2.1 Data Set

Ground-based induction magnetometers were used to observe EMIC waves. The global network of induction magnetometers enables us to continuously observe EMIC waves from various locations and to estimate the source region of EMIC waves. In this study, we used the induction magnetometers installed by the Canadian Array for Realtime Investigations of Magnetic Activity (CARISMA) (Mann et al., 2008) and the study of dynamical variation of particles and waves in the inner magnetosphere using ground-based network observations (PWING) (Shiokawa et al., 2017).

We used Radiation Belt Storm Probe data from three instruments. The Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument measures wave electric, magnetic, and DC magnetic fields (Kletzing et al., 2013). EMFISIS includes a triaxial fluxgate magnetometer (MAG) and a triaxial magnetic search coil magnetometer (MSC). This study used the MAG data to observe EMIC waves, derive the charged particle pitch angle, and calculate local ion gyrofrequencies. A high-frequency receiver was used to derive the local electron density from the upper hybrid resonance (UHR) frequency (Kurth et al., 2015). The RBSP-Energetic Particle, Composition, and Thermal plasma (ECT) suite (Spence et al., 2013) consists of three instruments: a helium-oxygen proton-electron (HOPE) sensor (Funsten et al., 2013), a magnetic electron ion spectrometer (MagEIS) (Blake et al., 2013), and a relativistic electron proton telescope (REPT) (Baker et al., 2013). This study used HOPE data to observe the ring current proton energy and pitch angle distributions below 50 keV. MagEIS and REPT data were used to observe the energy and spatial distributions of relativistic electrons trapped in the radiation belts. In addition, Radiation Belt Storm Probes Ion Composition Experiment (RBSPICE) data were used to observe the pitch angle and energy distributions of ring current protons with energies above 50 keV (Mitchell et al., 2013).

Polar Orbiting Environmental Satellites (POES), operated by the National Oceanic and Atmospheric Administration (NOAA), carries instruments that detect energetic ion and electron flux. These satellites are in sun-synchronous orbits at altitudes of 800–850 km with a period of 100 min. POES has a set of solid-state energetic particle detectors called medium-energy proton and electron detectors (MEPEDs). The proton detector monitors the intensity of protons in six energy bands over a range from 30 keV to 6,900 keV. The electron detector monitors the intensity of electrons in three energy bands in the range from 30 to 2,500 keV. The two identical detectors have different viewing directions: a 0° telescope and a 90° telescope. The 0° telescope generally samples a portion of the precipitating energetic particles in a bounce loss cone. The 90° telescope samples contain a mix of trapped or precipitating energetic particles, depending on the satellite location. Some MEPED proton channels can be contaminated by medium-energy electrons (Yando et al., 2011). This contamination occurs in channel P1 and decreases in the higher-energy channels. Channel P5 is the only MEPED channel that detects only protons and no electrons. Channel P6 has large contamination from relativistic electrons. Thus, the P6 channel has been used to monitor REP in the atmosphere (Millan et al., 2010; Miyoshi et al., 2008; Sandanger et al., 2009).

In addition to POES, we used VLF/LF radio waves at 10–100 kHz frequencies to detect the precipitation of electrons with energies higher than 50–150 keV (Rodger et al., 2012). The radio waves propagate from a transmitter to a receiver in the subionospheric waveguide. When electrons precipitate into the atmosphere and cause ionization in the lower ionosphere above the radio propagation path, the amplitude and phase of the radio waves are altered. We interpret this modulation as electron precipitation. In this study, we observed VLF/LF radio waves that are transmitted from stations in the United States: NDK (25.2 kHz, 46.37°N, 261.47°E, L = 3.0) and NLK (24.8 kHz, 48.20°N, 238.08°E, L = 2.9). The waves were received at Athabasca (ATH), Canada (54.6°N, 246.7°E, L = 4.3) (Hirai et al., 2018; Miyashita et al., 2020; Tsuchiya et al., 2018). This is a component of the Observation of CondiTion of ionized Atmosphere by VLF Experiment (OCTAVE), which is a network of VLF and LF radio wave receivers developed by Tohoku University and supported by the Institute for Space-Earth Environmental Research (ISEE), Nagoya University, and the National Institute of Polar Research (NIPR). The amplitude and phase of the transmitter signals are recorded with 0.1-s time resolution.

