Based on the measurements of ~100-keV to 10-MeV electrons from the Magnetic Electron Ion Spectrometer (MagEIS) and Relativistic Electron and Proton Telescope (REPT) on the Van Allen Probes, the radiation belt electron energy spectra characterization and evolution have been investigated systematically. The results show that the majority of radiation belt electron energy spectra can be represented by one of three types of distributions: exponential, power law, and bump-on-tail (BOT). The exponential spectra are generally dominant in the outer radiation belt outside the plasmasphere, power law spectra usually appear at high L-shells during injections of lower-energy electrons, and BOT spectra commonly dominate inside the plasmasphere at L>2.5 during relatively quiet times. The main features of three types of energy spectra have also been revealed. Specifically, for the BOT energy spectrum, the energy of local flux maximum usually ranges from approximately hundreds of keV to several MeV and the energy of local flux minimum varies from ~100 keV to ~MeV, both increasing as L-shell decreases, confirming the plasmaspheric hiss wave scattering to be the main mechanism forming the BOT energy spectra. Statistical results using 4-year observations from the Van Allen Probes on the relation between energy spectra and plasmapause location also show that the plasmasphere plays a critical role in shaping radiation belt electron energy spectrum: the peak location of BOT energy spectra is ~1 L-shell inside the minimum plasmapause, where BOT energy spectra mostly form in ~1–2 days as a result of hiss wave scattering.

Key Points

Most radiation belt electron energy spectra can be represented by one of three distributions: exponential, power law, and bump-on-tail
Exponential spectra dominate outside the plasmasphere; power law spectra often appear at high L during injections of lower-energy electrons
Bump-on-tail spectra dominate inside the plasmasphere at L<2.5 and are caused by hiss wave scattering

1 Introduction

The radiation belts are the regions where energetic electrons and protons are geomagnetically trapped and azimuthally drift around the Earth. Understanding the dynamics of radiation belt particles is critical due to both scientific interest and practical needs. The radiation belt electron energy spectrum, as an essential feature of radiation belt electrons, provides valuable information of physical mechanisms acting on the radiation belt electrons. Since 1960s, the radiation belt electron and proton energy spectra have attracted plenty of interest. Studies of the radiation belt proton and electron energy spectra have been carried out, and corresponding physical processes in the radiation belts were examined (Fischer et al., 1977; Freden et al., 1965; Galper et al., 1999; Imhof & Smith, 1965; Naugle & Kniffen, 1963; Paulikas et al., 1967; Pizzella et al., 1962). Pizzella et al. (1962) studied the 40- to 110-keV trapped electron energy spectrum in the inner belt and concluded that the energy spectrum of inner belt electrons is a power law spectrum with a differential exponent of – (1.0±0.2), which ruled out the neutron-albedo theory as the main source of inner belt trapped electrons. Imhof and Smith (1965) showed ~280-keV to 4.88-MeV electron energy spectrum measurements in October–November 1963, which were taken with a plastic scintillation spectrometer on a polar orbiting satellite with altitudes of 288–355 km. Their results indicated that the radiation belt electron energy spectrum can be fitted to exponential distributions, and significant temporal variations existed for the electron energy spectrum at L>3 during this time period, while generally the spectrum hardened at L=3-5 and softened at L>5 with increasing L. Galper et al. (1999) have also studied the energy spectrum of the long-lived unstable high-energy electron belt created on 24 March 1991 using measurements from the Mariya-2 magnetic time-of-flight spectrometer telescope. Their results suggested that 10- to 50-MeV electron energy spectrum in this unstable electron belt agreed well with a power law distribution E^-α with α=13±5. The majority of these early studies suggest that the energy spectra of radiation belt electrons primarily show fluxes steeply falling with increasing energies. However, there are also a few early studies that have suggested the existence of a different type of energy spectrum with higher fluxes at higher energies (Vakulov et al., 1975; West et al., 1981). Vakulov et al. (1975), using electron measurements of three energy bands (300–600 keV, 600–900 keV, and 900 keV–2.3 MeV) obtained from the Molniya 1, showed that during a moderate magnetic storm of December 1972, the energy spectra of outer belt electrons with a maximum in the energy band 600 – 900 keV were observed. They speculated that these observations could be due to the faster intensity decrease in the first energy channel. West et al. (1981), using 60-keV to 3-MeV electron data in seven differential energy channels from Ogo 5, studied the dynamics of energetic electrons in the Earth's outer belt during several storms in 1968 and early 1969. They showed the observations of energy spectra with a maximum at ~1.5 MeV and a minima at ~500 keV and suggested that these energy spectra were formed due to energy-dependent decay rate. However, these observations have not attracted much attention in the community mainly due to low quality of early data as well as lack of extensive spatial/temporal coverage of measurements.

