We considered 37 ICME-driven sheath regions in the Van Allen Probes era since the launch of the spacecraft in August 2012. The events were selected based on the sheath region list compiled by for the period 2012–2015, and we used the sheath list in for the period 2016–2018. We also added three events in 2016 that were identified by a visual inspection of the solar wind data. The timing of the shocks (i.e. sheath region front boundary) has been taken from the University of Helsinki Heliospheric Shock Database (http://www.ipshocks.fi, last access: 1 June 2020), and the ejecta leading edge (i.e. sheath region end boundary) were adjusted to match the boundary between the turbulent and compressed sheath plasma and the ejecta. The typical properties of sheath regions and ejecta, and the challenges in determining the boundary timings, are discussed, for example, in and and the references therein. We only included the cases with well-defined sheath and ejecta boundaries in this study.

The solar wind data were obtained from the Wind spacecraft that monitors solar wind at Lagrangian point L1. We used measurements from the Magnetic Field Investigation MFI; and Solar Wind Experiment SWE; on Wind. The Wind data were time shifted to the bow shock nose. The geomagnetic activity indices were taken from the OMNI database. The Wind and OMNI data were obtained through the NASA Goddard Space Flight Center (NASA–GSFC) Coordinated Data Analysis Web (CDAWeb, https://cdaweb.gsfc.nasa.gov/index.html/, last access: 1 June 2020).

The twin Van Allen Probes (formerly known as the Radiation Belt Storm Probes (RBSPs) and identified as RBSP-A and RBSP-B) are on highly elliptical orbits traversing through the inner and outer radiation belts . The outer belt electron flux is measured as a function of the radial distance and electron energy by the Magnetic Electron Ion Spectrometer MagEIS; and Relativistic Electron Proton Telescope REPT; in the Energetic Particle, Composition, and Thermal Plasma ECT; instrument suite on board the RBSP spacecraft. The Magnetic Electron Ion Spectrometer (MagEIS) covers electron energies from 30 keV to 1.5 MeV (source, seed, and core populations), while the core and ultrarelativistic electron populations are monitored by the REPT, which covers energies from 1.8 to 6.3 MeV. In this study, we employed level-2 spin-averaged differential electron flux data. For MagEIS electron fluxes, we only used the background-corrected data . The temporal resolution of these data is 11 s. We note that there is considerable variability in the energy scale of the MagEIS energy channels from early in the mission up to September 2013 . Our study includes 13 events during this period, and our results could be slightly affected by these changes. We focused our study on the outer radiation belt between L=2.5 and L=6. The lower bound was chosen to avoid the proton contamination of the REPT in the inner belt, and the upper bound was constrained by the Van Allen Probes apogee. The L parameter , which was computed by using the TS04D magnetic field model , was extracted from the magnetic ephemeris data available on the ECT website (https://rbsp-ect.lanl.gov/, last access: 1 June 2020).

The very low frequency (VLF) wave activity in the inner magnetosphere, including chorus waves and plasmaspheric hiss, was obtained from the Electric and Magnetic Field Instrument Suite and Integrated Science EMFISIS; on the Van Allen Probes. The utilised data product was the level-2 waveform receiver (WFR) diagonal spectral matrix, which contains the autocorrelations of electric and magnetic field components in 65 frequency bins. The frequency range spans from 2 Hz to 12 kHz, and the spectra are available with a 6 s time cadence. The EMFISIS team also provide electron densities estimated from the upper hybrid resonance frequency as level-4 data products .

Additionally, observations of wave activity in the ultra-low frequency (ULF) range were taken from the GOES-15 spacecraft at geostationary orbit (L∼6.6). The magnetic field data are sampled at 0.512 s by the GOES fluxgate magnetometers .

