MHD‐Test Particles Simulations of Moderate CME and CIR‐Driven Geomagnetic Storms at Solar Minimum

As part of the Whole Heliosphere and Planetary Interactions initiative, contrasting drivers of radiation belt electron response at solar minimum have been investigated with MHD‐test particle simulations for the May 13–14, 2019 Coronal Mass Ejection (CME)‐shock event and the August 30–September 3, 2019 high speed solar wind interval. Both solar wind drivers produced moderate geomagnetic storms characterized by a minimum Dst = −65 nT and −52 nT, respectively, with the August ‐ September event accompanied by prolonged substorm activity. The latter, with characteristic features of a Corotating Interaction Region (CIR)‐driven storm, produced the hardest relativistic electron spectrum observed by Van Allen Probes during the last two years of the mission, ending in October 2019. MHD simulations were performed using both the Lyon‐Fedder‐Mobarry global MHD code and recently developed GAMERA model coupled to the Rice Convection Model, run with measured L1 solar wind input for both events studied, and coupled with test particle simulations, including an initial trapped and injected population. Initial electron Phase Space Density (PSD) profiles used measurements from the Relativistic Electron Proton Telescope and MagEIS energetic particle instruments on Van Allen Probes for test particle weighting and updating of the injected population at apogee. Results were compared directly with measurements and found to reproduce magnetopause loss for the CME‐shock event and increased PSD for the CIR event. The two classes of events are contrasted for their impact on outer zone relativistic electrons near the end of Solar Cycle 24.

dynamics. CIRs develop from solar wind fast streams emanating from coronal holes which appear as dark regions in the corona due to open magnetic field topology, prominent at solar equatorial latitudes at solar minimum over many solar rotations (Golub & Pasachoff, 1997). CIRs recurrent with the solar rotation were seen throughout 2018 -2019 and dominated radiation belt electron variability during this time. Measurements from the Van Allen Probes twin satellites launched August 30, 2012 into a near equatorial-plane orbit inside 5.8 Earth radii (Mauk et al., 2013) were available throughout the declining phase of Solar Cycle 24, until mid-October 2019 when the Van Allen Probes mission ended.
High-energy electrons at geostationary orbit (L ∼ 6.6) show a clear relationship between high-speed solar wind and subsequent relativistic electron enhancements (Baker et al., 1979;Paulikas & Blake, 1979). This suggests that magnetospheric substorm activity driven by high solar wind speed and enhanced convection of the dayside to nightside reconnected magnetic flux may play an important role in providing plasmasheet seed electrons with energy up to a few hundred keV which are transported to the inner magnetosphere (Baker et al., 1986). Subsequent studies using data from the Solar, Anomalous, and Magnetospheric Particle Explorer and Polar spacecraft confirmed that high-speed solar wind streams are effective in producing outer radiation belt electron flux enhancements Kanekal et al., 1999). Using data from the Highly Elliptical Orbit spacecraft, it was demonstrated that strong relativistic electron acceleration occurs throughout the entire outer zone when the solar wind has a strong southward interplanetary magnetic field (IMF) component .