An rTEC map was used to identify the midlatitude trough. The rTEC value was defined as the total electron content (TEC) ratio to the average TEC value of 10 geomagnetically quiet days per month. The global TEC data were derived from Global Navigation Satellite System (GNSS) observation data in Receiver INdependent EXchange format from many regional GNSS receiver networks worldwide. A method to derive absolute GNSS-TEC data was described by Otsuka et al. (2002). Detailed information regarding the GNSS-TEC database is available in Tsugawa et al. (2007, 2018).

The geomagnetic indices (SYM-H, Kp and AE indices) and solar wind data were used to determine the geomagnetic condition during a period of the present analysis. The SYM-H and AL indices were provided by the World Data Centre for Geomagnetism, Kyoto. The solar wind data and the Kp index were provided by the OMNI database. The solar wind data in the OMNI data set are propagated to the nose of the bow shock (King & Papitashvili, 2005).

2.2 Solar Wind and Geomagnetic Conditions

Figure 1 shows the solar wind magnetic field and plasma, geomagnetic indices, and relativistic electron flux. The IPDP-type EMIC wave event investigated in this study was observed from 02:20-06:10 UT on 19 April 2017. The blue lines indicate the start and end times of the EMIC wave appearance. IMF B_z showed a southward direction during the event (Figure 1a). The solar wind flow speed gradually increased from 02:00 UT on 19 April (Figure 1b). The average flow speed during the event was approximately 422 km/s. The solar wind dynamic pressure increased at 16:40 UT on 18 April, reaching 10 nPa, then decreased (Figure 1c). The average dynamic pressure was about 5.6 nPa during the event. Substorms occurred during the EMIC event, and the peak value of the AE index was 907 nT at 05:30 UT (Figure 1d). The SYM-H index indicates the weak geomagnetic storms' main and early recovery phases during the event. This is a so-called Corotation Interaction Region driven storm. The minimum SYM-H value was −34 nT at 05:05 UT (Figure 1e). The SYM-H index began to decrease again at 00:00 UT on April 20. The Kp index was 4+ during the event (Figure 1f). Figures 1g and 1h show the 5.2 and 1.7 MeV electron fluxes obtained from REPT and MagEIS, respectively. RBSP-A crossed the L-shell twice in one orbit. As the orbital period of RBSP-A was about 9 hr, RBSP-A measured an L-distribution of the electron flux every 4.5 hr (5 or 6 times per day). In Figures 1g and 1h we have represented the observation time of the L-distribution as the center time of apogee and perigee of RBSP-A and constructed the electron flux distribution as a function of time and L-value. Electron fluxes were decreasing in wide L shells during the event.

2.3 Ground-Based Observations

Figure 2a shows the dynamic spectrum of total power obtained from EMFISIS. The magenta lines denote the local H⁺, He⁺, and O⁺ gyrofrequencies. Figures 2b–2e show the dynamic spectrum of total power obtained from induction magnetometers at Kapuskasing (KAP), Pinawa (PINA), Ministik Lake (MSTK), and Athabasca (ATH), Canada. Figures 2f and 2g show the VLF radio wave amplitudes transmitted from NDK and NLK, respectively. Both VLF radio waves are received at ATH. Figure 2h shows the location of each instrument. The magenta line indicates the RBSP-A footprint during this event. A red diamond indicates the VLF radio wave receiver at ATH. Green diamonds indicate VLF radio wave transmitters at NDK and NLK. The red lines connecting transmitters to receivers indicate the VLF radio wave propagation paths. The blue dashed lines indicate L-values from 2 to 6. The VLF radio waves are sensitive to ionization changes at L = 3–4. In Figures 2f and 2g, the black lines represent the received radio wave amplitudes at the time of the event, and the blue lines represent the average VLF values at each time in a month, including the event date (so-called “quiet day curve”). The VLF radio wave receiver detected the ionization changes above and around the propagation path. The smooth decrease in the amplitude detected by NDK around 02:40 UT and NLK around 03:40 UT were not caused by REP but were due to the ionization change in the lower ionosphere at sunset. Figure 2h shows that the RBSP-A footprint was close to ATH when RBSP-A observed EMIC waves from 03:20 to 06:00 UT. EMIC waves began to be observed when the background magnetic field strength decreased, as indicated by the decreased gyrofrequencies. He⁺-band EMIC waves were observed throughout the event and H⁺-band EMIC waves appeared at 05:08 UT. Clear IPDP-type EMIC waves were observed at all ground stations but did not appear simultaneously. First, IPDP began to be observed at KAP from 02:18 UT at ∼0.4 Hz. Although the wave power was weak, we observed EMIC waves at the same frequency at PINA and MSTK. EMIC waves with a higher wave power appeared at KAP from 03:16 UT and then started to appear from the east (near midnight) to the west (dusk sector) in the order of PINA, MSTK, and ATH. The wave frequency increased at KAP from 04:20 UT, and the EMIC waves terminated at 04:55 UT. At PINA, MSTK, and ATH, different waves were seen at lower frequencies than the waves observed at KAP, and their frequencies started to increase from 04:44 UT. EMIC waves terminated at PINA at 05:36 UT but continued until 06:00 UT at MSTK and ATH. These observations imply that at least two or more IPDP sources were observed on the ground. One source was likely near KAP, and the other was near MSTK and ATH because the EMIC waves from the latter source were not observed at KAP, and their wave power was higher at MSTK and ATH than at PINA. EMIC waves are mode-converted in the ionosphere, propagate horizontally, and are observed at stations distant from the source region (Fujita & Tamao, 1988). Figure 2h shows that the RBSP-A footprint is westward of MSTK and ATH. The source of the EMIC waves observed at MSTK and ATH was the same as that observed by RBSP-A. Figures 2f and 2g show that the amplitudes of the VLF signals significantly decreased during the event, indicating that EMIC waves caused the REP. In Figure 2f, the VLF signal amplitude decreased several times from 03:40 UT and returned to the quiet level at 05:44 UT. However, Figure 2g shows that the VLF signal amplitude decreased from 04:22 UT and returned to the average level at 05:55 UT. The locations of electron precipitation were connected to the EMIC wave source region in the magnetosphere through magnetic field lines. The VLF radio wave observations showed that electron precipitation started from the east side's propagation path, suggesting that the EMIC wave source region drifted or expanded westward. This is consistent with the results of the ground-based magnetometer observations.

