Modulation of Energetic Electron Precipitation Driven by Three Types of Whistler Mode Waves

Precipitation into the Earth's atmosphere due to pitch angle scattering by plasma waves has been recognized as one of the major loss mechanisms for energetic electrons. In this study, we quantitatively evaluate their roles in precipitating electrons during a conjunction event with modulated electron precipitation observed at low altitudes by Electron Loss and Fields INvestigation and three types of whistler mode waves (hiss, plume hiss, and chorus) measured near the equator by Time History of Events and Macroscale Interactions during Substorms. Electron precipitation was observed from ∼50 keV to <1 MeV with a spatial modulation, suggested by a good correlation between L shell‐sorted precipitation fluxes and wave intensities. A quasi‐linear analysis supports the observed energy range of precipitation and the ratio of precipitating‐to‐trapped flux. Our findings reveal that the modulated energetic electron precipitation is driven by hiss, plume hiss, and chorus waves.

• Modulated electron precipitation from tens to hundreds of keV over L shells of 4-9 is observed by Electron Loss and Fields INvestigation at low altitudes • A good correlation is observed between the spatial variations of electron precipitation and wave intensities of hiss, plume hiss, and chorus • Quasi-linear modeling based on the observed wave and plasma parameters reproduced the observed electron precipitation

Supporting Information:
Supporting Information may be found in the online version of this article.
plume hiss drive 0.3-1 erg/cm 2 /s electron precipitation at lower L shells (Ma et al., 2020. Based on both an event analysis and a statistical study, plume hiss is suggested to be more efficient in driving electron precipitation than plasmaspheric hiss (W. Li et al., 2019;Ma et al., 2021).
Modulated electron precipitation on ultra-low frequency (ULF) scales has been reported by several studies with a period in the Pc4 or Pc5 frequency range (e.g., Brito et al., 2012;Jaynes et al., 2015;Manninen et al., 2010;Motoba et al., 2013;Qin et al., 2021;Rae et al., 2007Rae et al., , 2018Spanswick et al., 2005;Xia et al., 2016;. During these reported events, ULF oscillations modulated whistler mode wave amplitude and/or the size of the bounce loss cone and hence modulated the electron precipitation rates. On a longer timescale, the so-called "breathing mode," due to the solar wind buffeting of the magnetosphere, can also produce modulated electron precipitation (e.g., Breneman et al., 2015).
However, the observed precipitation modulation cannot always be explained by temporal variations due to ULF waves or solar wind variations. Furthermore, before the launch of Electron Loss and Fields INvestigation (ELFIN), electron measurements at low altitudes typically did not provide full pitch angle coverage with sufficient energy resolution to distinguish precipitating electrons from trapped electrons without ambiguity. In this study, we take advantage of the conjugate observation of electron distribution at low altitudes by ELFIN and wave and plasma distributions near the equator by Time History of Events and Macroscale Interactions during Substorms (THEMIS) to reveal the drivers of the modulated energetic electron precipitation.

Modulated Electron Precipitation at Low Altitudes
We use low-altitude observations from the ELFIN CubeSats to provide measurements of precipitating and mirroring energetic electrons over a broad L shell range (Angelopoulos et al., 2020). ELFIN is a dual-probe CubeSat mission launched on September 15, 2018, orbiting at an altitude of ∼450 km with an orbital period of ∼1.5 hr. Each probe is equipped with an Energetic Particle Detector (EPD) that measures electrons from ∼50 keV to 6 MeV with full pitch angle coverage. The time resolution of ELFIN EPD data is ∼0.14 s. In a full spin period (∼3 s), there are ∼20 electron measurements with varying looking directions. In this study, we binned the data into each 3-s time window in 18 pitch angle sectors covering from 0° to 180°. Figure 1 presents the ELFIN measurements of electron distributions as well as the solar wind and geomagnetic conditions during an interesting event, which occurred from 14:21 to 14:24 UT on November 27, 2020. The solar wind dynamic pressure remained relatively steady in the range of 1.5-2.5 nPa over 5 hr before the observed precipitation event (Figure 1a). The interplanetary magnetic field (IMF) was mostly southward until an hour before the event (Figure 1a), which is preferential for substorm activity when electrons are injected toward Earth. The Sym-H index, an indicator of the ring current strength, ranged from −24 to −8 nT, which was not intense ( Figure 1b). The AE index was continuously above 300 nT with the peak value reaching ∼800 nT during the preceding 5 hr, indicating on-going substorm activity ( Figure 1b). ELFIN-A observed modulated trapped and precipitating energetic electron flux in this event within 3 min covering L shells from 4 to nine on the dayside at magnetic local time (MLT) ∼11 hr (Figures 1c and 1d). The trapped electron flux was high (∼60 keV to <1 MeV at L > 6, and up to 3 MeV at L < 6), while the precipitating electrons were mainly below 1 MeV. The ratio of precipitating-to-trapped electrons was approaching one at tens to hundreds of keV, indicative of almost full loss cone, but remained <0.1 at higher energies ( Figure 1e). Electron pitch angle distributions (Figures 1f-1i) exhibited asymmetric distributions with higher electron flux within the loss cone (black solid lines) than that within the anti-loss cone (black dashed lines) at various energy channels. However, electron precipitation at >1 MeV was not intense and mostly occurred near the edge of the bounce loss cone (Figure 1i).
We suggest that the observed electron precipitation at tens to hundreds of keV energies is related to pitch angle scattering by whistler mode waves, instead of electromagnetic ion cyclotron (EMIC) waves, which typically account for electron precipitation at energies above several hundreds of keV (e.g., Blum et al., 2015;Capannolo, Li, Ma, Chen, et al., 2019;Jordanova et al., 2008;Z. Li et al., 2014;Miyoshi et al., 2008;Qin et al., 2018;.

