Direct Observations of Energetic Electron Scattering and Precipitation Due To Whistler‐Mode Waves in the Dayside High‐Density Regions

Plasmaspheric hiss waves play an important role in electron precipitation, leading to the formation of slot region in the Earth's radiation belt. Previous studies indicate that the electron density and the background magnetic field strength are responsible for the intensity of whistler‐mode waves and resultant electron precipitation. Nevertheless, no direct evidence of the strong pitch angle scattering of energetic electrons by hiss waves inside the plasmasphere has been obtained due to the small loss cone near the magnetic equator, where the scattering occurs. Furthermore, the density and magnetic field structures have not been investigated simultaneously and on the same magnetic field lines as the hiss wave enhancement and electron precipitation. With high angular resolution data of ∼10–100 keV electron flux obtained by the Medium‐Energy Particle experiments‐electron analyzer onboard the Exploration of energization and Radiation in Geospace satellite, we identified two events of the strong electron precipitation. A detailed examination revealed that the precipitation occurs in association with the amplitude enhancement of hiss waves. Moreover, strong scattering occurs simultaneously with electron density enhancements, while the magnetic field strength hardly correlates with the wave intensity. Our direct observations indicate that the electron density and its spatial structure (gradient) are crucial to electron precipitation. The observations also indicate that strong scattering leading to substantial loss cone filling occurs up to the magnetic latitude of ∼15° for the events.

time domain structures consisting of complicated electrostatic fluctuations and kinetic Alfven waves (Khazanov et al., 2021) cause electron precipitation in a wide energy range.
In the plasmasphere and plumes, where the electron density is high, pitch angle scattering by whistler-mode hiss waves is believed to be the primary mechanism for the energetic electron precipitation and formation of the slot region (Lyons et al., 1972). Hiss waves are relatively broadband and incoherent whistler-mode electromagnetic waves between a few hundred Hz and a few kHz (Thorne et al., 1973). They are frequently observed in the plasmasphere and plumes during various geomagnetic conditions. The cause of hiss wave generation as well as the essential difference between hiss waves and chorus waves are still under active discussion (e.g., Abel & Thorne, 1998;Bortnik et al., 2008;Omura et al., 2015). Some studies proposed that hiss waves comprise discrete rising and falling tone elements with a shorter time scale than chorus (e.g., Summers et al., 2014). In the absence of high-resolution data to investigate such fine structures, whistler-mode waves in the plasmasphere and plume are often referred to as hiss in previous studies (Breneman et al., 2015;Ma et al., 2016Ma et al., , 2022, which is also the case for events shown in this paper. Measured decay rates of electron flux in the slot region are in good agreement with that expected from pitch angle scattering by plasmaspheric hiss waves (Albert, 2000;Meredith et al., 2009). Quasi-linear diffusion models considering pitch angle scattering by plasmaspheric hiss waves reproduce well the slot region as the steady state structure (e.g., Lyons et al., 1972). Recent satellite observations revealed the L-shell-dependent and energy-dependent structure of the energetic electron flux in the slot region (e.g., Reeves et al., 2016). The structure's time evolution is explained by quasi-linear diffusion simulations considering pitch angle scattering by hiss waves (Ripoll et al., 2016).