Previous studies on the radiation belt electron energy spectrum suffer from quality of satellites' data and limited measurements. Since the launch of the Van Allen Probes, which operates in an elliptical orbit with an apogee of ~5.8 R_E, a perigee of ~600 km, and an inclination of ~10°, clean radiation belt electron measurements with wide energy and L-shell coverage as well as very fine energy resolution enabled more detailed studies of radiation belt dynamics. Event-based electron energy spectrum studies have been performed using data from the Van Allen Probes and underlying physical mechanisms have been studied. For the inner belt and slot region, Fennell et al. (2015) presented observations of ~30-keV to 4-MeV inner belt and slot region electrons from the Magnetic Electron Ion Spectrometer (MagEIS) on the Van Allen Probes and showed that with no MeV electrons observed above background level in the inner belt, the energy spectrum in the low L region are steeply falling for energies above ~400 keV and relatively flat below ~100 keV. Li et al. (2015) studied MeV electrons in the inner belt using data from the Relativistic Electron-Proton Telescope (REPT) on the Van Allen Probes and derived the energy spectrum for the upper limit of MeV electrons in the inner belt, which is more steeply falling than the model predictions. Ukhorskiy et al. (2014), using observations from the Radiation Belt Storm Probes Ion Composition Experiment (RBSPICE) on the Van Allen Probes, showed highly structured features in the energy versus L-shell distribution of tens to hundreds of keV electrons in the inner belt, confirming the previous observations from low-altitude measurements (e.g., Imhof et al., 1981; Imhof & Smith, 1965; Sauvaud et al., 2013). Their modeling results suggested that the formation of such unexpected “zebra stripes” are produced by Earth's rotation. Liu et al. (2016), also using RBSPICE measurements, showed that an analytic model of particle distribution under a monochromatic or static azimuthal electric field can well reproduce the structural features and evolution properties of the observed zebra stripes, while the amplitude of the zebra stripes also has a positive correlation with the geomagnetic activity. Zhao, Baker, Califf, et al. (2017), using data from MagEIS instruments, studied the magnetic local time (MLT)-dependent energy spectra of energetic electrons in the slot region during an injection event, which suggested the existence of an MLT-dependent mechanism in the low L region accounting for the deep penetration of energetic electrons. Zhang et al. (2019) and Xiang et al. (2019), using data from the Demeter satellite as well as the Van Allen Probes combined with modeling, showed that the hundreds of keV quasi-trapped electron energy spectrum at the inner edge of the inner belt fit CRAND spectrum very well, further confirming the results of Li et al. (2017) that the CRAND is the major source for quasi-trapped electrons in the inner edge of the inner belt. For the outer belt, Jaynes et al. (2015) focused on the time interval of 13–22 September 2014 using data from MagEIS and REPT instruments on the Van Allen Probes and showed the energy spectra evolution during this time interval. They found that during times of active solar wind forcing the energy spectrum can be better described as an exponential distribution, while during the times of electron enhancements the energy spectrum is featured with broad and almost flat distribution from ~100 keV to ~ 1 MeV. Zhao et al. (2016), Zhao, Baker, Jaynes, et al. (2017), using data from MagEIS and REPT instruments on the Van Allen Probes, showed the energy-dependent features of electron flux variations and its correlation with solar wind parameters/geomagnetic indices. Most recently, Reeves et al. (2016) studied the energy and L-shell dependence of radiation belt electrons using data from Helium Oxygen Proton Electron and MagEIS instruments on the Van Allen Probes. They found that electron flux enhancements at all L-shells, especially the slot region and inner zone, are more common at lower energies, while the energy- and L shell-dependent losses, which are likely caused by whistler mode hiss wave scattering often produce S-shaped outer belt boundary where the fluxes of higher energy electrons, are higher than lower energy electrons. Combining the radial diffusion with a data-driven whistler mode hiss wave scattering model, Ripoll, Loridan, et al. (2016), Ripoll, Reeves, et al. (2016) confirmed that the observed energy- and L-dependent features of radiation belt electrons are indeed caused by hiss wave scattering through detailed simulations. Similarly, Ma et al. (2016), using a 3-D diffusion simulation, demonstrated that the energy-dependent electron flux variations in the slot region are caused by the energy-dependent radial diffusion and local plasma wave scattering. Also, using a 3-D diffusion simulation, Ripoll et al. (2019) further confirmed that the energy-, L-, and pitch angle-dependent electron flux variations in the slot region during quiet times are consistent with hiss wave scattering. From the perspective of energy spectrum, Zhao, Ni, et al. (2019) reported the observations of a reversed energy spectrum with more high-energy electrons and fewer low-energy electrons in the energy range of hundreds of keV to ~2 MeV, called the bump-on-tail (BOT) energy spectrum, using data from the Van Allen Probes. They showed that inside the plasmasphere at L≳2.6, the BOT energy spectrum is actually the most prevalent energy spectrum, and the formation of this specific type of energy spectrum can be attributed to the energy-dependent losses caused by plasmaspheric hiss wave scattering. Furthermore, through detailed modeling, Ni et al. (2019) showed that the formation and evolution of the BOT energy spectrum inside the plasmasphere are highly sensitive to the ambient magnetic field as well as hiss wave frequency spectral distribution.