Conjugate Observations of Plasma Waves Near the Equator
To identify the driver of modulated energetic electron precipitation and determine whether the observed modulation is spatial or temporal, we use plasma and wave measurements from the electrostatic analyzer, solid state telescope, search coil magnetometer (SCM), and fluxgate magnetometer (FGM) instruments onboard one of the five THEMIS probes (Angelopoulos, 2008;Auster et al., 2008;McFadden et al., 2008;Roux et al., 2008), which was orbiting near the magnetic equator and had two tight conjunctions with ELFIN-A and ELFIN-B (see Figure  S2 in Supporting Information S1 for ELFIN-B observations) near ∼1423 and 1545 UT, respectively (Figures 2a  and 2b). During the two tight conjunctions, the separation between the two probes is less than 1.5 hr in MLT. THEMIS-E took 3 hr (∼1400-1700 UT) to travel through L shells from 4 to 9, which is much longer than the ∼3 min used by ELFIN at low altitudes. Based on the total electron density inferred from the spacecraft potential, one can see that THEMIS-E was traveling from the plasmasphere to plasmaspheric plume regions near L∼6 and then entered the plasma trough region at higher L shells (Figure 2c). Measurements of wave magnetic and electric fields indicate the intensification of hiss, plume hiss, and chorus waves in the three different regions, respectively (Figures 2d and 2e). The magnetic field data from SCM on THEMIS-E are still pending calibration beyond 2017, although the relative intensity showing wave activities is not affected X.-J. Zhang et al., 2022). Measurements of magnetic spectral density from the Plasma Wave Experiment onboard Arase (Kasahara et al., 2018) during a conjunction period within this day (see Figure S1 in Supporting Information S1 for detailed information) were used to calibrate the magnetic spectral density values from THEMIS-E (e.g., Dudok de Wit et al., 2022;Santolík et al., 2021). The magnetic spectral density was scaled up by a factor of 2 to match the observations from Arase during the conjunction. Hiss and plume hiss were intense with wave amplitudes reaching ∼100-200 pT, while chorus waves were not strong (10-20 pT) (Figure 2f). These observations show the plasma wave activity near the equatorial plane in the L shell range of 4-9, which is the region where modulated electron precipitation was observed by ELFIN. Whistler mode waves, including hiss, plume hiss, and chorus waves, with modulating amplitudes together with varying plasma conditions at different L shells, may contribute to the observed modulated electron precipitation. From ∼16:00 to 18:30 UT (at L > 7.5), H + band EMIC wave activities were also observed by THEMIS-E with wave magnetic amplitudes, integrated over frequencies from the helium gyrofrequency to the hydrogen gyrofrequency, less than 0.2 nT (not shown).