In the superposed epoch analysis, the median of a given parameter is calculated from the data of all the events aligned with respect to some reference time (i.e. the zero epoch time). This technique has been used in various studies to investigate solar wind properties, wave activity, and electron fluxes statistically, for example e.g.. We chose the zero epoch time to be at the shock and set an additional reference time at the ICME ejecta leading edge (i.e. at the end of the sheath region). We resampled the data during sheath regions to unify their durations. This double-epoch analysis allows us to study the general trends in the solar wind parameters and inner magnetospheric activity during driver structures that cover a large range of durations for similar methods see, e.g.,. The duration of the studied sheath regions varied widely, from 3.0 to 22.7 h, with a standard deviation of 5.3 h. The mean sheath duration was 12.0 h. We resampled the sheath regions to match this mean sheath duration . First, the data during the sheath were rescaled to start at 0 and end at 12.0 h, and then the data were linearly interpolated to share the same time step in each event. For data that can vary over orders of magnitude (i.e. electron fluxes and wave power), we linearly interpolated the logarithm of these data. We note that some fluctuations can be averaged out when stretching or compressing the sheaths with linear interpolation. However, this should not significantly affect the results; the superposed epoch analysis of sheaths, with durations close to the mean duration of 12.0 h and ranging from 10 to 14 h (not shown), presented trends that are similar to the full set of events. The superposed epoch analysis was performed for geomagnetic indices, solar wind parameters, inner magnetospheric wave activity, and electron flux in the heart of the outer radiation belt (L = 3.5–5).

We considered wave activity in the very low and ultra-low frequency ranges in the superposed epoch analysis. Chorus waves appear outside the plasmasphere (where plasma density is approximately <50–100 cm-3) in the following two distinct frequency bands : the lower band (0.1–0.5 fce) and the upper band (0.5–0.8 fce), where fce is the electron cyclotron frequency. Plasmaspheric hiss waves occur inside the plasmasphere in a frequency range from about 100 Hz to 0.1 fce. We included a study of hiss waves for completeness but we note that the timescales they operate on in outer belt electrons >2 d; are longer than the sheath durations. We calculated the electron cyclotron frequency fce based on the TS04D geomagnetic field model . To determine whether the spacecraft was located inside or outside the plasmasphere at the time of the wave measurement, we estimated the plasmapause location with the auroral electrojet (AE)-index-based and magnetic local time (MLT)-dependent model by . A plasmapause model was used because the density estimate data are sporadic.

For ultra-low frequency waves, we calculated the wave power spectral density with a wavelet analysis from the magnetic field magnitude measured by GOES-15 at geostationary orbit. We calculated the Pc5 wave power in the range from 2.5 to 10 min (2–7 mHz) and the EMIC wave power in the range from 0.2 to 10 s (0.1–5 Hz), which corresponds to the range of Pc1 and Pc2 pulsations given by . The power spectral densities were averaged in the given frequency ranges of the wave modes to obtain the wave power data for the superposed epoch analysis, and resampling was performed after this averaging. We note that the GOES measurements taken at geostationary orbit might not always reflect the ULF–Pc5 and EMIC wave activity at the position of the Van Allen Probes .

For the electron flux in the superposed epoch analysis, we considered the median flux in the heart of the outer belt at L = 3.5–5. The MagEIS and REPT electron flux measurements were binned in time (Δt=4 h) and L shell (ΔL=0.1) to combine the data from the two spacecraft. The 4 h cadence was chosen to reduce the effect of the Van Allen Probes orbits and in order to minimise the data gaps in the binned flux data during all events. We note that a 4 h cadence leaves us with only 4 data points during the sheath, but here we are mostly interested in the overall trend during the events, which is similar at higher time resolutions. We selected four energy channels to represent the source (54 keV), seed (346 keV), core (1064 keV), and ultrarelativistic (4.2 MeV) populations. We also calculated the mean electron flux at L = 3.5–5 with the same time and L-shell bins (not shown), and we noted that the trends are very similar to the median values.