Though many previous studies involved the radiation belt electron energy spectra analysis, detailed systematic analysis on radiation belt electron energy spectra have not yet been conducted. A thorough examination of radiation belt electron energy spectra can provide important information on the relative effectiveness of physical mechanisms for electrons with different energies in different regions under different geomagnetic conditions. In this study, using data from MagEIS and REPT instruments on the Van Allen Probes, we examined the characterization and evolution of radiation belt electron energy spectra through both event studies and statistical analysis. Detailed observations of radiation belt electron energy spectra during one intense and one moderate storms are shown in section 2. Categorization and characterization of electron energy spectra during the two storms are shown in section 3. In section 4 we show the statistics of radiation belt electron energy spectra and the relation between the radiation belt electron energy spectra distribution and the plasmapause location. Section 5 provides a summary.

2 Radiation Belt Electron Energy Spectrum Evolution During Two Storms

In this section, we focus on the energy spectrum evolution during two geomagnetic storms, one intense storm and one moderate storm, using data from MagEIS and REPT instruments on the Van Allen Probes. Figure 1 shows the 1-min-averaged fluxes of ~470 keV, 900 keV, 2.1 MeV, 5.2 MeV, and 7.7 MeV electrons during 6–11 September 2017, along with the Dst and AE indices. The L-shell used in this study is the McIlwain L in T89D model (Tsyganenko, 1989). During this time period, an intense geomagnetic storm occurred with minimum Dst index of -142 nT and elevated AE index up to ~1,500 nT. During this intense storm, in the outer belt, fluxes of electrons of all energies shown in Figure 1 increased significantly, and faster flux enhancements occurred for lower-energy electrons. Electrons with energies of hundreds of keV all the way up to ~1 MeV have penetrated into the low L region during this storm (Claudepierre et al., 2019), while multi-MeV electrons did not penetrate deeply into the slot region, which is also consistent with the reported impenetrable barrier (Baker et al., 2014). Note that in this study we use MagEIS background-corrected data only, which are mostly available for ≳230-keV electrons on the Van Allen Probes-A during the whole mission and ≳30 keV electrons on the Van Allen Probes-B since March 2014.

Details are in the caption following the image — **Figure 1**
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One-minute-averaged fluxes of radiation belt electrons with various energies, using data from Magnetic Electron Ion Spectrometer (MagEIS) and Relativistic Electron-Proton Telescope (REPT) instruments on the Van Allen Probes, along with the Dst index (in black) and AE index (in red) during 6 – 11 September 2017.

Figure 2 shows the evolution of energy spectra of ~100-keV to 10-MeV electrons at L=3.0, 3.5, 4.0, 4.5, 5.0, and 5.5 during the September 2017 storm. In this study, we use MagEIS background-corrected data for <2 MeV electrons and REPT data for >2-MeV electrons. As shown in Figure 2, during the intense storm of September 2017, the electron fluxes increased dramatically at L~3 – 4 across a wide energy range, while at higher L-shells the electron fluxes showed different behaviors. During the main phase of the storm, flux decreases especially at higher L for higher energy electrons were observed, which are likely due to the adiabatic effect (e.g., Li et al., 1997), while some could also be due to the actual loss of electrons (e.g., Hudson et al., 2015; Xiang et al., 2017). During the recovery phase, the electron fluxes started to increase, while fluxes of lower-energy electrons increased faster and after the enhancements the loss rate was also higher, and higher-energy electron fluxes increased more gradually (e.g., Zhao, Baker, Jaynes, et al., 2017; Zhao, Baker, et al., 2018, 2019). The BOT energy spectra were also clearly observed at L=3.5 and 4 prior to the storm, with local flux maxima at ~1 MeV, local flux minima at ~300–400 keV, and the flux differences between maxima and minima up to ~1–2 orders of magnitude. The BOT energy spectra disappeared during the storm when the significant flux enhancements of hundreds of keV electrons occurred.