2.4 RBSP-A Observation

Figure 3 shows the observation results of RBSP-A. Figure 3a is the same as Figure 2a. Figures 3b and 3c show the 50–500 and 1–50 keV proton fluxes obtained from RBSPICE and HOPE, respectively. Figure 3d shows the electron density from the Level 4 EMIFISIS data. The UHR frequency determined from the EMIFISIS data was used to derive the electron number density. Figure 3e shows the RBSP-A orbit on the X-Y plane in GSM coordinates at 00:00-06:00 UT on 19 April 2017. The bold line indicates the orbit at 03:20-06:00 UT when the EMIC waves were observed. RBSP-A passed from ∼6 to ∼3.5 L in the dusk sector during an EMIC wave event. Figures 3b and 3c show sudden enhancements of the 2–30 keV proton flux with the EMIC wave onset. The peak flux was ∼20 keV in this interval. The energy range of the enhanced proton flux expanded to 80 keV at 04:50 UT. The flux peak energy decreased to less than 10 keV. RBSP-A was out of the ring current region at 06:10 UT. In Figure 3d, the electron density was 26.6 cm⁻³ at the start time of the EMIC waves and increased as the RBSP-A traveled earthward. No clear plasmapause was seen.

3.1 Comparison of Observations With Proposed IPDP Models

We examined whether the two mechanisms proposed in previous studies for the IPDP frequency increase apply to this event. From here on, we describe the mechanism of the frequency increase due to energy dispersion in the westward drift proposed by Fukunishi (1969) as the “westward drift model” and the mechanism proposed by Gendrin et al. (1967) as the “inward drift model”, in which the frequency increase is caused by increased ion gyrofrequency due to inward drift. To distinguish between these two mechanisms, we investigated the azimuthal and radial drifts of the EMIC source region during the frequency increase and discussed the contribution of drift to the frequency increase of the EMIC wave event.