Scattering processes of shorter time scales and their effects on the radiation belt structure have also been extensively investigated by past studies. Simulations of pitch angle diffusion based on observations show that strong diffusion occurs by hiss waves (the pitch angle diffusion coefficients >10 −5 ∕s ) (Ma et al., 2016(Ma et al., , 2021(Ma et al., , 2022. Simultaneous satellite and balloon observations have shown a clear correlation between the hiss wave intensity and bremsstrahlung X-rays generated by the energetic electron precipitation (Breneman et al., 2015). In addition, Breneman et al. (2015) pointed out that the ultralow-frequency (ULF) fluctuations in the enhanced electron density and the depressed magnetic field create conditions favorable for the growth of hiss waves, which cause electron precipitation. Other studies have reported the role of the electron density on the intensity of whistler-mode waves. Koons (1989) demonstrated that strong enhancements of whistler-mode wave intensity are correlated with density enhancements called the density duct in the outer plasmasphere. Whistler-mode waves are trapped inside the density duct due to the refraction (e.g., Moullard et al., 2002;Smith, 1961), and achieve a higher liner growth rate (Li et al., 2011). Furthermore, recent particle-in-cell simulations have demonstrated that the waves trapped inside the enhanced density ducts remain in quasi-parallel propagation through high magnetic latitudes. They frequently obtain a larger amplitude than waves outside the density ducts because of less Landau damping, an energy-focusing effect, and a larger nonlinear growth rate (Ke et al., 2021). These studies imply that not only the absolute value but also the spatial structure of the electron density are important for the occurrence of strong hiss waves and the resulting electron precipitation.
Although both observational and theoretical studies suggested the relation between hiss waves and strong scattering of energetic electrons, the efficiency of the electron scattering by hiss waves has yet to be quantified by direct observations due to technical difficulties. The large acceptance angle of conventional space plasma/ particle instruments prevents them from exclusively measuring electron fluxes inside small loss cones in the equatorial magnetosphere. Therefore, electron precipitation to the atmosphere has not been examined near the magnetic equator in the plasmasphere and plume. Furthermore, due to such difficulty in direct observations of precipitating electrons, in situ simultaneous observations and investigations of magnetospheric structures such as the electron density, hiss wave intensity, and electron precipitation remain to be done. However, Medium-Energy Particle experiments-electron analyzer (MEP-e) (S.  onboard the Exploration of energization and Radiation in Geospace (ERG) satellite (Miyoshi, Shinohara, et al., 2018) has successfully distinguished the loss cone electron flux from the flux outside the loss cone and enabled us to examine the efficiency of scattering by whistler-mode chorus waves in the low-density (∼3 cc −1 ) region (S. Kasahara, Miyoshi, et al., 2018). Nevertheless, these in situ observations in previous works have not discussed the relation between electron precipitation and ambient electron density.
In this study, we used the MEP-e instrument, which measures the energy and the direction of each incoming electron in the range of 7-87 keV and has high angular resolution with a full-width at half-maximum of 3.5° to 3 of 12 directly observe energetic electrons scattered by whistler-mode hiss waves in the plasmasphere and plume. The time resolution of the MEP-e is ∼15.6 ms for one energy step. In addition, with the wave data from PWE/OFA (the Plasma Wave Experiment/Onboard Frequency Analyzer) (Kasaba et al., 2017;Matsuda et al., 2018;Ozaki et al., 2018), the density data from PWE/HFA (High-Frequency Analyzer)  and the magnetic field data from MGF (Magnetic Field Experiment) (Matsuoka et al., 2018) onboard the ERG (Arase) satellite, we investigated the electron density at the time and location where the strong diffusion occurs to directly determine the effect of the density modulation on the flux of electron precipitation. The events we report below are the first observations to directly examine hiss waves, electron precipitation, and the electron density on the same magnetic field lines and clarify their relationships.

Observations
In this study, we investigated events in which strong hiss waves were observed in the high-density regions inside the plasmasphere. We found about 20 events in the ERG satellite data from March 2017 to October 2020 with counts inside the loss cone that are different from noise due to the radiation penetration, such as events with apparently correlated electron flux enhancement at wave enhancement or events with the north-south anisotropic electron flux. In this paper, we show two of such events: one is with the strong modulation in the electron density, and the other is with the little modulation to indicate that the modulation of the loss cone flux is small when that of the ambient electron density is small. First, we present the observations from 11:00 to 15:00 on 5 February 2018 (Case 1). In this event, the hiss wave intensity was modulated, similarly to the previous conjunction observations, which showed simultaneous bremsstrahlung X-ray (Breneman et al., 2015). In the second event, strong hiss waves were detected without clear modulation from 05:00 to 06:00 on 11 May 2019 (Case 2). During each event, the geomagnetic condition was moderate. The 3 hourly Kp index was in the range of 2− to 3, and the SYM-H index was from −1 to −6 nT for Case 1, while the Kp index was 4− and the SYM-H index was from −19 to −32 nT for Case 2.