Figure 3 shows the radiation belt electron fluxes during a moderate geomagnetic storm of 23 August 2016. The format of Figure 3 is the same as Figure 1. This moderate geomagnetic storm has a minimum Dst index of -74 nT and AE index up to ~800 nT. Comparing electron fluxes before and after the storm, as shown in Figure 3, flux enhancements of hundreds of keV electrons were observed, while for ≳1 MeV electrons the fluxes decreased during this storm.

Figure 4 shows the evolution of electron energy spectra at different L-shells during the storm of August 2016. The format of Figure 4 is the same as Figure 2. It is clear from Figure 4 that comparing prestorm and poststorm observations, fluxes of hundreds of keV electrons increased significantly at L ~ 3.5–5.5, while ≳1 MeV electron fluxes decreased notably at L~4 – 5. The flux decreases at the storm main phase were also observed, which still suggests the adiabatic effect and actual loss. It is also clear that as the electron fluxes recovered, the fluxes of lower-energy electrons increased first and higher-energy electron fluxes increased later, while lower-energy electrons also decayed faster afterward, which is consistent with the observations during the storm of September 2017. The BOT energy spectra were still present prior to this moderate storm and even at a wider L range comparing to the storm of September 2017. Prior to the storm, the BOT spectra were observed at L=3.5 – 5, with local flux maxima at ~1 – 2 MeV and local flux minima at several hundreds of keV. As the storm occurred, the BOT energy spectra disappeared at L~4 – 5 due to the dramatically increased fluxes of hundreds of keV electrons and also decreased MeV electron fluxes. At L~3.5, though fluxes of electrons with energies less than ~700 keV also increased significantly, fluxes of ≳700-keV electrons remained almost unchanged and the BOT spectra were preserved in this region during this storm. It is also intriguing from Figure 4 that during the storm recovery phase, at L=4, as the fluxes of ~100- to 200-keV electrons decreased faster than higher-energy electrons after the enhancements, a new bump in the energy spectrum started to form (as the red trace shows), with the flux maximum located at ~400–500 keV and the flux minimum at ~200 keV.

3 Radiation Belt Electron Energy Spectra Categorization and Characterization During Two Storms

In section 2, radiation belt electron energy spectrum evolution during one intense geomagnetic storm and one moderate storm are shown and some intriguing features have been discussed. In this section, to study the energy spectrum evolution in detail, we focus on the categorization and characterization of radiation belt electron energy spectra during the two storms.

Based on the observations during the two storms, most electron energy spectra in the radiation belts can be categorized into one of three distributions: exponential distribution, power law distribution, and BOT distribution. To categorize the energy spectra, we use <2-MeV electron background-corrected data from MagEIS and >2 MeV electron data from REPT on the Van Allen Probes-B. It is worth mentioning that sometimes >5-MeV electrons have very low fluxes close to background level likely caused by the contamination from galactic cosmic rays and including those data could interfere with the categorization process, thus data of >5 MeV electrons are only included if the fluxes are greater than 10^-2/cm²/s/sr/keV. For each energy spectrum, we categorize it as follows: (1) first, using the same criteria as Zhao, Ni, et al. (2019), if a flux maximum and a flux minimum can be identified with corresponding energy of flux maximum greater than that of flux minimum, and the ratio of the flux maximum to the minimum is greater than 3, then the energy spectrum is identified as the BOT energy spectrum, and (2) if an energy spectrum is not identified as the BOT spectrum, then the energy spectrum is fitted to the exponential distribution $urn:x-wiley:21699380:media:jgra55019:jgra55019-math-0001$ and the power law distribution j = j₀E^−α, where j is the spin-averaged fluxes, E is the electron energy, j₀, α, and E₀ are free parameters. The root-mean-square deviation ( $urn:x-wiley:21699380:media:jgra55019:jgra55019-math-0002$ , where $urn:x-wiley:21699380:media:jgra55019:jgra55019-math-0003$ is the fitting results of fluxes and n is the number of data points) is then calculated between fitting results and observations and the energy spectrum is categorized as the one distribution with smaller RMSD. However, if RMSDs of fittings to both distributions are greater than 0.5, which indicates bad fits to these distributions, the energy spectrum is then categorized as the undefined energy spectrum.