3.1.1 Westward Drift Model

The data obtained at stations KAP, PINA, and MSTK, separated longitudinally, were analyzed. Figures 4a, 4c, and 4e show the dynamic spectra of magnetic fields calculated from the data from the three stations. The blue, magenta and red horizontal dashed lines indicate 0.5, 1.0, and 1.5 Hz, respectively. Figures 4b, 4d, and 4f show the power spectrum density at 0.5 (blue), 1.0 (magenta), and 1.5 (red) Hz. 10⁻³ nT²/Hz, represented by a black line, was the threshold power to determine the IPDP start time at each frequency. The start times are indicated by vertical dashed lines of the same color as the respective frequencies. Because the wave structures were complicated, we also referred to the similarity of spectral structures appearing in the dynamic spectra by visual inspection. IPDP started earlier for stations in the east and later for stations in the west. Figure 4g showed the MLT of each station when the IPDP event started. Cross, rhombus, and triangle symbols represent KAP, PINA, and MSTK. Blue, magenta, and red lines indicate 0.5, 1.0, and 1.5 Hz, respectively. After ring current protons are injected in the night side, the protons drift westward. Suppose we assume that EMIC waves observed at the three stations were excited by the same ion populations. In that case, when certain frequency waves start to be observed may be when ions with the same energy arrive at the longitude of a station. With the linear curve, we approximated the relationship between MLT and the IPDP start time at the three stations shown in Figure 4g. The slope of each approximate curve represents the longitudinal IPDP drift rate. The westward drift rates were 4.83, 4.41, and 4.89 MLT/h at 0.5, 1.0, and 1.5 Hz, respectively. The westward drift rates of each frequency were not significantly different. In the westward drift model, higher-energy ions excite waves with a lower frequency, while lower-energy ions excite waves with a higher frequency through cyclotron resonance. In addition, this model predicts that the frequency-time slope becomes small as the longitude separation between the observation point and the injection region becomes large. In this result, however, the drift rate at 0.5 Hz was not significantly different from that at 1.5 Hz, and the drift rate at 1.0 Hz shows the smallest value. In the dynamic spectra shown in Figures 4a, 4c, and 4e, the frequency-time slopes of the waves observed at each station did not change significantly. These results suggest that protons exciting the IPDP cause westward drift but do not contribute to increasing the IPDP frequency. We discuss the quantitative evaluation of the westward ion drift and the difference in the IPDP start time observed at the three stations in Section 3.3.

3.1.2 Inward Drift Model

We investigated whether the source region of EMIC waves drifted inward and whether its drift caused an increase in the IPDP frequency. The radial distance at which the electrons scattered by the EMIC waves precipitated were identified using the MEPED onboard the POES. EMIC waves scatter both relativistic electrons and ∼1–100 keV protons and then cause them to precipitate into the atmosphere. Carson et al. (2013) used the characteristics of EMIC waves and developed an algorithm to automatically detect REP caused by EMIC waves using POES. Their results suggested that the simultaneous presence of short-lived precipitation spikes in the POES loss cone data from 30 to 80 keV protons (P1 channel) and >800 keV electrons (P6 channel) should indicate EMIC wave activity (Miyoshi et al., 2008). Thus, we used the detection method of Carson et al. (2013) as a reference. The data from five satellites (METOP1, METOP2, NOAA15, NOAA18, and NOAA19) were used. Simultaneous flux enhancements detected by the 0° detector at both P1 and P6 without flux enhancement in the 0° detector at P5 were defined as EMIC wave-driven REP events. To estimate the source region of EMIC waves at the magnetic equator, the locations of the POES at which EMIC wave-driven REP was detected were traced to the equatorial plane using the TS04 model (Tsyganenko & Sitnov, 2005). The five satellites detected 11 EMIC wave-driven REP events from 02:00 to 06:00 UT. Five and six events occurred in North America and the conjugated region. Figures 5a and 5b show the MLT and radial distance where 11 EMIC wave-driven REP events were detected by POES, respectively. The MLT range corresponds to the region where EMIC waves appeared and were not significantly different between 20 and 21 MLT. The radial distance decreased from about 6 R_E to 3.5 R_E. The slope was −0.5 R_E/hour. The decreased radial distance indicated that the EMIC wave source region moved inward.

We next verified whether the inward drift of the source region caused an increase in the IPDP frequency. In the inward drift model, the magnetic field strength in the source region controls the wave frequency because the ion gyrofrequencies are proportional to the magnetic field strength. In fact, Figure 2a shows that the EMIC wave frequency observed by RBSP-A increased with the local helium gyrofrequency. This indicates that the wave frequency is controlled by the local magnetic field strength. Assuming that the IPDP frequency depends on the magnitude of the magnetic field in the equatorial plane, the distance of the source region from the Earth in the equatorial plane can be estimated from the frequencies of the observed IPDP. We compared the temporal variation in the radial distance of the source region to that of the source region inferred from POES observations and found that the inward drift model could be applied to this event. We made two assumptions. (a) On the ground, EMIC waves are observed at the same longitude as the source region of EMIC waves. (b) The observed EMIC waves were in the He⁺ band between the helium and oxygen gyrofrequencies. First, we determined the minimum (f_min) and maximum (f_max) IPDP frequency values from ground induction magnetometer data. We used a threshold of the power spectrum density 10⁻⁴ nT²/Hz to determine the IPDP frequency range. We calculated the magnetic field strength from 1 R_E to 7 R_E in the equatorial plane at the same meridian as the stations with induction magnetometers using the TS04 model. The helium and oxygen gyrofrequencies were calculated from the magnetic field strength. The range of radial distances for which the frequency range from f_min to f_max is the He ⁺ band is the range of the region where EMIC waves can generate. We analyzed this using data from the magnetometers at KAP, PINA, and MSTK. The black, blue, and green areas shown in Figure 6 show the possible radial distance range of the source region in the equatorial plane estimated from the IPDP frequencies observed at KAP, PINA, and MSTK, respectively. All the source regions moved inward. Figure 6 combines the results from the three stations and the locations of EMIC wave-driven REP detected by POES. We found that the variation in the EMIC wave-driven REP locations corresponds well to that of the source regions estimated from the IPDP frequencies. This result suggests that the inward drift of the source region explains the increases in the IPDP frequency.