Figures 1a and 1b show a wave magnetic field spectrogram and the cold electron density for Case 1. These panels illustrate that the wave magnetic field intensity and the electron density are modulated and that strong whistler-mode waves tend to be observed in the higher density region (>∼100/cc). The relation between the wave and density modulations and electron precipitation is reported in Section 3 in detail. Figures 1c and 1d show the trajectory of the ERG (Arase) satellite in the SM coordinates. The satellite was located on the dayside and near the magnetic equator. Figure 2 is the same format as Figure 1 for Case 2. Figures 2a and 2b show that this event's wave and density modulations are relatively small.

Results
Figure 3 presents the ERG observations for Case 1. Top panel (a) shows the magnetic field spectrogram. The second to fourth panels (b-d) are energy-time spectrograms of electrons within the northward loss cone (local pitch angle of 0°−2°), trapped (local pitch angle of 10°−20°), and within the southward loss cone (local pitch angle of 178°−180°), respectively. The loss cone fluxes are shown in limited regions of the time-energy space as the instrument covers the loss cone direction only intermittently. Using these flux data, we calculated the ratio of precipitating electron to trapped electron flux in the northward and southward directions, shown in Figures 3e and 3f, respectively. As shown in these figures, strong electron precipitation (the precipitating/trapped ratio ∼1) is observed in both northward and southward directions, indicated by red arrows. Precipitating electrons have a flux of ∼10 6 #/s cm 2 str keV. The vertical dashed lines show the timing of the precipitation. This indicates that precipitation occurs in association with wave enhancements. Furthermore, the hiss wave enhancements and electron precipitation correlate with the electron density enhancements. In panel (h), blue and red lines show resonance energies calculated for 100 and 3,000 Hz whistler-mode waves, respectively. The resonance energy for hiss waves is consistent with the energy of detected precipitating electrons. Figure 4 is a zoomed-in view of Case 1 from 11:10 to 11:40. Electron precipitation with the precipitating-trapped flux ratio 0.1 is detected in both northward and southward directions (shown by red arrows) during 11:20-11:40. On the other hand, during 11:10-11:20, strong precipitation is detected only in the northward direction and little precipitation in the southward direction (shown by a blue arrow). This result implies that the scattering might have occurred up to at least ∼15° MLAT (magnetic latitude), at a lower magnetic latitude than the satellite position at 11:20. In other words, from 11:20 to 11:40, the satellite was located between the scattering regions and detected the precipitation in both directions. Vertical dashed lines in Figure 4 separate relatively strong and weak wave strength periods. There is a correlation between the flux of electron precipitation and the wave magnetic power spectral density (see also Figure 5). They are not strongly correlated during some periods such as 11:20-11:30 in the parallel direction and 11:10-11:20 in the antiparallel direction. That is maybe because the field of view of the electron sensors missed the parallel loss cone (11:20-11:30) or the antiparallel loss cone (11:10-11:20) when the sensors scanned for low energies (∼10 keV), where the loss cone electron flux should be large considering the resonance condition and the trapped electron flux. Figure 4g is the high-pass-filtered density data to clearly show the modulation with a time scale shorter than 10 min. "High-pass-filtered" means that we subtracted 10-min-smoothed data from the raw data. Local maxima of the electron flux tend to occur roughly during periods of strong waves.