In addition, to analyze the characteristics of the BOT energy spectrum in more detail, the energy spectrum identified as BOT is fitted to the distribution $urn:x-wiley:21699380:media:jgra55019:jgra55019-math-0004$ , where j is the spin-averaged flux, E is the electron energy, and j₀, j₁, α, E₀, and σ are free parameters. This distribution represents the BOT as a combination of a power law distribution and a Gaussian distribution. This distribution can well represent most observed BOT energy spectra: based on the fitting results of BOT energy spectra during 2017, ~ 97% of BOT energy spectra have fitting results with RMSDs less than 0.5.

Figure 5 shows examples of different energy spectra and the categorization process. In Figure 5, the black cross signs and diamond signs represent data used in the categorization process from MagEIS and REPT instruments, respectively. The gray diamond signs show data from REPT, which are not included in the categorization process due to very low fluxes. Three energy spectra are identified as exponential (left panel), power law (middle panel), and BOT spectrum (right panel), respectively. As the right panel shows, for this energy spectrum, a flux maximum and a minimum (as indicated by dotted lines) are identified with energy of the flux maximum greater than that of the flux minimum, and the ratio of the flux maximum to the minimum is greater than 3; thus, this energy spectrum is identified as the BOT spectrum. This spectrum is then fitted to the BOT distribution, and the red dashed line shows the fitting results. As a comparison, we also show the fitting results of this spectrum to the exponential (purple dashed line) and power law distributions (cyan dashed line). It is clear that this energy spectrum can be well represented by the BOT distribution, and the corresponding RMSD (shown at the bottom of the panel) between fitting results and observations is very small; while the exponential and power law distributions fail to represent the main features of this energy spectrum and the corresponding RMSDs are quite large. The energy spectra in the left and middle panels do not meet the criteria for BOT spectrum, so they are fitted to exponential and power law distributions and identified as the corresponding spectrum with smaller RMSD.

Using these criteria, the radiation belt electron energy spectra are categorized and the fitting parameters are calculated during the two storms discussed in section 2. Figure 6 shows the categorization of energy spectra and the corresponding fit parameters of each type of energy spectra, during the intense storm of September 2017 (left panels) and the moderate storm of August 2016 (right panels). Note that no results at L<2.5 are shown due to potential contamination from inner belt protons. Comparing to Figures 2 and 4, by categorizing and fitting energy spectra, Figure 6 shows more detailed information of evolution of energy spectra during these two storms.

Figures 6a and 6j show the categorization of energy spectra during the two storms, with exponential spectra in purple, power law spectra in cyan, BOT spectra in red, and undefined spectra in grey. The black lines show the minimum L (across all MLT) of the plasmapause using the empirical model from Liu et al. (2015), which is a function of SYM-H, AE, AL, AU, and Kp indices and is established based on THEMIS measurements during 2009 – 2013. It is clear from Figure 6a that prior to the storm of September 2017, the exponential energy spectra dominated at L~4 – 6, while BOT energy spectra dominated at L~3 – 4 inside the plasmapause. As soon as the storm occurred, the power law energy spectra replaced exponential energy spectra at L~4 – 6, which is likely due to the injection of lower-energy electrons and flux decrease of higher energy electrons, while BOT energy spectra also disappeared mainly due to the significant flux enhancements of hundreds of keV electrons. During the storm recovery phase, the energy spectra in the outer radiation belt were mainly exponential spectra. The situation is similar with the storm of August 2016, with some differences regarding the BOT energy spectra. Prior to the storm of August 2016, as Figure 6j shows, the BOT energy spectra were observed at an even wider L range (~3 – 5), while as soon as the storm occurred, though those BOT energy spectra at higher L disappeared, the BOT energy spectra at lower L (~3-3.5) preserved over this time period due to insufficient flux enhancements of lower-energy electrons at low L region.

Figures 6b and 6k show the coefficient E₀ of exponential energy spectra during the two storms. As for the exponential energy spectra, higher E₀ suggests a harder energy spectrum with more high-energy electrons and fewer low-energy electrons. Prior to both storms, E₀ of exponential energy spectra was ranging between ~400 and ~700 keV, with higher E₀ at lower L-shells, suggesting higher fluxes of higher-energy electrons at the center of outer radiation belt. When the storms occurred, E₀ suddenly decreased to ~200 – 300 keV across a wide L range. The sudden decrease of E₀ at the storm main phases indicates that the energy spectrum became softer, which is mainly caused by the fast flux enhancements of lower-energy electrons and flux decreases of higher-energy electrons due to adiabatic effect and real loss. This is consistent with the observations shown in Reeves et al. (2016). As the storm recovered, E₀ dramatically increased for September 2017 storm, indicating the significant flux enhancements of >MeV electrons during the recovery phase of this storm along with the faster loss of lower energy electrons consistent with the results shown in Reeves et al. (2016) and Ripoll, Loridan, et al. (2016), Ripoll, Reeves, et al. (2016), Ripoll et al. (2019); however, for August 2016 storm, E₀ almost did not change during the recovery phase, suggesting that during this storm >MeV electrons did not exhibit significant flux enhancements in the outer belt. Comparing E₀ before and after the storms, it is clear that the storm of September 2017 caused significant flux enhancements of higher-energy electrons, which lead to harder energy spectra in the center of outer belt, while the storm of August 2016 softened the energy spectra in the outer belt potentially due to loss and lack of acceleration of higher-energy electrons.