This earlier work demonstrated that many geomagnetic storms produce relativistic electron flux enhancements at GEO (geostationary orbit), while other storms do not Reeves et al., 2003;Summers et al., 2004). Reeves et al. (2011) found that the relativistic electron-solar wind speed relationship is not a simple linear one as posed by Paulikas and Blake (1979). Li et al. (2011) examined 15 years of solar wind data and compared with GEO observations of MeV electron flux finding that high solar wind speeds are not necessary for MeV enhancements when strong southward IMF Bz is present. The separation between high speed solar wind in CIRs and extended periods of southward IMF Bz associated with CME-shock driven storms can explain these disparate statistical conclusions about solar wind drivers of geomagnetic storms and their effective enhancement of outer zone electrons. Recent overviews of outer zone electron variability can be found in Li and Hudson (2019) and Ripoll et al. (2020).   in three energy ranges from January 1, 2018 until the end of the mission. A CME-shock induced enhancement in flux at 1.8 and 4.2 MeV on May 14, 2019 is indicated which was accompanied by a Dst = −65 nT geomagnetic storm. The time axis is expanded in Figure S1a in Supporting Information S1, showing that the enhancement was preceded by a dropout. Measured solar wind parameters at L1 for this event are shown in Figure 2a from NASA OMNIWeb. Recurrent CIRs which map to a coronal hole on the sun produced flux enhancements seen throughout summer 2019 in the lower energy channels of Figure 1. Recurring enhancement in radiation belt electron flux at the solar rotation period has long been measured at geosynchronous orbit (Reeves, 1998). The first enhancement in the 7.7 MeV channel since September 7-8, 2017 (not shown) was seen for the August-September CIR event (the time axis is expanded in Figure S1b in Supporting Information S1). The 7.7 MeV enhancement at the beginning of September occurs over several days, as will be seen in closer examination of this high-speed stream event, similar to the CME-shock driven enhancement of lower energy flux May 15-16 following a flux dropout May 14. It is typical of these two types of solar wind drivers of radiation belt flux changes that the CME-shock driven case produces a prompt change while the CIR case modifies radiation belt electrons over a period of days, accompanied by a longer interval of high solar wind velocity as seen in Figure 2b. Figure 2 is discussed further in each event study.
Previous work has shown that the dynamic outer zone electron radiation belt evolves differently during storms driven by the two drivers (e.g., Denton et al., 2006;Kataoka & Miyoshi, 2006;Yuan & Zong, 2012). A study by Shen et al. (2017) compared CME-shock and CIR-driven storm effects on outer zone electrons using Van Allen Probes measurements, and found that CIR-driven events cause stronger enhancements at higher L values while CME-shock driven storms have a greater effect at lower L values in a statistical sense. Their study of 28 CME-shock driven and 31 CIR events between March 2013 through July 2016 spanned the transition from dominance of CME-shock to CIR-driven storms in the Van Allen Probes data set, corresponding to the declining phase of Solar Cycle 24.
In the present study we focus on two cases at solar minimum. The CME-shock driven storm of May 13-14, 2019 was by no means the most dramatic example of the Solar Cycle 24 declining phase in terms of either the geomagnetic storm strength or radiation belt electron enhancement (Baker et al., 2019), but it serves to demonstrate distinct physical mechanisms which dominate this type of event as contrasted with the integral effect of the CIR interval in our second case studied, August 30 -September 3, 2019. In the next section we describe models used to simulate the time evolution of outer zone electrons from an initial radial profile taken directly from Van Allen Probes measurements. We then compare MHD-test particle simulations for the two events and show that the electron Phase Space Density (PSD) at fixed first invariant evolves over a longer time interval in the August-September case, while changes occur faster for the CME-shock driven case of May 13-14, 2019, consistent with observations. We examine the relative contribution of the initially trapped electrons versus those transported earthward from the plasmasheet in both event studies. We conclude with discussion of how both types of events played a role in maintaining outer zone electron fluxes during the Solar Cycle 24 minimum.