RBSP-A observed the EMIC waves in radial distance range from 6 to 3 R_E (see Figure 3a). On the other hand, Figure 6 shows that the instantaneous radial extent of the EMIC source is around 1 R_E at most. It is interpreted that RBSP-A traveled from 6 to 3 R_E with the inward-moving IPDP source region. The radial range of the EMIC waves observed by RBSP-A not only reflects the source region's radial extent but also affects the source region's motion with respect to the observer. Paulson et al. (2017) showed that the radial extent of most EMIC source regions was concentrated within 0.5 R_E, and some events extend up to around 1 R_E. The radial extent of the EMIC wave source region reported here is wider than the typical EMIC wave events. An example of significantly large EMIC source regions has been reported by Engebretson et al. (2018).

3.2 Mechanism of the Inward Drift of the IPDP Source Region

Heacock (1967) and Gendrin et al. (1967) argued that the frequency increase is due to the inward drift of hot ions under a large-scale electric field. The studies by Kangas et al. (1974), Heacock et al. (1976), Lukkari et al. (1977), and Pikkarainen et al. (1983) suggest that the IPDP source region exhibits inward drift and that the electric field has a dominant role in this process. To verify whether the IPDP event analyzed in the previous section could be explained by an electric field, we compared the plasmapause location with the source region because the plasmapause location changes with the dawn-to-dusk electric field. The mid-latitude trough observed in the GNSS-TEC data was used for this analysis instead of the location of the plasmapause in the equatorial plane.

The location of the mid-latitude trough was derived from the minimum GNSS-TEC value in the subauroral and mid-latitude regions. The mid-latitude trough was characterized by significant plasma depletion in the F region of the ionosphere. The structure of the mid-latitude trough showed latitudinally narrow density depletion with a wide longitudinal extent. The plasmapause in the inner magnetosphere closely connects to the midlatitude trough in the ionosphere along the same magnetic field line (Yizengaw & Moldwin, 2005). Shinbori et al. (2021) indicated that the mid-latitude trough minimum tends to be located near the plasmapause in the evening-midnight sectors during storm periods. In this study, the mid-latitude trough was traced to the equatorial plane using the TS04 model, and the mid-latitude trough's radial distance was determined. The red lines in Figures 6b–6d show the location of the mid-latitude trough in the meridian for each station. The source regions are located at almost the same position as the mid-latitude trough or outside the mid-latitude trough. In Figure 3d, RBSP-A observed electron densities of 20–1,000 cm⁻³ during this period, and no clear plasmapause was present. These results suggest a high plasma density region outside the mid-latitude trough. It is clear from Figures 6b–6d that the mid-latitude trough was moving inward over time. To interpret these results, we assumed that the mid-latitude trough reflects the Alfvn layer of zero-energy charged particles, which is the separatrix between the open and closed drift paths of cold plasma. As the separatrix shrinks because of an enhanced convection electric field, the cold, dense plasma just outside the separatrix moves sunward and is going to be stripped away from the plasmasphere. EMIC waves are generated by the overlap of the ring current ions transported from the night side and the dense cold plasma region outside the separatrix. The increased IPDP frequency is caused by a further inward shift of the source region by a convective electric field or substorm injection.

3.3 Mechanism of the Westward Drift of the IPDP Source Region

We considered the westward drift of ring current ions and the EMIC wave source region. In Figure 7g, the EMIC source locations shown in Figure 6a are mapped on the magnetic equatorial plane. We assumed that the black shaded area in Figure 7g indicated the radial distance range of hot protons, contributing to the excitation of EMIC waves observed at KAP. We calculated the hot proton trajectory to investigate the evolution of the EMIC wave source region at the longitude of PINA and MSTK due to proton drift. We started protons from the radial distance range of the source region at the longitude of KAP when EMIC waves were observed at that longitude. We next calculated the proton drift trajectories under the electric and magnetic fields described below.