In addition to investigating the median sheath properties of all 37 events, we divided the events based on the level of associated geomagnetic activity inferred from the SYM-H index. The SYM-H index is derived from perturbations in the horizontal component (H) of the geomagnetic field that is affected by changes in the ring current. The SYM-H index is essentially the same as the hourly Dst index but with a higher time resolution of 1 min, and it is also more sensitive to substorm activity. The strength of a geomagnetic storm is usually characterised by the minimum Dst value, where the thresholds for small, moderate, and intense storms are -30, -50, and -100 nT, respectively . In previous studies, typically only moderate or larger storms with Dst or SYM-H less than -50 nT were considered e.g.. However, due to the relatively low number of well-defined sheath events during Van Allen Probes measurements, only 9 events out of our total of 37 events have a SYM-H minimum below -50 nT during the sheath region or 2 h afterwards. Therefore, we set the threshold to -30 nT to obtain a statistically adequate subset of 17 geoeffective events. The interval from which we took the minimum was extended to 2 h after the sheath to accommodate for lag in the ring current response. Note that the geomagnetic disturbance of the ICME ejecta was not considered.

We binned the MagEIS and REPT spin-averaged electron flux data from both spacecraft in 0.1 L-shell bins and 1 h time bins, which differed from the superposed epoch analysis, in order to have a higher time resolution. Based on the methodology of and , we define the outer belt electron response (R) as the ratio of post-event flux to pre-event flux. The pre-event flux was obtained by averaging the electron flux over a 6 h interval before the sheath region, and the post-event flux was obtained by averaging over 6 h after the sheath region. The response parameter R was computed for each electron energy and L-shell bin considered. The response was categorised as enhancement when the post-event flux had increased by over a factor of 2 when compared to the pre-event flux (R>2), depletion when it had decreased by over a factor of 2 (R<0.5), and no change when the flux level had not changed significantly (0.5≤R≤2).

In previous studies , the pre- and post-event fluxes were defined as the maximum flux from >12 h up to a few days before and after the event because the outer radiation belt response to entire geomagnetic storms was examined. These studies also excluded the 24 h period during the storm. In this study we use the mean flux values close to the sheath region because we only focus on the outer belt response to the sheath region, and all sheaths did not generate geomagnetic storms (in 20 out of 37 events the SYM-H index does not drop below -30 nT). A post-sheath maximum flux value is not meaningful because it would be embedded in the ICME ejecta and subject to possible fluctuations driven by the ejecta. The 6 h averaging period aims to capture the changes generated by the sheath while excluding the main response to the ejecta, which is expected to occur later (mean duration of the ejecta was 28.4 h, with a standard deviation of 11.1 h).

Figure  shows the solar wind conditions and geomagnetic indices when an interplanetary coronal mass ejection (ICME) driving a sheath region impacted the Earth during 7–9 February 2014. The shock (first red vertical line in Fig. ) was identified as an abrupt and simultaneous increase in the magnetic field and solar wind speed, as well as a small increase in dynamic pressure. Both the sheath and ICME were relatively slow (≈400–450 kms-1). The shock was also quite weak, as the speed jump across the shock was about 100 kms-1. The sheath was characterised by a fluctuating magnetic field and variable dynamic pressure that had high values (≈20 nPa) in the trailing half of the sheath. The ejecta had a smoother field and a clearly lower dynamic pressure. This ICME is included in the Richardson and Cane ICME list (http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm, last access: 1 June 2020; ) and is recorded as a “magnetic cloud” there (i.e. the event shows signatures of a magnetic flux rope). This is because the magnetic field components (Fig. b) show some organised rotation during the ICME, and the north–south magnetic field component (BZ) rotates from north to south. In the sheath, the field was predominantly northward.

The event was only mildly geoeffective (Fig. f and g). The SYM-H index dropped to -29 nT in the middle of the sheath (and briefly below -30 nT 1 h after the sheath ended), and the ICME only caused a weak storm. The substorm activity was also weak (but quite continuous) as shown in the substorm activity (AL) index.