Figures 6c and 6l show the coefficient α of power law energy spectra. The power law energy spectra were not dominant in the radiation belt during these two storms. At the storm main phases, power law energy spectra appeared at high L mainly due to injection of lower-energy electrons and α was ~4 – 5 for both storms; during the recovery phase of August 2016 storm, power law energy spectra were present at L~4 with α decreasing with time, suggesting hardening energy spectra after the storm which could be caused by faster loss of low-energy electrons due to hiss wave scattering, consistent with the results from Reeves et al. (2016) and Ripoll, Loridan, et al. (2016), Ripoll, Reeves, et al. (2016), Ripoll et al. (2019). At L~2.5 – 3 some undefined spectra were present, suggesting bad fits which are mainly because of very low fluxes of >MeV electrons in the slot region.

Figures 6d–6f and 6m–6o show the parameters of BOT energy spectra using observations only: the energy channel corresponding to flux maximum, the energy channel corresponding to flux minimum, and the ratio of flux maximum to minimum. For the storm of September 2017, BOT energy spectra were seen inside the plasmapause prior to the storm, the peak of the bump was located at ~1 – 2 MeV, and the energy of flux minimum was around hundreds of keV, while the ratio of flux maximum to minimum ranged from ~3 to ~10. When the storm occurred, BOT energy spectra disappeared mainly due to the flux enhancements of hundreds of keV electrons. Prior to the storm of August 2016, due to a more expanded plasmasphere, BOT energy spectra were seen over a wider L range; while as the storm occurred, BOT spectra disappeared at higher L but at L~3 – 3.5 BOT spectra persisted during this storm. The energy channel of flux maximum was still ~1 – 2 MeV, and the energy of flux minimum ranged from ~300 keV to ~1 MeV. The ratio of flux maximum to minimum was even higher compared to the storm of September 2017, which was ~10 – 100 prior to the storm and ~ 10 during the storm, suggesting very significant BOT energy spectra. Note that during the main phases of both storms, some energy spectra at very high L were occasionally identified as BOT energy spectra, which could be due to the discrepancies between measurements of different instruments.

It is worth noting that the observations have some limitations in characterizing BOT energy spectra: though the agreement between MagEIS and REPT as well as between different units of MagEIS is quite good, some calibration differences are still present. Thus, as shown in Figures 6d and 6m, the energy channel corresponding to BOT flux maximum was generally located at ~1.1 MeV (the first energy channel of the MagEIS HIGH unit) and 2.1 MeV (the first REPT channel used in this study). To get more detailed information of BOT energy spectra, we choose to fit the BOT energy spectra to the BOT distribution function as introduced earlier in this section. Some calibration differences between different units/instruments can be compensated with fitting. Figures 6g-6i and 6p-6r show the parameters of BOT energy spectra from the fitting results during the two storms. Here only those good fits with RMSD < 0.5 are shown. Comparing panels (g) and (p) with panels (d) and (m), while data only show flux maximum located at ~1.1 and ~2.1 MeV, fitting results are able to show more detailed information: the energy of flux maximum ranged from ~1 to 2.5 MeV with higher values at lower L-shells, while at a fixed L-shell the energy of flux maximum generally remained the same during each storm. The observations and fitting results of energy corresponding to the flux minimum are quite consistent, which also validates our fitting method. The ratios of flux maximum to minimum derived from the fitting results are slightly lower than observations due to the nature of fitting. Note that fitting results have some limitations too: by fitting the energy spectrum to the BOT distribution, we assumed that the specific energy spectrum can be represented by a power law distribution plus a Gaussian distribution. Though this is likely true for most observed BOT energy spectra (since RMSDs are overall small between fitting results and observations), large differences between fitting results and observations could still exist in some fits, and fitting results also tend to overestimate the energy of flux maximum in the low L region while underestimating the ratio between flux maximum and minimum. Thus, the combination of observations and fitting results will give us more comprehensive knowledge about the BOT energy spectra in the radiation belts.