Models
We use global 3D MHD and test particle modeling tools developed to simulate magnetospheric response to measured upstream solar wind input. We begin with the Lyon-Fedder-Mobarry tilted dipole model (Lyon et al., 2004) coupled to the Rice Convection Model (Pembroke et al., 2012;Wiltberger et al., 2017) to incorporate drift physics in the inner magnetosphere, with a Gallagher et al. (2000) Kp = 3 plasmasphere density weighting of the zeroeth energy channel of RCM to model a fixed average plasmasphere over the course of the event simulation. LFM fields were used in test particle simulations for the May CME-shock event. A parallel set of MHD simulations were run for the two events studied using the newer GAMERA MHD model which draws heritage from LFM, but has greater computational efficiency for longer runs (Sorathia et al., 2020;Zhang et al., 2019). The GAMERA model is again coupled to the Rice Convection Model, with the zeroeth energy channel of RCM initialized with a Kp = 2 plasmasphere profile characteristic of early in the storm (Gallagher et al., 2000), which is then allowed to evolve in the MHD fields with a fixed refilling rate (Pham et al., 2021). MHD input parameters for both event simulations were taken from OMNIWeb data shown in Figure 2 and discussed further along with results below. The LFM model uses a computational domain extending from +30 Re to −300 Re along the sun-earth line (SMx) and from −150 Re to +150 Re along SM-y and SM-z (−110 Re to +110 Re for GAMERA along SM-y,z). All MHD input variables are assumed to be uniform in y and z at the upstream boundary. The LFM grid resolution  Vsw exceeds 600 km/s after 09 UT Aug 31. The magnetopause location remains well outside geosynchronous for both events, however it is compressed inward to L = 8 for the CMEshock event. OMNIWeb time shift of L1 data to the noon bow shock is described at: https://omniweb.gsfc.nasa.gov/html/ow_data.html#time_shift.
is 106 x 96 x 128 along radial, azimuthal and polar directions. The GAMERA grid resolution is 96 x 96 x 128 along the same directions. The inner boundary for LFM simulations is at 2 Re and for GAMERA is at 1.5 Re geocentric radius, with coupling to the ionosphere using an electrostatic potential solver incorporating changes in field-aligned currents and dynamic conductivities for both models (Merkin & Lyon, 2010). The 3D MHD fields are dumped at 1 min cadence.
For this project we use the 2D particle tracing code developed by Elkington et al. (2002) which follows the drift motion of guiding center electrons on a Cartesian grid in the GSM equatorial plane of the 3D MHD fields. For stronger CME-shock events, 3D particle tracing with a switch to Lorentz trajectories in the presence of strong magnetic field gradients has been used Kress et al., 2007), however 2D guiding center simulations are deemed adequate for the present comparative study of two moderate solar minimum storms. Test particle electrons are initiated on the equatorial plane between 3 and 5.8 Re for the trapped population with a flat azimuthal distribution across all MLT for a total of 2 million test particles, used in both event simulations. ULF wave electric and magnetic field fluctuations are self-consistently resolved by MHD simulations and act directly on the test particle motion producing the observed radial transport. The field fluctuation are produced either by fluctuations in input solar wind MHD parameters or Kelvin Helmholtz instability along the magnetopause due to shear flow . As a post-processing step the test particles are weighted using the measured electron PSD calculated at fixed first and second invariants from flux measured by the ECT instrument suite on Van Allen Probes (Spence et al., 2013), which includes high energies (>2 MeV) measured by REPT and energies below 2 MeV measured by the MagEIS instrument . The weighting algorithm uses the orbit prior to the beginning of each test particle simulation to serve as an initial radial profile. The injected population is launched continuously throughout the simulation from an annulus sector which spans a 30 degree width centered on midnight with a radial location of 5.8 -6 Re. The PSD in the annulus is updated in the simulations at the value corresponding to the measured PSD at apogee from Van Allen Probes, which takes into account increased PSD due to plasmasheet injections and any local heating that increases PSD beyond the apogee of the Van Allen Probes (Boyd et al., 2018). The first invariant is chosen to be 2,000 MeV/G and 5,000 MeV/G to cover the energy ranges shown in Figure 1 (nominal 1.8, 4.2 and 7.8 MeV differential energy channels, Baker et al., 2013) in the inner magnetosphere. Test particles representing a plasmasheet source are injected at 140,000/hr, randomly distributed in the anulus centered on midnight shown