Despite the low geoeffectiveness of both the sheath and ejecta, there were clear changes in the outer radiation belt electron fluxes at source, seed, core, and ultrarelativistic energies as shown in Fig. . Note that, for this particular event, background-corrected fluxes are not available for L>3 at source energies. Before the shock arrived, the outer belt showed typical undisturbed conditions e.g., and the seed and core electron fluxes were higher at the highest L shells. The ultrarelativistic electrons, in turn, peaked at L∼4. After the shock arrival, the fluxes increased at seed and higher energies. The most distinct increase was detected in the ultrarelativistic (4.2 MeV) energies. The fluxes at seed, core, and ultrarelativistic energies also widened towards lower L shells during the sheath. The flux of the source population (54 keV) increased significantly at the end of the sheath. At higher energies, on the other hand, the flux was depleted near the sheath–ejecta boundary. Interestingly, the ultrarelativistic electron fluxes were already enhanced in the front part of the ICME ejecta after the sheath, while the seed and core electron fluxes clearly only increased near the middle of the ejecta.

The wave activity in the inner magnetosphere during the event is illustrated by Fig. , which shows the wave power spectral density of both the very low and ultra-low frequency waves as measured by RBSP-B and GOES-15, respectively. Some chorus activity (Fig. a) appeared immediately after the shock, and it was enhanced in the latter half of the sheath region. Chorus activity persisted during the ejecta. The chorus waves might have caused some acceleration – the enhancement of 1 MeV electrons during the ejecta, for example – but the waves would not yet have acted long enough to cause the enhancement of ultrarelativistic electrons during the sheath e.g..

The ULF wave power in the Pc5 and EMIC ranges was elevated during the sheath (Fig. f). The widening of the electron fluxes towards lower L shells could thus be a result of inward radial transport by ULF waves e.g.. EMIC waves can also be responsible for the loss of relativistic electrons . The subsolar magnetopause was located at about 12.7 RE before the shock arrival, according to the model (Fig. e). The shock pushed the magnetopause nose inward, and it was located closest to Earth (≈7.5 RE) at the end of the sheath when the depletion occurred. At the ejecta leading edge, the magnetosphere started to recover and the subsolar magnetopause stayed at about 10 RE during the ejecta. Therefore, losses at the magnetopause (i.e. magnetopause shadowing) could be the main driver of the depletion, which was possibly coupled with outward transport by ULF waves . During the ejecta, the chorus waves continued but the ULF–Pc5 waves, and the EMIC wave activity in particular, weakened. The enhancement of seed and core fluxes in the ejecta was thus likely associated with continued chorus activity and possibly also with inward transport by ULF–Pc5 waves.

Statistics from the superposed epoch analysis of 37 events with sheath regions are presented in Fig. . Results are also shown for 10 h of solar wind before the shock and for 1 d of the ICME ejecta after the sheath (note that, unlike the sheath regions, the ejecta were not resampled). The results in panels (a)–(d) show the general characteristics of sheath regions e.g. as follows: lower magnetic field magnitude than in the ejecta (but about twice as strong as in the quiet solar wind); elevated dynamic pressure (and solar wind density) compared to quiet solar wind conditions and the ejecta; and contracted magnetopause nose due to the high dynamic pressure sheath. The SYM-H index usually has a positive peak at the shock, which corresponds to the storm's sudden commencement and initial phase or sudden impulse, and then it gradually decreases during the sheath (Fig. e). However, on average, the main geomagnetic storm impact is imposed by the ejecta. In 17 events, the SYM-H index dropped below -30 nT (weak storm) during the sheath or 2 h afterwards, and it dropped below -50 nT (moderate storm) in only 9 events. On average, only weak substorm activity is evidenced by the AL index during the sheath region and ejecta (Fig. f).

Panels (g)–(l) of Fig.  show the statistics of different wave modes in the inner magnetosphere during the selected events. The ULF–Pc5 wave power peaks in the sheath, which shows a growing trend from the shock towards the end of the sheath region (Fig. g). The mean of the median Pc5 wave power in the sheath is about 102 nT2Hz-1, as measured by GOES-15 at L∼6.6, which is 1 order of magnitude larger than during quiet solar wind. The wave power of Pc5 waves declines during the ejecta. The EMIC wave power is also larger in the sheath than during the ejecta and quiet solar wind, with a median wave power of about 10-2.5 nT2Hz-1 (Fig. h). The median EMIC wave power quickly decreases to the pre-event level of about 10-3 nT2Hz-1 in the ejecta.