Quantification of Electron Precipitation Using Quasi-Linear Theory
To estimate the ratio of precipitating-to-trapped electron fluxes due to wave-particle interactions, we apply the UCLA Full Diffusion Code (Ma et al., 2020Ni et al., 2008Ni et al., , 2011 based on quasi-linear theory to compute the diffusion coefficients. We use wave spectra and surrounding plasma parameters, including total electron density and magnetic field magnitude, at three time snapshots (14:19, 14:48, and 15:45 UT, see orange dashed lines in Figure 2) for hiss, plume hiss, and chorus waves, respectively. Survey mode plasma wave measurements from THEMIS-E do not provide the wave normal angle (WNA) and the burst mode was not operating during this event. Thus, we assume a Gaussian distribution of WNA with the peak WNA to be parallel to the magnetic field line and a WNA width of 30° (Hartley et al., 2018;Santolík et al., 2014;Taubenschuss et al., 2014). Resonant harmonic numbers from −10 to 10 and magnetic latitudes within 50° are used in the calculation including effects from both cyclotron and Landau resonances. The calculated bounce-averaged electron pitch angle diffusion rates are shown in Figures 3a-3c. Parameters including L shell, background magnetic field magnitude, the ratio of plasma to electron gyro frequency, and wave amplitude, used to calculate the pitch angle diffusion rates, are included in Table S1 in Supporting Information S1. For the three wave modes, the energies of electrons subject to efficient scattering are in the range of several keV to hundreds of keV. Landau resonance occurred at low energies or near pitch angles close to 90°. In this study, we focus on the diffusion rates near the loss cone indicated by the magenta dashed lines to evaluate electron precipitation. Among the three waves, chorus waves drive the least efficient pitch angle scattering of electrons due to the low wave amplitude (19 pT). The hiss and plume hiss drive more efficient pitch angle scattering given their large wave amplitudes (222 and 121 pT) at the selected times.
The pitch angle diffusion rates at the loss cone and the strong diffusion limit ( ) for varying energies are plotted in Figures 3d-3f as red solid and dashed lines, respectively. The derived pitch angle diffusion rate due to plume hiss is very close to the strong diffusion limit at tens to hundreds of keV, although the diffusion rates due to all three wave modes do not exceed the strong diffusion limit. The diffusion rates decrease significantly at energies below 10 keV for hiss and plume hiss waves but remain high down to ∼4 keV for chorus waves since their upper-frequency limit is higher to interact with lower energy electrons. However, this difference cannot be captured by ELFIN since electron measurements only extend down to ∼60 keV.
Based on these diffusion rates near the loss cone, we calculate the loss cone filling index (Ni et al., 2014), which is similar to the ratio of precipitating-to-trapped electrons from the ELFIN observations, as following where 0 is the modified Bessel function of the first kind, 0 = √ (< >| ) is the square root of the ratio of strong diffusion limit and pitch angle diffusion rate at the loss cone at various energies, and is an integration variable. The calculated loss cone filling index is shown in Figures 3d-3f as green lines. The peak loss cone filling index is around tens of keV and drops to below 0.1 at 1 MeV for the three wave modes.
To better compare the observed and modeled electron precipitation, we binned observations from both THEMIS and ELFIN and the modeling results into L-shell bins of 0.05 width, from L = 4 to L = 9 (Figure 4). Note that the color bar in this plot represents the universal time (UT). Electron density and wave amplitude variations (Figures 4a and 4b) near the edge of the plasmasphere and plume regions become smoother and less distinct than those shown in Figure 2 due to binning. Within the blue and orange shaded areas (corresponding to the region where hiss and chorus waves were observed by THEMIS), THEMIS and ELFIN were located at a similar L shell and UT. Within the green shaded region, THEMIS and ELFIN were crossing a similar L shell, but with ∼0.5-1 hr time difference. The observed electron precipitation at 100 keV shows a similar trend to the observed whistler mode wave amplitude variations, especially during the two tight conjunctions (Figure 4c). Figure 4d is the modeled loss cone filling index at 100 keV binned by L shell, and it well reproduced the observed ratio of precipitating-to-trapped electron flux by ELFIN-A. The hiss-driven precipitation leads to a ratio of precipitating-to-trapped electrons reaching 0.8 with two peak structures, while chorus waves, in this case, only drive electron precipitation with a ratio around 0.4. The modeled plume hiss-driven precipitation ratio is lower than the observed, which may be due to the UT difference in this case. THEMIS provided plume hiss measurements (∼14:50 UT) ∼30 min later than the ELFIN measurements of electron precipitation (∼14:23 UT) during the recovery of a substorm, indicated by the AE index (Figure 1b). The underestimated electron precipitation reproduced based on the THEMIS measurements may be due to the decrease in plume hiss wave intensity or the narrowing of plumes due to the temporal evolution. However, the trend of precipitation ratio as a function of L shell is overall well reproduced. The peaks in L shell shift within 0.2 L are reasonable considering the uncertainties in the IGRF magnetic field models. At the higher energy of 500 keV (Figures 4e and 4f), the precipitation ratio becomes lower; it decreased to ∼0.2 for hiss-driven precipitation and ∼0.1 for chorus-driven precipitation. Due to the low counts of electrons at high energies (>100s keV), the obtained precipitation ratio at 500 keV shown in Figure 4e becomes sparse at L > ∼7 during this event. Nevertheless, the available measurements show remarkable agreement between the observations and modeling, especially in terms of the trend of precipitation ratio as a function of L shell.