in Figure 3. Both populations are weighted in a post-processing step with the same methods from Nunn (1993) so as to conserve PSD according to Liouville's theorem. Figure 2a shows OMNIWeb solar wind parameters used as input to MHD test particle simulations of the May 13-14 CME shock event along with the magnetopause location from the Shue et al. (1998) model and SymH, which indicates changes in magnetospheric current systems, primarily the ring current. The disturbance arrival at L1 is at 2326 UT in the Cane and Richardson list of ICMEs (http://www.srl.caltech.edu/ACE/ASC/DATA/ level3/icmetable2.htm) while the OMNIWeb data shown in Figure 2a, including all MHD plasma and magnetic field parameters, are propagated to the bow shock nose assuming purely radial propagation in GSE coordinates at the measured solar wind velocity. Solar wind velocity, density and pressure increase around 00 UT on May 14 in Figure 2a with southward turning of IMF Bz seen around 04 UT driving buildup of the ring current and a SymH minimum. Figure 3a shows the initial configuration of the GAMERA simulations (LFM is comparable, and Bz from the two models is compared in Figure S6 in Supporting Information S1 at 0530 UT May 14), including dipole tilt evident in the meridional plot of MHD pressure on the right, with northern and southern hemispheric field aligned currents in the polar regions shown as inserts. On the left, residual Bz (dipole subtracted) is plotted along with an insert showing RCM pressure in the inner magnetosphere. The LFM simulation was run from 2100 UT on May 13 to 1000 UT on May 14. Test particle simulations were begun at 2300 UT on May 13 for a total run time of 11 hr to capture the rapid CME-shock impact effects on the magnetosphere. A longer multiday simulation was run for the August-September CIR event. Figure 3b shows the initial location of test particles traced in the MHD fields, with the initial trapped population in black and injected electrons in red. Figure 4 shows the PSD profile for 2,000 MeV/G electrons measured by the ECT instrument on the Van Allen Probes used for initial test particle weighting in the simulation studies, beginning with blue curves shown at 00 UT on May 13 and 00 UT on August 29, respectively, with subsequent orbits indicated by the color bar on the right over the next 2 days. The black curve indicates the PSD profile used for weighting the trapped test particle  (Pham et al., 2021). Meridional plot of MHD pressure is shown on the right, with northern and southern hemispheric field aligned currents in the polar regions shown as inserts. On the left, residual Bz (dipole subtracted) is plotted along with an insert showing RCM pressure in the inner magnetosphere. Upstream solar wind input is taken from OMNIWeb ( Figure 2) propagated to the 30 Re upstream boundary. (b) Initial test particle populations in the GSM equatorial plane, noon to the right. Injected (red) and trapped (black) are the same for both May and August-September 2019 event studies prior to weighting with Phase Space Density measured from Van Allen Probes. population chosen to reflect the initial radial profile for each event, for example prior to the interplanetary shock for the May event. Note (a) that initial PSD is a factor 100 times higher for the May case and (b) flat at higher L, while increasing at higher L for the August-September case. An assumption must be made about assigning PSD to test particles, which is then conserved according to Liouville's Theorem. McCollough et al. (2009) implement the areal weighting scheme of Nunn (1993), used here in the 2D test particle simulations. Here PSD is plotted versus L* (Roederer, 1970) using the TS04 magnetic field model (Tsyganenko & Sitnov, 2005), which is inversely proportional to flux inside an electron drift orbit adiabatically conserved in the absence of field variations on the electron drift time. Figure 5 shows simulated PSD using LFM-RCM fields to advance test particles, updating the outer boundary test particle weighting of injected electrons with measured PSD at apogee (5.8 Re) every 9 hr for each spacecraft. The initial measured radial profile from Van Allen Probes plotted as the black curve in Figure 5a is used to initialize the radial weighting profile of the trapped population, while the plasmasheet population is injected between r = 5.8 and 6 Re in a 30 degree anulus with PSD weighting that matches the measured PSD at apogee, see  Figure 5, most prominent after 0400 UT. Outward radial transport to L* = 6 (outer boundary of plot only) is apparent over the whole 11 hr shown. PSD at constant first and second invariants is calculated from weighted test particle counts as a function of L mapped into L* using the LANLstar artificial neural network trained using the TS04D magnetic field model (https://spacepy. github.io/lanlstar.html). The 10 min time-varying solar wind parameters and TS04D coefficients were obtained from Tsyganenko's database archive (https://geo.phys.spbu.ru/∼tsyganenko/TS05_data_and_stuff/) to perform the test particle weighting. The use of a magnetic field model to convert flux to PSD in L* produces a quantity which is averaged over longitudinal drift and removes dependence on spacecraft longitude. Dst reaches a minimum around 08 UT and adiabatic relaxation of the magnetic field during recovery phase (Kim & Chan, 1997) contributes to inward radial transport. However, mapping PSD in L* (within uncertainties of the L-L* mapping algorithm) should remove dominance of adiabatic relaxation, so radial transport seen in Figure 5 suggests that radial diffusion is occurring, as seen and modeled in other CME-shock driven storms (Hudson et al., 2014Li et al., 2017 and references). The PSD plot combines contributions from plasmasheet injection with the initial trapped population. As seen in Figure S3 in Supporting Information S1, significant loss of the initial trapped population occurs after 0400 UT while the injected population fills in PSD at later times. At the end of the  (Roederer, 1970) using the TS04D magnetic field model (Tsyganenko & Sitnov, 2005). Initial orbit is shown (blue) and subsequent orbits indicated over 48 hr from 0 UT May 13 (left) and 0 UT August 29 (right). Black curve is used for simulated initial PSD radial profile of the trapped population for each event. For reference Van Allen Probes a apogee was a) postnoon and b) at noon for the two events, see Figure S2. 11-hr simulation, the percentage of injected and trapped electrons remaining overall is 38.6% injected and 61.4% trapped. Radial loss to the outer boundary indicated by the arrow in Figure 5 is a significant feature of this and other CME-shock driven storms (Hudson et al., 2014. Results for 5,000 MeV/G are shown in Figure S5 in Supporting Information S1. Figure 6 shows the evolution of PSD for the August -September event for 2,000 MeV/G electrons using GAM-ERA fields. The test particle simulations are run longer for the August-September event (00 UT August 30 to 00 UT September 3) to capture the time interval of CIR driving of outer zone electron response in contrast with the CME-shock event study (11 hr) which evolves faster. Kp reached a maximum of 6 on September 1 (Figure 2), indicating strong substorm activity. Ten substorms occurred during the time interval simulated, see Table S1 in Supporting Information S1. The contributions of the injected and initial trapped population are plotted separately in Figure S4 in Supporting Information S1, with a factor 10 2 lower initial radial PSD profile (Figure 4b) than for the May event (Figure 4a). While loss to the magnetopause is a prominent feature for the CME-shock driven case, the CIR-driven storm is characterized by emergence of a local peak in PSD evident in Figure 6 around L* ∼ 5 and associated with updating the PSD carried by injected test particles at the Van Allen Probe A apogee every 9 hr (Van Allen Probe B ceased operations July 19, 2019), spreading to higher and lower L* through radial transport. At the end of the 4-day simulation, the percentage of injected and trapped electrons remaining overall is 88.1% injected and 11.9% trapped. Figures 5 and 6 provide a stark contrast in radial profiles between the two types of events studied, which will next be compared directly with measured PSD. Figure 7 (top panels) compares the measured PSD at 2,000 and 5,000 MeV/G for the May CME-shock event over 48 hr starting at 0 UT May 13 with the simulated PSD at 34 hr (10 UT May 14) shown in black dots. The initial orbit of measured PSD is shown in dark blue and subsequent orbits of the two Van Allen Probes spacecraft are indicated over 2 days from 0 UT May 13 to 0 UT May 15 shown in yellow. Black dots indicate the radial profile at the end of the simulation shown in Figure 5. Inward radial transport relative to the initial radial profile is evident in both simulated and measured PSD. Loss at higher L is captured for both first invariants (compare black dots with green at 34 hr). Atmospheric loss processes produced by higher frequency whistler mode or EMIC waves are not included in the MHD simulations (see review by . However, the decrease in PSD at higher L values is consistent with magnetopause loss seen in other MHD-test particle simulations where loss due  Figure 2a. The blue patch of low PSD in the upper left corner is due to mapping from L to L* since test particles are initialized inside L = 6 Re, see Figure 3b, which is inside L* = 6 Re using the TS04D magnetic field model for mapping. Second invariant K = 0 in these 2D simulations. L* is always defined in results shown for K = 0 up to L* = 6. Arrow indicates radial loss.