The main power of chorus waves is in the lower band, where the order of magnitude during the sheath is 10-9 nT2Hz-1 (Fig. j). The median wave power of the upper-band chorus is 1 order of magnitude lower, but in a quarter of the cases the power can reach values comparable to lower-band waves as shown in the upper-quartile curve (Fig. k). The chorus wave power is very similar in the sheath and the ejecta, and it is also only about 4 times higher on average during the sheath than during the pre-event conditions. The chorus wave power increases gradually for a few hours before the shock arrival. This could be driven by the very weak substorm activity in front of the ICME event. Plasmaspheric hiss is not affected by the sheath or ejecta, and its median wave power remains at about 10-8 nT2Hz-1 throughout the event (Fig. l).

The behaviour of the median electron fluxes in the heart of the outer belt (L = 3.5–5) is shown in panels (m)–(p) of Fig. . The flux of the source population increases during the sheath region and it mostly stays at a constant level during the ejecta. A comparison of the pre-sheath to post-sheath fluxes shows that the median response of 54 keV electrons is an enhancement by a factor of 5. For the seed population, the flux is slightly enhanced at the shock but, on average, the flux remains unaffected in the sheath. However, the flux suddenly increases after the sheath ends and continues to be enhanced in the ejecta. The 346 keV electron median flux increases by a factor of about 25. At MeV energies, the flux in the heart of the outer belt remains mostly unchanged when considering the median response. The flux in the ejecta is less than a factor of 2 larger than before the sheath, based on the medians for both 1064 keV and 4.2 MeV. However, the upper quartile of the core population at 1064 keV shows a slight increase and the lower quartile a slight decrease, thereby evidencing that these opposite responses are averaged out in the median. Both the upper and lower quartiles for 4.2 MeV electrons indicate a slight decrease in the flux.

The superposed epoch analysis of the plasmapause location from an AE-index-based model is shown in Fig.  as both independent of magnetic local time (MLT) throughout the event and as MLT-dependent for the pre-event time (-6 h from shock), sheath region (+6 h), and ejecta (+18 h). One event in 2018 was excluded from the analysis due to the AE index data not being available. The MLT dependence of the model shows that the plasmapause is closer to the Earth on the dayside and further away on the nightside during both quiet and disturbed times. In the preceding solar wind, the plasmapause is located at about 5 RE. During the sheath, the plasmasphere moves earthward, and it moves even further earthward during the ejecta. The variation is consistent with the general AL levels in the preceding solar wind, sheath, and ejecta (the AE index should roughly follow AL behaviour). At noon MLT, the median plasmapause location moves from about 4.4 RE during the quiet solar wind conditions to 3.6 RE in the middle of the sheath. At 6 h after the sheath region, i.e. 18 h after the shock, the median distance has decreased to 3.3 RE.

The electron flux response of the whole outer radiation belt for a wider selection of energies than in the superposed epoch analysis is shown in Fig. , where the response is divided to the three categories of enhancement, depletion, and no change. The source population at L>3.5 is enhanced in 80 % of the cases and is practically never depleted. Moreover, closer to the inner boundary of the outer belt, the no-change events are very common at all energies. Electrons at seed energies are enhanced in about half of the cases throughout the belt, with a higher possibility for enhancement in the heart of the outer belt. In a small subset (<15 %) of the seed electrons, depletion occurs near L∼3. Depletion is most common in the ∼1–3 MeV core population at high L shells (L>4.5). At lower L shells, core electron flux is enhanced in 10 % of the cases at most, and in a major fraction of the events (>60 %) the core electron fluxes do not change significantly below L∼4.5.

Interestingly, a feature of the outer belt response is that the depletion progresses to lower energies when L increases. At L∼4.5 the depletion dominates only at >2 MeV energies, while at L∼6 it extends to seed energies at around 500 keV.