In Figure 5, black lines indicate the ratio of integral number fluxes of precipitating to trapped electrons from 7 to 87 keV in the northward (a) and southward (b) directions. Red lines show the averaged wave magnetic field intensity near 1 kHz. While the modulation of electron precipitation with a time scale of <∼1 min (or spatial scale in L-shell direction of ∼0.01 ) poorly correlates with that of wave intensity, the modulation with a time scale of ∼5 min (or spatial scale in L-shell direction of ∼0.05 ) have good correlation. The correlation coefficient between the flux ratio and the wave intensity, as evaluated for a sliding 10-min window, has the highest value of 0.73 during 11:10-11:20 and 0.87 during 11:21-11:31 for the parallel and antiparallel loss cone flux, respectively.   Figure 6a shows that the waves have large intensity and little temporal variation. Figures 6e and 6f indicate strong electron precipitation (the precipitating/trapped ratio ∼1) with energies less than 30 keV within the northward loss cone. In this case, precipitation occurs while hiss waves are enhanced. On the other hand, little precipitation is observed within the southward loss cone. This indicates that the scattering occurred near the equator rather than the near-satellite position. Furthermore, the highly asymmetric loss cones imply that the noise level due to radiations penetrating the electron analyzer (e.g., MeV electrons) is much smaller than the count level of 10-100 keV electrons, which are the subject of this study. Figure 6g shows that the density is stable. In the bottom panel (h), blue and red lines show the local resonance energy estimated for 100 and 3,000 Hz whistler-mode waves, respectively. Although not shown in the figure, the PWE/EFD data confirm that the whistler-wave intensity is small, below 100 Hz during Case 2. The resonance energy is consistent with the energy of the detected precipitating electrons (<30 keV). Breneman et al. (2015) suggested that the ULF fluctuations in the plasma density and the magnetic field strength modulate the whistler-mode wave intensity and subsequent electron precipitation. In Figures 7a-7c, we show the averaged power spectral density of the wave magnetic field, the high-pass-filtered density, and the high-pass-filtered background magnetic field strength. Here "high-pass-filtered" indicates that we have subtracted 10-min-smoothed values from the original time series. Red vertical dashed lines indicate the timing of the high-pass-filtered density local maxima. Figure 7 shows that both the density and the magnetic field fluctuate with a frequency of 1-3 mHz, which falls within the Pc5 range. The wave intensity often has local maxima when the electron density is enhanced.
On the other hand, even though the magnetic field fluctuates with an amplitude of a few nT, the magnetic field intensity poorly correlates with the density modulation. In this event, we conclude that the density modulation changes the wave intensity and the flux of electron precipitation rather than the background magnetic field modulation. The weak correlation between the magnetic field modulation and the wave intensity may be because the amplitude of the magnetic field modulation is small. In addition, the effect of the magnetic field variation on the linear growth rate is smaller than the effect of other factors on the wave intensity. Indeed, in previous studies, no clear correlation between the micropulsations in the ambient magnetic field and the modulation of whistler-wave intensity was found (Tsurutani & Smith, 1974). As indicated in Section 1, various effects of density modulation on the wave intensity have been reported in previous studies. However, future theoretical work is needed to identify the most influential factors for this event among those effects.