The equatorial pitch angle of the drifting protons was set to 90°. To compare our calculated result with the observation, we recorded when the protons reached the longitude of PINA and MSTK and the radial distance at these longitudes. Then we compared the recorded radial distance with the estimated source region at the longitude of PINA and MSTK shown in Figure 7g. The electric field used in the test particle calculations was the co-rotating and convection electric fields, expressed by the Volland-Stern model (Maynard & Chen, 1975; Stern, 1975; Volland, 1973). The Kp index was set to 4+ at the time of the event. The magnetic field is expressed in terms of the dipole field as B = B₀/L³. However, for consistency with the magnetic field strength observed by RBSP-A during this event, we adopted B₀ = 2.5 × 10⁻⁵ T.

Figures 7a–7f show the results of the test particle simulations at various first adiabatic invariants represented by μ from 5.0 eV/nT (1 keV at L = 5) to 250.0 eV/nT (50 keV at L = 5). The black region indicates the source region of EMIC waves at KAP, which is the initial position of protons for the test particle calculations. The positions of the protons reaching the longitudes of PINA and MSTK are shown in blue and green, respectively. In Figure 7a, they get closer to the Earth than the EMIC wave source region at KAP and extend eastward. In Figures 7b7f, however, the protons reaching PINA and MSTK extend west of the EMIC wave source region at KAP. The longitudinal extents of the protons reaching PINA and MSTK in Figure 7c are close to those of the source regions in Figure 7g, which suggests that the westward drift of the EMIC source region can be explained by the 5 keV proton which drifts westward at L = 5. In contrast, the results in Figures 7e and 7f are closer to the source regions shown in Figure 7g in terms of the radial extent. Because this simulation used a constant convection electric field, the inward drift of the source region shown in Figure 6 was not considered.

3.4 The Resonant Energy of Ring Current Proton

The first adiabatic invariant used in Figure 7c was derived by assuming 5 keV protons drifting at L = 5. To examine whether this value was consistent with the event, we investigated the energy range of protons that could excite EMIC waves, as observed by RBSP-A. Figure 8a shows EMIC waves observed by RBSP-A, which are the same as in Figure 3a. The black lines indicate 3/4 and half of the helium gyrofrequencies ( and ). The event was divided into three periods according to the appearance of EMIC waves: (a) 04:00-05:00 UT, (b) 05:10-05:30 UT, and (c) 05:40-06:00 UT. EMIC waves occurring in period (a) appear in the frequency band at approximately . EMIC waves occurring in period (2) appear at approximately and have a maximum frequency of approximately . EMIC waves in period (3) appear around . The perpendicular temperature anisotropy of ring-current ions is a favorable condition for EMIC wave excitation (Cornwall, 1965; Cornwall et al., 1970; Kennel & Petschek, 1966). To confirm the consistency between the energy range of the ring current ion anisotropy and the resonance energy of the ions, we compared the proton pitch angle anisotropy distribution with the minimum resonance energy for protons. Figure 8b shows the proton pitch angle anisotropy distribution calculated from the HOPE data. The energy dependence of the pitch angle anisotropy is given by

(1)