Summary
In the present paper, we analyzed an intriguing event of modulated electron precipitation due to whistler mode hiss, plume hiss, and chorus waves. The modulation of low-altitude electron precipitation is highly correlated with spatial variations of whistler mode wave amplitudes of hiss, plume hiss, and chorus waves in the plasmasphere, plume, and plasma trough, respectively. Using quasi-linear modeling, the observed ratio of precipitating-to-trapped electrons is well reproduced. These three types of whistler mode waves overall drive electron precipitation with energies ranging from tens of keV to less than 1 MeV, while chorus waves drive electron precipitation at slightly lower energies because of the higher wave frequency. The reproduced precipitation ratio (peaking at ∼0.4) due to plume hiss is lower than the observed one (peaking at ∼1), which is likely due to the ∼0.5 hr difference in UT between THEMIS and ELFIN, and associated variability of hiss wave intensity. The plume region may become narrower as time goes on and the spatially averaged wave amplitude becomes smaller ( Figure 4). However, the two-peak structure is well reproduced. Moreover, plume hiss within the plume regions can still produce a ratio of precipitating to trapped electrons close to 1 at tens of keV, although they may become narrower spatially (Figures 3b and 3e). Therefore, the plume hiss can drive very efficient electron precipitation (Figure 3b), in agreement with previous studies (W. Li et al., 2019;Ma et al., 2021) showing the importance of plume hiss in driving electron precipitation compared to the other two whistler mode waves. Overall, the remarkable correlation between the ELFIN observations of electron precipitation, THEMIS observations of whistler mode wave amplitudes, and the modeled precipitation ratio suggest that the observed modulation of electron precipitation is likely a spatial variation in this event.
These results, obtained by combining observations and modeling, suggest that whistler mode waves, including hiss, plume hiss, and chorus at various regions from plasmasphere, plume, and trough, contribute together to modulated electron precipitation (tens to hundreds of keV) into the upper atmosphere in an extensive region of the coupled magnetosphere-ionosphere system. The spatial variation of their wave amplitude and ambient plasma conditions affects the efficiency of electron pitch angle scattering, which leads to the modulated energetic electron precipitation observed at low altitudes. Since plasmaspheric hiss, plume hiss, and chorus occur over a wide range of MLT sectors on the dayside, our findings imply that modulations of electron precipitation caused by the three types of whistler mode waves are likely common in the broad region of the dayside magnetosphere, particularly when a plume region exists.

Data Availability Statement
Data from the THEMIS are publicly available at http://themis.ssl.berkeley.edu/data/themis. Data from the ELFIN are publicly available at https://data.elfin.ucla.edu/. Data from the Arase are publicly available at https://ergsc. isee.nagoya-u.ac.jp/. The authors use SPEDAS in IDL to process data files . XS, WL, and QM would like to acknowledge the NASA Grants 80NSSC19K0845, 80NSSC20K0698, 80NSSC20K0196, and 80NSSC21K1312, NSF Grants AGS-2019950 and AGS-1847818, and the Alfred P. Sloan Research Fellowship FG-2018-10936. The UCLA team acknowledges NASA awards 80NSSC22K1005 and NAS5-02099 and NSF Grant AGS-2019950. The authors acknowledge the ELFIN mission for providing electron measurements at low altitude. The authors also thank the following individuals for data from the THEMIS mission: J. W. Bonnell and F. S. Mozer for EFI data, O. LeContel for SCM data, and K. H. Glassmeier, U. Auster and W. Baumjohann for FGM data provided under the lead of the TU-BS and with financial support through the German Ministry for Economy and Technology and DLR under contract 50 OC 0302.