnetic field strength for Interval 1 is lower than that for Interval 2, and both increase slowly over time. Compared with the previous plots in Figure 3, the variation of bend-over length becomes flatter in regions within one day of the zero epoch, the turbulence level remains high at the HCS crossing, and the diffusion coefficients do not change a great deal, except for a more fluctuating variation over time, owing to the fact that there are fewer cases. The particle count rates exhibit a peak centered at the HCS, and decline away from the zero epoch. This result is consistent with those of previously reported models (Kota & Jokipii 1983) and observations (Newkirk & Lockwood 1981), which show that cosmic rays accumulate near the HCS via the drift mechanism, and decrease on both sides as they diffuse away from the HCS. Unlike the work of Thomas et al. (2014), we make no distinction between the sector boundaries corresponding to Away-Toward and Toward-Away field polarity changes. It seems that the peak value of GCR counts for Interval 2 is approximately twice that for Interval 1, indicating that the GCRs are more strongly affected during the A > 0 cycle than during the A < 0 cycle, which is in agreement with previous observations made by ground-based neutron monitors (El-Borie et al. 1998).
We now summarize our inferences regarding the influences of stream interfaces and current sheets on GCR variations, based on the SEA data presented above. SI crossings are always associated with a significant drop in diffusion coefficients. During Interval 1, this results in a significant enhancement in particle concentration ahead of the interface ("snow plow"), followed by a rapid drop across the slow-fast wind transition. The effective transport coefficients, which reflect the diffusion and drift effects, are expected to follow the pattern of "slow-slowest-fast" when transiting from the fast solar wind, SI, and slow solar wind. However, the absence of "snow plow" and the depletion of GCR counts subsequent to SI crossing during Interval 2 may be caused by the escape of GCR particles in the fast solar wind. The pattern of effective transport will therefore be "fast-slowest-slow" during the interval. The GCR variation near the HCS indicates that GCRs also have a higher concentration near the HCS, highlighting the important role played by current-sheet drifts. where r is the heliocentric distance, Δr and Δf respectively denote the solar wind movement in terms of radial distance and azimuthal angle within ∼0.5 day, and Δκ rr and Δκ ff are the corresponding changes in the diffusion coefficient components.
For typical values of κ rr ; κ ff = 5.0 × 10 21 cm 2 s −1 , Δκ rr ; Δκ ff = 3.0 × 10 21 cm 2 s −1 , Δr = 2.16 × 10 12 cm, and Δf = π/25, the diffusion speed is ∼ (0.334 ± 1.39) × 10 4 km s −1 along the radial direction, and ∼ ( − 1.0 ± 0.206) × 10 4 km s −1 along the azimuthal direction, at 1 au. Here, the plus (+) and minus (−) signs correspond respectively to the increase and drop in the diffusion coefficients near SIs. In the uniform solar wind, if the spatial dependences of the various diffusion coefficients were neglected for simplicity, the effective diffusion speeds could be approximated as k k ~r r r r ( · ) and along the radial and azimuthal directions, respectively. For a typical value of κ rr ; κ ff = 5.0 × 10 21 cm 2 s −1 , the diffusion speed is ∼ 3.34 × 10 3 km s −1 along the radial direction, and ∼ − 1.0 × 10 4 km s −1 along the azimuthal direction. This shows that the estimated diffusion speed is much larger than the solar wind speed, being consistent with previous calculations, based on observations (Ghanbari et al. 2019), and computer simulations (Guo & Florinski 2016). Although it has been demonstrated that GCR counts are often found to correlate with solar wind speed at 1 au (Leske et al. 2013), and the modulation parameters of GCRs are proportional to the product of solar wind speed and magnetic field strength, theoretical analysis indicates that this phenomenon is directly caused by the similar dependence of the diffusion coefficients (e.g., Guo & Florinski 2014); the convection effect is therefore not significant, as compared with diffusion.