The parallel proton flux was considered as the average flux at pitch angles of 4.5°, 18°, and 36°. The perpendicular proton flux was considered as the flux at a pitch angle of 90°. A pitch angle anisotropy close to 1, represented by red, indicates a perpendicular proton flux higher than the parallel proton flux. This is a favorable condition for EMIC wave excitation from temperature anisotropy. The proton pitch angle anisotropy was plotted only when the total proton flux at each energy level was greater than 50,000 cm⁻²s⁻¹sr⁻¹ keV⁻¹. Then, we calculated the minimum resonant energy E_min for protons. The wave frequencies were set to and , which were within the frequency band of the observed EMIC waves. The magnetic field strength and electron density observed by RBSP-A were used to calculate E_min. We assumed ion compositions of 70% of H⁺ and 30% of He⁺. The black lines in Figure 8b indicate E_min for the wave frequencies at and . Figure 8c shows the ratio of the local electron plasma frequency concerning the local electron gyrofrequency, f_p/f_c. The minimum resonant energy is expected to be low due to high f_p/f_c. In period (1), a perpendicular proton flux enhancement was observed around E_min for . In period (2), perpendicular proton flux enhancement was observed around E_min for and at energies higher than E_min for . In period (3), perpendicular proton flux enhancement was observed at energies higher than E_min for . The energy range of the anisotropic ring current protons and the E_min of EMIC waves overlapped whenever strong EMIC waves occurred. According to the RBSP-A observations, this energy range corresponds to ∼2–10 keV, distributed around L = 3.5–6 (see Figure 3c). The first adiabatic invariant shown in Figure 7c (5 keV at L = 5) was consistent with the resonant energy derived based on the RBSP-A observations. These results suggest that protons cause the westward drift of the EMIC wave source region with significant pitch angle anisotropy. It should be noted that we assumed the ion composition inside the plasmasphere to be constant (70% of H⁺ and 30% of He⁺) along the RBSP-A orbit since there was no observation of the cold ion composition in the plasmasphere. We have also calculated the minimum resonant energies of protons with EMIC waves for different sets of proton and helium compositions and compared them with the energy range of the high proton anisotropy. The results are shown in Supporting Information S1. It is confirmed that the minimum proton resonant energy increases with decreasing helium composition and 70% proton and 30% helium are most consistent with the observation. Thus, we consider that ∼2–10 keV protons with pitch angle anisotropy contribute to EMIC wave excitation. The helium composition of 30% is a possible value but seems to be out of the typical values. Summers and Thorne (2003) described that the fractional helium density typically varies from 2% to 10% during solar minimum, from 5% to 25% during solar maximum, and can reach 30% as an extreme value. Farrugia et al. (1989) reported that the concentration of He⁺ relative to H⁺ is variable, ranging from ∼1% to occasionally over 100%, but the most common values are in the range ∼2 − 6%.

3.5 Statistical Characteristics of the Maximum IPDP Frequency

We statistically examined whether the mechanism underlying the frequency increase identified from the IPDP event on 19 April 2017, can also apply to other IPDP events. We detected EMIC waves with visibly increasing frequency using the induction magnetometer data at ATH from 1 November 2016, to 31 October 2018. During this period, we identified 104 IPDP events. The statistical characteristics of the correspondence between the convection electric field enhancement and the increased IPDP frequency are discussed below. The polar cap potential is the potential difference across the polar cap along the dawn-dusk meridian and is used as a measure of the convection electric field in the magnetosphere (Shepherd, 2007). In this study, the polar cap potential was derived from the PC index, which indicates the magnetic activity at the polar caps (Troshichev & Andrezen, 1985; Troshichev et al., 1988). The conversion from the PC index to the polar cap potential is Φ(kV) = 19.35PC + 8.78, where PC is the PC index (Troshichev et al., 1996). Figure 9 shows a scatter plot of the maximum polar cap potentials and the upper frequencies of IPDP. The blue dotted line represents the least squares line. The correlation coefficient was 0.56. We confirmed that the lower frequencies of 104 events were not so different, which indicates that IPDP with high upper frequencies has a large frequency increase. As shown in Figure 9, the upper frequencies of IPDP are positively correlated with the maximum polar cap potential. This can mean that the enhancement of the convection electric field causes a shift in the ring current region to a lower L shell, resulting in an increased IPDP frequency.

4.1 Temporal and Spatial Evolution of the Source Region of EMIC Waves

We consider IPDP-type EMIC wave formation based on the event analysis. The wave formation occurs in the following three stages: (a) At the beginning of the main phase of a magnetic storm, hot protons are transported from the plasma sheet in the night side to the inner magnetosphere due to the convection electric field. Protons drift westward, and EMIC waves are excited in the region where ions encounter a cold plasma population. (b) The source region expands in the local time direction with a continuous inflow of protons from the night side. (c) As the convection electric field grows or a substorm-induced electric field appears, the ring current proton drift paths move closer to the Earth. The cold plasma in the plasmasphere is stripped away in the sunward direction by the enhanced electric field, causing the plasmasphere to shrink. Thus, the region where the ring current and cold plasma overlap approaches the Earth. This process causes the source region to move inward and westward. As the source region moves inward, the local ion gyrofrequency increases with increasing the magnetic field strength, and IPDP is observed on the ground. Based on IPDP formation and the magnetospheric conditions described above, we discuss whether IPDP is more likely to cause REP than other EMIC waves. A high cold plasma density lowers the resonance energy of the electrons interacting with EMIC waves. Thus, stage (a) is already favorable for EMIC waves to cause a REP. The source region of EMIC waves is considered to be radially narrow (Mann et al., 2014). However, EMIC waves are distributed over a wide range of L shells when the enhanced convection electric field causes the source region to move inward. This makes it easier for EMIC waves to encounter the outer radiation belt. As a result, EMIC waves scatter relativistic electrons over a wide range of L shells, leading to electron precipitation into the atmosphere. This mechanism suggests that IPDP-type EMIC waves are more likely to scatter relativistic electrons than other EMIC waves and more strongly contribute to losing the outer radiation belt electrons due to the nature of frequency increase.