Results for May 13-14 CME-Shock Driven Geomagnetic Storm
to radial transport and inward motion of the magnetopause dominates (Hudson et al., 2014. Decrease in PSD at higher L is greater at 5,000 MeV/G than at 2,000 MeV/G, consistent with the shorter timestep for a random walk in the radial variable (radial diffusion) as the drift period decreases with higher first invariant. Figure 7 (bottom panels) compares the measured PSD at 2,000 and 5,000 MeV/G for the August-September CIR-driven event. Note that the timescale for the CIR event shown is 4 days versus 11 hours for the CME-shock event comparison, since the evolution occurs over a longer timescale for CIR driving than for CME-shocks producing more abrupt changes, in particular magnetopause loss (Hudson et al., 2014. While the CME-shock event produced a loss of PSD over the timescale shown, the CIR event produced a substantial increase in PSD over three orders of magnitude at 2,000 and 5,000 MeV/G (compare black dots with yellow at 0 UT on September 3). There is good agreement between simulated and measured PSD at high and low L*, however the simulation does not capture the peak in PSD evident by 0 UT September 3 (yellow), likely due to local heating not included in the simulations (Boyd et al., 2018; see review by . Figure S7 in Supporting Information S1 plots a chorus wave power proxy from POES measurements of electron precipitation (Chen et al., 2014) for the CIR event period studied which was much weaker during the 11-hr CME simulation interval (not shown). While both event simulations capture the PSD plateau around Van Allen Probes apogee and observed inward radial transport at low L*, and simulations reproduce a net decrease in PSD for the CME event and increase for the CIR event at high L*, the observed peak in PSD around L* = 4-4.5 prominent in measurements for the CIR event, and greater at higher first invariant, suggests that local heating due to higher frequency waves not resolved by MHD simulations played a role in the CIR event (Li & Hudson, 2019 and references;Thorne et al., 2013).

Discussion and Conclusions
In contrasting the two events studied, the CME-shock produced solar wind drivers characterized by a moderate solar wind pressure impulse at 0 UT on May 14 in Figure 2a and increase in solar wind velocity from 300 to 500 km/s, with IMF Bz turning southward to -13 nT for 4 hr, and increased magnetospheric convection during this time building up the ring current as reflected in SymH. A second stronger pressure impulse occurred as Bz increased sharply around 07 UT on May 14 and is reflected in SymH. Otherwise, this event has characteristic solar wind driving features seen in other CME-shock driven storms which are distinct from the features seen in the August-September CIR event in Figure 2b. For neither event was the ring current as strong a modifier of PSD as it was, for example, for the March 17 2015 CME-shock driven storm which has been studied with RCM coupled to LFM and shown to reproduce ring current effects such as Dst variation . The CIR event is characterized by ∼4 days of high solar wind velocity exceeding 600 km/s and a long but very moderate enhancement of the ring current reflected in SymH, beginning 00 UT August 31 and extending over a week, typical of CIR driven storms (Tsurutani et al., 2006). Embedded in this period of enhanced solar wind velocity characteristic of CIRs, Alfvenic fluctuations typically drive recurring substorms, providing a seed population for radiation belt electron enhancement when plasmasheet electrons are efficiently transported earthward via enhanced convection and dipolarization events . The plasmasheet has been shown in many studies to be a sufficient source population for outer zone electrons (Taylor et al., 2004;Turner et al., 2021). Neither of the events studied were solar energetic electron events such as seen with the strong "Halloween storm" CME-shock event of 2003 (Kress et al., 2007. Table S1 in Supporting Information S1 provides a list of substorms during the CIR event. Five substorms occurred on August 30, just prior to the drop in SymH, with subsequent days of multiple substorm occurrence (2 and 3 September). Kp reached an event high of 6 on September 1 (Figure 2). Injected electrons dominate the final state for the CIR event, competing with magnetopause loss for the CMEshock event and a higher initial trapped flux than for the CIR event.