4 Statistical Results of Radiation Belt Electron Energy Spectra

In this section, using the method described in section 4, survey plots of radiation belt electron energy spectra during a longer time period are presented. Figure 7 shows the survey plot of radiation belt electron energy spectra categorization and coefficients of exponential and power law energy spectra, along with the 1-min-averaged fluxes of electrons with different energies measured by Van Allen Probes-B during the year of 2017. Daily-averaged Dst and AE indices are also shown. Still, no results are shown at L<2.5 due to potential contamination from inner belt protons.

The distribution of energy spectra and its correlation with plasmapause location can be clearly seen from Figure 7a. Based on our categorization results, during 2017, over 95% of energy spectra at L>2.5 can be described as one of the three distributions: the exponential, power law, and BOT, while ~67% of all energy spectra were exponential energy spectra, ~24% were BOT energy spectra, and ~4% were power law spectra. The energy spectra in the outer belt outside the plasmasphere are generally dominated by the exponential spectra with the coefficient E₀ ranging from ~200 to 800 keV, and as shown in Figure 7b, E₀ is often higher at lower L-shells, suggesting harder energy spectra at the center of the outer belt. As the storm occurs, usually, E₀ exhibits sudden decrease and then gradual increase. This suggests that when the storm occurs, the energy spectra in the outer belt often soften first due to faster flux enhancements of lower-energy electrons; afterward the energy spectra harden gradually due to both faster loss of lower-energy electrons and delayed enhancements of higher-energy electrons, consistent with the results shown in Reeves et al. (2016) and Ripoll, Loridan, et al. (2016), Ripoll, Reeves, et al. (2016), Ripoll et al. (2019). Power law energy spectra usually exist in the high L region during injection times. Figure 7c shows that the coefficient α of power law energy spectra ranges from ~2 to ~6 and decreases as L gets lower, which could be caused by limited injections of hundreds of keV electrons into the lower L region (e.g., Turner et al., 2015; Zhao & Li, 2013) and also higher fluxes of higher-energy electrons in the center of outer belt.

Figure 7a also shows that the BOT energy spectrum is the most prevalent energy spectrum inside the plasmasphere at L>2.5, consistent with the results of Zhao, Ni, et al. (2019). More detailed results regarding BOT energy spectra are shown in Figure 8. Figure 8 shows the energy of flux maximum, energy of flux minimum, and ratio of flux maximum to minimum from both (a – c) observations and (d – f) fitting results during 2017 using data from the Van Allen Probes-B. Figure 8a shows that based on the observations, the energy of flux maximum is usually observed between ~600 keV and 2.6 MeV, while during the majority of time it is located at ~1 – 2 MeV. During relatively quiet times, generally, the energy of flux maximum is higher at lower L, and at a fixed L it gradually increases with time. These features can be seen even clearer in fitting results as shown in Figure 8d, though in the low L region the energy of flux maximum is likely overestimated by fitting. As shown in Figures 8b and 8e, the energy of flux minimum during quiet times is also higher at lower L. These behaviors are consistent with plasmaspheric hiss wave scattering (e.g., Ni et al., 2019; Reeves et al., 2016; Ripoll, Loridan, et al., 2016; Ripoll, Reeves, et al., 2016; Ripoll et al., 2019; Zhao, Ni, et al., 2019). Theoretical calculation of hiss wave scattering shows that inside the plasmasphere, the loss timescale of energetic electrons caused by hiss wave scattering depends on both electron energy and L-shell (e.g., Hua et al., 2019; Lyons & Thorne, 1973; Meredith et al., 2007; Ni et al., 2013, 2014, 2017; Ripoll et al., 2019): as the L gets lower, the energy of electrons with fastest loss gets higher. Also, Zhao, Ni, et al. (2019), using a 2-D Fokker-Planck simulation with a time-varying, data-driven model of plasmaspheric hiss waves, confirmed that the formation of a BOT energy spectrum after the 17 March 2015 storm is actually due to the energy-dependent scattering caused by hiss waves inside the plasmasphere. On the other hand, as the storm occurs, sudden increase of energy of the flux minimum is often observed starting from the higher L region and extending to lower L. This is mainly due to the flux enhancement of lower-energy electrons, which usually starts at higher L and subsequently extends to lower L. Figures 8c and 8f show that the ratio between flux maximum and minimum generally ranges from ~1 to 2 orders of magnitude, with the fitting results showing slightly lower ratio than observations due to the nature of fitting.