4.2 Loss of Radiation Belt Electrons During IPDP-Type EMIC Wave Events

We discuss a possible contribution of EMIC wave-driven REP to radiation belt electron loss.

Figure 10 shows phase space density (PSD) of energetic electrons on 18–21 April 2017. The PSD was derived from the ECT instrument onboard RBSP-A and RBSP-B. Figure 10a shows the PSD observed by RBSP-A. The PSD data were provided from the Van Allen Probes science gateway. The first and second adiabatic invariants were set to 700 MeV/G and 0.11 R_EG^1/2, respectively. 700 MeV/G corresponds to the electron energies of ∼2.4 MeV at L* = 3.0, ∼1.2 MeV at L* = 4.0, and ∼0.9 MeV at L* = 5.0. The TS04 magnetic field model was selected to map the RBSP-A location to the L*value. MagEIS and REPT instruments determined the PSD in the L*-value ranges above and below 3.5, respectively. Figure 10b uses the same format as Figure 10a but shows the RBSP-B data. Figure 10c shows the SYM-H index. The two red vertical lines indicate the occurrence time of the IPDP observed by the induction magnetometer at ATH. Figure 10 shows that the outer radiation belt is outside L* ∼ 3. The PSD of the outer belt decreased during the main phase of the geomagnetic storm on 19 April 2017.

Figure 10e shows the PSD as a function of L*-value and the first adiabatic invariant observed in the inbound path of RBSP-A starting at 02:51 UT. It represents the PSD distribution just before the PSD decrease in the outer radiation belt. Figure 10f is the same format as Figure 10e but shows the PSD observed in the outbound starting at 07:20 UT, which represents the PSD distribution just after the PSD decrease in the outer radiation belt. Figure 10d shows the ratio of the PSDs shown in Figures 10e and 10f and indicates the changes in the PSD between two paths. The PSD decrease occurred at L* >3.4 and showed significant energy dependence. As the energy increases, the decrease in the PSD becomes larger. At the highest first adiabatic invariant, 5,000 MeV/G, the PSD decreases by 1/100. During this event, in-situ measurements of the local plasma density, magnetic field, and EMIC waves were available from RBSP-A, which enabled us to estimate the minimum resonant energy of relativistic electrons interacting with EMIC waves. The three black lines in Figure 10d indicate the minimum resonance value of the first adiabatic invariant for cases of wave frequencies at , , and . These values were chosen from typical EMIC wave frequencies observed by RBSP-A. The ion composition is assumed to be 70% of H⁺ and 30% of He⁺ to calculate the minimum resonant energy of electrons.

We discuss whether the characteristics of the PSD reduction described above can be interpreted as being caused by IPDP-type EMIC waves. Figure 6 shows the L*-value range of the EMIC wave source regions in this event. The smallest L*-value at which the POES observed EMIC wave-driven electron precipitation was 3.5. This value is almost consistent with the smallest L*-value at which the PSD decrease was observed. In Figure 10d, the PSD of the electrons at 2,000 MeV/G decreases by more than 1/10 at L* > 3.4. The PSD in an energy range higher than the minimum resonant energy of electrons interacting with EMIC waves at 0.5f_He + decreases significantly. This PSD decrease observed by RBSP-A is consistent with the characteristics of relativistic electron scattering and precipitation caused by EMIC waves. Although we cannot rule out other loss processes, these results may be interpreted as a decreased PSD due to electron scattering by EMIC waves. We also investigated the dependence of the resonance energy on the helium ion composition and the results are shown in Supporting Information S2. The electron resonance energy increases as the helium composition decreases. Since the dependence of the resonance energy on the helium composition is weak, the assumption of the ion composition does not affect the conclusion on the relativistic electron loss discussed above.

To quantitatively verify the amount of PSD decrease, it is necessary to evaluate the pitch angle diffusion coefficient based on the spectrum of EMIC waves observed by RBSP-A and to estimate the amount of REP caused by EMIC waves from the spatial structure of the source region of EMIC waves. These questions will be addressed in a future study.