These contrasting scenarios of solar wind driving for the CME-shock and CIR events explain the different timescales for PSD evolution seen in the two cases. The CME-shock event initiated by an L1 disturbance at 2326 UT  Figures 5 and 6 (black dots, indicated also on color bar) with measured PSD profiles from Van Allen Probes over sequential orbits. Initial orbit is shown (blue) and subsequent orbits are indicated over 2 days from 0 UT May 13 (top) and 4 days from 0 UT August 30 (bottom). Black dots indicate end of the simulation (after 34 hr of data at 10 UT May 14 for the May event and at 0 UT on September 3 for the September event) using PSD updated at apogee every 9 hr for the RBSPA and RBSP B spacecraft as available, with data combined for the May event and only RBSP A measurements available every 9 hr for the September event. Measured PSD has K = 0.05 Re-G 0.5 as in Figure 4, and K = 0 for 2D simulations.
on May 13 was followed by another CME-shock at 2100 UT on May 16, the third and fourth of five ICME shocks in the Cane-Richardson ICME shock list for May 2019, and the only ICME shocks arriving at L1 between September 23, 2018 andOctober 29, 2019 (http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm), all five from the same active region on the sun. The May 13-14 event caused initial loss from inward motion of the magnetopause, characteristic of CME-shock driven storms (Hudson et al., 2014. We focused on the dropout period for the May event since recovery likely involves local heating by whistler mode chorus not contained in the MHD-test particle model . Outer zone electron dropout events are a common feature of geomagnetic storms at higher L shells (e.g., Green & Kivelson, 2004;Matsumura et al., 2011;Millan & Thorne, 2007;Morley et al., 2010;Ni et al., 2013;Onsager et al., 2002;Shprits et al., 2006;Su et al., 2017;Turner & Ukhorskiy, 2020;Turner, Angelopoulos, Morley, et al., 2014;Ukhorskiy et al., 2015;Xiang et al., 2017). Dropouts as seen at LEO are compared with Van Allen Probes equatorial dropouts in Pierrard et al. (2021). Rapid radial loss is observed with CME shock-driven storms (Hudson et al., 2014) and well correlated with the last closed drift shell during strong magnetopause compression (Albert et al., 2018;Olifer et al., 2018). Drift shell splitting is enhanced during such events with electrons near 90° pitch angle moving to larger radial distance on the dayside conserving their first adiabatic invariant (Roederer 1970). They may then be preferentially lost to the magnetopause. Fast inward motion of the magnetopause can produce a negative PSD gradient which leads to outward radial diffusion (e.g., Shprits et al., 2006), particularly in the presence of enhanced ULF wave power which follows such compressions (e.g., Hudson et al., 2014Hudson et al., , 2015Zong et al., 2009Zong et al., , 2017. Li et al. (2015Li et al. ( , 2016 have analyzed the ULF wave mode structure contained in MHD electric and magnetic field fluctuations, similar to simulations performed here, which cause radial transport. A comparison between direct MHD-test particle simulations as performed here and calculation of transport coefficients from MHD electric and magnetic field fluctuations implemented in a Fokker Planck formalism shows that ULF wave-driven radial transport is well-represented by both formalisms (Li et al., 2021). Outward radial diffusion contributes to magnetopause loss even when the magnetopause (L ∼ 8, Figure 2) is well outside geosynchronous orbit, as in the moderate storms studied here. The Dst effect (Kim & Chan, 1997) is weak for the moderate storms in the present study, however calculating PSD from measured and simulated flux using a model magnetic field (TS04D) allows for inclusion of adiabatic reduction in flux due to buildup of the ring current and outward motion of electrons conserving their magnetic flux through a drift orbit, the third adiabatic invariant. The local magnetic field is weakened by the opposing magnetic field due to the ring current (Kim & Chan, 1997).