Discussion
The results reported here are the first direct observations of strong electron scattering during hiss wave enhancements inside the plasmasphere. The simultaneous occurrence indicates that hiss waves in the high-density region Figure 3. In situ observations made by the Exploration of energization and Radiation in Geospace (ERG) satellite from 5 February 2018, 11:00 to 15:00 (Case 1). A frequency-time spectrogram for the wave magnetic field is shown in the top panel (a). Orange and blue lines indicate 1 f ce , and 0.1 f ce . Energy-time spectrograms for differential fluxes of electrons (expressed in electrons/cm 2 sr s eV) outside the loss cone (local pitch angle of 10°−20° in (c)) and inside the loss cone (local pitch angle of 0°−2° in (b) and 178°−180° in (d)) are shown. Blank indicates that the field of view of the electron sensor misses the loss cone. (e, f) The flux ratio between the loss cone flux and bouncing electrons for the northward and southward directions, respectively. The flux ratios are masked when the count of trapped electrons' energy is zero. Red arrows indicate strong scattering events (ratio ∼ 1). Vertical dashed lines represent the timing of those events. The electron density is shown in (g). In (h), blue and red lines indicate resonance energy with whistler-mode waves with frequency of 100 and 3,000 Hz calculated by using formula of the cyclotron resonance and the cold plasma dispersion relation (Millan & Thorne, 2007), respectively. Horizontal black lines represent the 10 and 100 keV. 7 of 12 can cause pitch angle scattering leading to the loss of energetic electrons into the atmosphere. This result is consistent with previous close conjunction observations made in the equatorial magnetosphere and the upper atmosphere (Breneman et al., 2015;Ma et al., 2022). Ma et al. (2022) indicated that the simulated ionospheric electron density enhancement due to electron precipitation by hiss waves overall agrees with the observations of ground-based radar, while the temporal variation of the simulated ionospheric electron density did not match the observations. They implied that the temporal difference is due to the spatial structure of hiss waves, which is smaller than the L-shell difference between the satellite and the radar. By directly measuring the loss cone flux of electrons in the magnetosphere, we have succeeded in analyzing the data of precipitating electrons and waves obtained simultaneously on the same magnetic field line, which was difficult in previous conjunctive observations, and have revealed that the modulations of electron precipitation with a time scale of ∼5 min (or spatial scale in the L-shell direction of ∼0.05 ) can correlate with that of wave intensity. During most of the time window of the events reported in Ma et al. (2022), the magnetospheric and ground-based observation sites were offset by ∼0.05 or more in L-shell, and the spatial scale of hiss wave modulation might be smaller than the difference in distance between those two sites. The correlation between the flux of electrons and the intensity of hiss waves is not necessarily always clear, because the electron sensors can miss the loss cone for a certain range of energy, preventing us from accurately evaluating the correlation with the loss cone flux.
Our measurements directly show that whistler-mode waves are enhanced and electrons are scattered where the ambient electron density is high. Previous studies indicated that high-density is important for wave growth (e.g., Figure 4. Zoomed-in view of the Case 1 from 11:10 to 11:40. The format of (a-f and h) is same as Figure 3. Vertical dashed lines separate when relatively intense and week waves are observed. When the intense waves are observed, strong electron fluxes (ratio 0.1) are detected shown by red arrows. On the other hand, during 11:00-11:20, only weak precipitations are observed in southward direction shown by a blue arrow. A panel (g) indicates a high-pass-filtered density to emphasize the variation in the time scale of wave modulation. Li et al., 2011). They also showed that the density duct plays a role in guiding waves in a direction nearly parallel to the magnetic field lines up to high-latitude, decreasing Landau damping and increasing nonlinear growth rates (e.g., Ke et al., 2021). As shown in Figure 4, the small modulation inside the high-density region correlates with the whistler-mode wave intensity and electron precipitation. This observation might imply that in addition to the high-density leading to high growth rates, the enhanced density duct, where the waves are confined, promotes electron precipitation. These results present the first direct evidence that hiss waves inside the density duct scatter electrons into the loss cone, resulting in their precipitation. While the observations show that the hiss waves scatter 10-100 keV electrons, ducted waves may propagate to higher magnetic latitude than nonducted waves and play a significant role in the loss of even higher energy (including relativistic) electrons (e.g., Miyoshi et al., 2020) depending on the conditions of density and magnetic field.
Case 2 shows strong diffusion of electrons during the enhancement of structureless hiss waves. Compared to Case 1, there are fewer variations in the precipitating electron flux, where hiss waves are less modulated. This is consistent with our suggestion that the hiss wave intensity is important for scattering electrons.