In a weakly turbulent solar wind, the drift velocity is approximated as where v is the particle speed, and q is its charge. In a Parker heliospheric field, the average drift velocity, 〈v d 〉, over a region with a distance of two particle gyroradii about the current sheet is approximated to be 0.167v at 1 au, where the magnetic field strength is taken as 5 nT (Burger & Potgieter 1989). The drift is parallel to the current sheet, and perpendicular to the magnetic field. For a 200 MeV/n oxygen ion, the drift is respectively inward and outward during Intervals 1 and 2, and v d ∼ 2.8 × 10 4 km s −1 , which is much larger than the above diffusion speed. This result indicates that the drift effect dominates over the diffusion effect during the two solar minima. Based on a simplified HCS model, in which the magnetic field strength does not change across the sheet, previous simulations would indicate that drift effects are less important than diffusion at 1 au (Guo & Florinski 2016), and it seems that the HCS does not organize GCR variation. In reality, the geometry of the HCS is much more complicated than is assumed in the model. For instance, not only the direction, but also the strength of the magnetic field changes across the sheet in some cases (e.g., Jian et al. 2019). Note that the drift effects will be reduced in a highly turbulent background; for example, the drift-reduction factor could be less than 0.5 in the case of a turbulence level where d > B B 1.0 2 ( ) (e.g., Engelbrecht et al. 2017). In our work, the turbulence level, dB B 2 ( ) , is larger than 1.0 near HCS, indicating that drift effects will be dramatically reduced against such a high-turbulence background. However, based on Figure 4, it is apparent that the GCRs accumulate near individual sector boundaries for the two intervals, indicating that the drift effect along HCS are important. This result seems to contradict the theoretical prediction of drift reduction, such that further analysis will be required to reconcile this discrepancy in the future.
Whereas the particle energies used here (100-500 MeV/n) are much smaller than those measured by neutron monitors on the ground (beyond several GeV/n), the SEA results are similar to those based on neutron monitor count rates (Thomas et al. 2014). As mentioned above, convection effects are much weaker than diffusive effects, and we may conclude that during the past two solar minima, drift plays more important role in GCR transport at 1 au, in comparison with diffusion and convection. Numerical simulations of GCR transport in the inner heliosphere (e.g., Qin & Shen 2017;Moloto et al. 2018;Moloto & Eugene Engelbrecht 2020), should prompt a more sophisticated investigation of the key role of drift with respect to the above three effects, with due consideration for the observed small-scale parameters of the solar wind (e.g., the magnetic variance, bend-over length).

Conclusion
In this work, we have studied the variation in solar wind properties and galactic cosmic ray count rates during two solar minimum periods: 2007.0-2009.0 (Interval 1), and 2016.5-2018.5 (Interval 2), based on ACE observations. The relationships between the GCR count rates and the two common solar wind structures, the fast-slow stream interfaces, and magnetic sector boundaries, were investigated via the SEA method. The data was grouped into three species: the crossing time of SIs, all HCS, and isolated HCS. During Interval 1, cosmic rays piled up in front of the SIs, creating the "snow plow" effect, before experiencing a rapid drop across the interface. This phenomenon is believed to be associated with the insufficient transport of GCRs at the SIs. Moreover, the large and small gradients of GCR count rates appeared, respectively, in slow and fast solar winds. This result indicated that effective transport efficiency (diffusion and drift) is low in slow solar wind, and high in fast solar wind. In the case of Interval 2, the GCRs remained nearly constant before the SI, then dropped rapidly after the SI crossing, and recovered to some extent over the next several days. The transport efficiency was opposite to that found for Interval 1 because the gradients of GCR count rates respectively became small and large in slow and fast solar winds. In addition, the GCRs were found to peak near the HCS for the two time intervals under consideration, showing that the current sheet was an important channel for GCR transport. Based on theoretical analysis, we may conclude that, during the two recent solar minima, drift effects rival the other two effects (diffusion and convection) in relation to GCR transport at 1 au.