The August-September CIR driven storm was weaker and the initial PSD at 2,000 MeV/G was lower by two orders of magnitude as seen in Figure 4 relative to the CME-shock event. Nonetheless, a strong enhancement is seen both at 2,000 and 5,000 MeV/G for the August-September event, see Figure 7 bottom, with a three order of magnitude enhancement in PSD at 2,000 and 5,000 MeV/G. Note that the flux enhancement occurs first at lower energies, at 1.8 then at 4.2 MeV in Figure 1 (expanded in Figure S1 in Supporting Information S1), before enhancement is seen at 7.7 MeV. This delayed enhancement at higher energies is commonly observed and expected both for energization due to inward radial transport conserving the first invariant and for local acceleration by whistler mode chorus, a process which is expected during recurring substorms. Jaynes et al. (2015) have identified two distinct electron populations resulting from magnetospheric substorm activity which are crucial for the acceleration of highly relativistic electrons in the outer zone: a source population (tens of keV) that gives rise to whistler mode chorus growth and a seed population (hundreds of keV) that is accelerated via interaction with the chorus to much higher energies . By updating the simulations with measured PSD at the Van Allen Probes apogee, we effectively capture the enhanced seed population transported from the plasmasheet; however additional local acceleration and atmospheric loss due to higher frequency waves than captured by MHD physics (higher than the ion gyrofrequency) are not included in our simulations. The importance of these processes is expected to be greater over the longer timescale of a CIR event. However, the overall radial profile evolution of both events is well captured, with decrease in the initial trapped population dominating the CME-shock driven storm during main phase and increase in PSD due to the injected population dominating the CIR-driven storm. MHD-test particle simulations have also captured well CME-shock driven prompt injection events such as March 17, 2015  and July 16, 2017 (Patel et al., 2019), wherein a stronger CME-shock produces a coherent magnetosonic wave disturbance inside the magnetosphere with an azimuthal electric field transporting trapped MeV electrons inward ahead of the magnetopause compression (Hudson et al., 2020 reviews this type of event; Li et al., 1993). For the weaker CMEshock event studied May 13-14, 2019, magnetopause loss is the dominant early signature of the event with no evidence of prompt injection in the REPT data. Later recovery over May 15-16, shown in greater detail than Figure 1 in Figure S1 in Supporting Information S1, may be due to a combination of local heating by VLF waves and inward radial transport to which ULF waves contribute (see  for a review of both processes).
Overall our conclusions in comparing the impact on outer zone electrons of a moderate CME-shock driven storm with a 4-day CIR event, more characteristic of solar minimum, supports our earlier conclusions about these two distinct types of solar wind drivers based on separate studies (Hudson et al., 2012(Hudson et al., , 2014. Here we use well-developed MHD-test particle tools with input parameters calibrated to measured PSD at 5.8 Re to study both events. Increased MHD grid resolution and coupling to RCM significantly advances our prior 4-day CIR study for the Whole Heliosphere Interval at the last solar minimum (Hudson et al., 2012), bringing code resolution and representation of the ring current up to the level of recent work on CME-shock driven storms during the Van Allen Probes era. Future work will make further quantitative comparisons using the newly developed GAMERA code which allows for longer simulation studies at higher efficiency (Pham et al., 2021;Sorathia et al., 2020;Zhang et al., 2019). It remains for us to add a model for the atmospheric losses which accumulate over longer runs like the August-September CIR event.