Strong diffusion (precipitating/trapped ratio ∼1) is sometimes observed in the presence of strong hiss waves. The strong diffusion rate of electrons with ∼10 keV calculated with the formula of Summers and Thorne (2003) is ≈ 3.2 × 10 −3 /s at = 5 and ≈ 8.3 × 10 −4 /s at = 7 . The fact that the strong diffusion is observed during hiss waves enhancement is consistent with calculations of previous studies based on the observations of hiss wave intensity (Ma et al., 2016(Ma et al., , 2021. Furthermore, the electron loss time scales calculated in previous studies by enhanced hiss waves are consistent with our study (e.g., Ripoll et al., 2016).
The reported events suggest that the electron scattering leading to precipitation occurs near the magnetic equator up to ∼15° MLAT in Case 1, while within ∼20° MLAT in Case 2. The scattering region in Case 1 extends to higher latitude than the typical one of whistler-mode chorus waves in the midnight-to-dawn sector, |MLAT| < ∼10° (S. Kasahara et al., 2019). The observed high-latitude scattering could be explained by the distribution of dayside hiss waves (e.g., Meredith et al., 2018) expanding up to higher latitude than that of the nightside chorus waves (e.g., Meredith et al., 2012). However, future statistical analysis is needed to determine whether this high-latitude scattering occurs frequently in resonance with hiss waves or whether it happens in these particular cases by accident.

Summary
We directly detected electron precipitation during hiss wave enhancements with in situ measurements made by ERG/MEP-e with a high angular resolution. Furthermore, we examined the background conditions (the electron density and magnetic field strength) for strong diffusion to occur. The ERG satellite observed intense hiss waves with the power spectral density of >∼100 pT 2 /Hz and a typical frequency of 100-1,000 Hz on the dayside on 5 July 2018 (Case 1) and 11 May 2019 (Case 2) in association with electron flux enhancements in the loss cone. Case 1 with the ambient electron density modulation indicated that hiss waves are stronger in the higher density region and strong electron scattering occurs. Our direct measurements of precipitating electrons suggest that the density enhancement promotes the electron precipitation as implied by previous studies (Breneman et al., 2015;Smith, 1961). Case 2, where the density is high without significant modulations, showed that the structureless hiss waves also cause strong electron precipitation without clear modulation. On the other hand, the magnetic field intensity hardly correlates with the wave and the density in the events of our study. Our direct observations also indicate the occurrence of strong scattering leading to substantial loss cone filling at low latitudes, up to |MLAT| ∼ 15°.

Data Availability Statement
Science data of the ERG (Arase) satellite were obtained from the ERG Science Center (ERG-SC) operated by ISAS/JAXA and ISEE/Nagoya University (https://ergsc.isee.nagoya-u.ac.jp/index.shtml.en; Miyoshi, Hori, et al., 2018). In this study, we used the MEP-e L2-v01_01 (3Dflux), PWE/OFA L2-v02_03, PWE/HFA L3-v03_05, and MGF L2-v03_04 data obtained by ERG. The ERG orbital data L2-v03 were also used. The SPEDAS software (Angelopoulos et al., 2019) and ERG Plug-in tools were used for data analysis. Averaged power spectral density of wave magnetic field between ∼100 and ∼1,000 Hz (a), the high-pass-filtered density (b), and the high-pass-filtered background magnetic field strength (c). The electron density and magnetic field strength are normalized by 10-min smoothing of raw data. Vertical dashed lines indicate the timing of the high-pass-filtered density local maximum.

Acknowledgments
The work was supported by JSPS Kakenhi (20H01957, 18H03727, and 20H01959). Part of the work of T.H. and Y.M. was done at ERG-SC. The present study analyzed the MEP-e L2-v01_01 (3Dflux), PWE/OFA L2-v02_03, PWE/HFA L3-v03_05, and MGF L2-v03_04 data obtained by ERG. The ERG orbital data L2-v03 were also used. The ERG data were analyzed using the SPEDAS (the Space Physics Environment Data Analysis Software) framework (Angelopoulos et al., 2019) and ERG Plug-in tools.