After dividing the 37 studied sheath events based on the geomagnetic disturbance they cause, which was inferred from the SYM-H index (≤-30 nT for geoeffective events) during the sheath region and 2 h after it, we found a different response in the outer radiation belt. The superposed epoch analysis results presented in Figs.  and show that geoeffective events are associated with larger dynamic pressure and magnetic field magnitude in the sheath and tend to have higher speeds. Geoeffective sheaths are also more often accompanied by strongly geoeffective ejecta than sheaths where the SYM-H index remains close to 0 nT. Geoeffective sheaths also have larger positive SYM-H peaks at the shock, which is likely due to their tendency for high dynamic pressure, and, as expected, the substorm activity is greater during geoeffective events as evidenced by the AL index.

The wave power of Pc5, EMIC, and chorus waves is higher by a factor of about 6 in geoeffective sheaths when compared to non-geoeffective ones. In geoeffective events, the jump in wave power at the shock is larger in all considered wave modes. For example, the median Pc5 wave power is about 50 times higher during the sheath than before the shock arrival in geoeffective events, whereas in non-geoeffective cases it is only about 20 times higher. The Pc5 wave power also gradually decreases in geoeffective ejecta, but it remains at an approximately constant level that is lower than the median power in the sheath during less-effective ejecta; however, the wave power has a slightly increasing trend near the end of the considered period. The median EMIC wave power behaves similarly between the two groups of events.

While the median chorus wave power in geoeffective events increases, on average, by 1 order of magnitude from pre-event conditions to the sheath region, the chorus activity does not differ significantly between the sheath and ejecta, where it is about 10-8 nT2Hz-1 for lower band and 10-9 nT2Hz-1 for upper band chorus. We also note that in a quarter of the geoeffective cases the upper band chorus wave power is significantly enhanced at the shock (Fig. k). Non-geoeffective sheaths that are associated with modest substorm activity drive the chorus waves in only about a quarter of the events, and the median chorus wave power remains at roughly the pre-event level throughout the ICME (10-9 nT2Hz-1 for lower band and 10-10 nT2Hz-1 for upper band chorus), which is opposed to the geoeffective events where substorm injections excite stronger chorus activity during the ICME. The median wave power of plasmaspheric hiss is, on average, twice as high during geoeffective events than during non-geoeffective events.

The median fluxes in the heart of the outer belt experience enhancement at all the considered energies in the geoeffective events. The strongest increase occurs in the seed population, whose median flux increases by almost 2 orders of magnitude. During the sheath the flux gradually increases at the source and seed energies, while it decreases and is the lowest during the sheath at MeV energies.

For non-geoeffective events the source and seed populations are enhanced, but the flux at core energies does not change significantly and the ultrarelativistic population is depleted. This differs from the geoeffective case in which enhancement occurred at all four energies. The median electron flux at 54 keV increases throughout the event, but the seed population at 346 keV remains at the same level during the sheath after an initial large increase at the shock, and the flux begins to increase again after only a few hours in the ejecta. The 1064 keV electron flux is slightly enhanced during the sheath before the depletion, while electron losses at 4.2 MeV energies already take place at the shock. The change in median fluxes is also lower than in geoeffective events, with the largest change being an increase by a factor of 20 at seed energies in non-geoeffective events.

Again, the outer belt response as a function of L shell and a wider range of electron energies is considered, and the results are shown separately for geoeffective and non-geoeffective events in Fig. . It is immediately evident that, for geoeffective sheaths, enhancement events are more common at all energies and L shells, and the source and seed populations are practically always enhanced in the heart of the outer belt (L = 3.5–5). However, >MeV electrons experience depletion more frequently in geoeffective events throughout the outer belt, which deviates from the superposed epoch analysis results. In non-geoeffective events depletion only begins to dominate the core population response at around L>5. Virtually all non-geoeffective events result in no significant change at low L shells (L<4.5) at almost all energies, while flux enhancements practically only take place at source energies and are limited to L>4.