Figure 7a suggests that the plasmasphere plays a critical role in shaping radiation belt electron energy spectra. To highlight the relation between energy spectrum and plasmasphere, we conducted a statistical analysis of the relative position of different energy spectrum types to the plasmapause location using energy spectra measured by the Van Allen Probes-B from March 2014 to February 2018. The minimum plasmapause location was calculated in each day using model from Liu et al. (2015). The percentages of each energy spectrum type as a function of L-shell relative to the minimum plasmapause location (L_pp) at the same day are shown in Figure 9a. In Figure 9a, different colors show the percentages of different energy spectra, with exponential in purple, power law in cyan, BOT in red, and undefined in grey. The black curve shows the total number of energy spectra as a function of L-L_pp. To ensure enough statistics, only data with more than 100 energy spectra have been plotted. Figure 9a clearly shows that statistically, the majority of BOT energy spectra are located inside the minimum plasmapause location, and the peak location of BOT energy spectra is located at L~L_pp-1, where statistically over 70% of energy spectra are BOT energy spectra. The exponential energy spectra dominate outside the plasmasphere, with a peak percentage of ~85% at L~L_pp+2. The power law energy spectra are mostly present much farther away from the plasmapause, which is likely a result of particle injections during very active times. These results are consistent with the observed S-shaped features in Reeves et al. (2016), which are shown to be caused by energy-dependent hiss wave scattering inside the plasmasphere (Ripoll et al., 2019; Ripoll, Loridan, et al., 2016; Ripoll, Reeves, et al., 2016). It has been demonstrated that the formation of BOT energy spectra inside the plasmasphere is due to the plasmaspheric hiss wave scattering (Zhao, Ni, et al., 2019). Here we also examine the time required for hiss wave scattering to form the BOT energy spectra. Figure 9b shows the percentage of BOT energy spectra as a function of L relative to the minimum plasmapause location at the same day t and at the day of t − 1, … , t − 6. It shows that statistically, BOT energy spectra take ~0 – 3 days to form, with the most BOT energy spectra form in ~1 – 2 days at ~0.3 – 1.5 L inside the minimum plasmapause location.

Note that the results shown in this study are based on the spin-averaged fluxes measured by the Van Allen Probes. However, since the effects of various physical mechanisms on radiation belt electrons are pitch angle dependent (e.g., Zhao et al., 2014a; Zhao et al., 2014b; Zhao, Friedel, et al., 2018), the energy spectra could also be pitch angle dependent. Zhao, Ni, et al. (2019) showed that the BOT energy spectrum is likely present at a large range of equatorial pitch angles though detailed work regarding the energy spectra of electrons with different pitch angles were not shown. Future work will be conducted to investigate the pitch angle dependence of radiation belt electron energy spectrum distribution and evolution.

5 Summary

In this study, using data from the Van Allen Probes, we conducted a systematic analysis of the characteristics and evolution of radiation belt electron energy spectra of ~100-keV to 10-MeV electrons through both event studies and statistical analysis. The main conclusions include the following:

The energy spectrum evolution is examined during one intense storm and one moderate storm. Prior to both storms, the exponential energy spectra dominate outside the plasmasphere, while the BOT energy spectra dominate inside the plasmasphere at L>2.5. When the storms occurred, electron fluxes of a wide energy range decreased suddenly due to adiabatic effect and/or actual loss, then faster enhancements of lower-energy electrons were observed, causing the softening of exponential energy spectra, the disappearance of BOT energy spectra at all L during the intense storm and at high L during the moderate storm, and the formation of power law energy spectra in the high L region. During the recovery phases, lower-energy electrons were lost faster, while higher-energy electron fluxes gradually enhanced, which formed and hardened the exponential energy spectra.
Statistically, the majority of radiation belt electron energy spectra can be categorized into three types: exponential, power law, and BOT energy spectra. Based on the Van Allen Probes-B measurements, during 2017 at L>2.5, ~67% of all energy spectra were exponential energy spectra, ~24% were BOT energy spectra, and ~4% were power law spectra. The exponential spectra generally dominate in the outer radiation belt outside the plasmasphere, BOT spectra dominate inside the plasmasphere at L>2.5, and power law spectra usually appear at high L-shells during injections of lower-energy electrons.
For the exponential spectra $urn:x-wiley:21699380:media:jgra55019:jgra55019-math-0005$ , the coefficient E₀ generally ranges from ~200 keV to 800 keV and is usually higher at lower L in the outer belt, suggesting harder energy spectra at the center of outer belt. E₀ also varies dramatically during storm times. A sudden decrease of E₀ is usually seen when the storm occurs, which is mainly due to the fast enhancements of lower-energy electrons and/or loss of higher-energy electrons. Afterward, E₀ gradually increases as lower-energy electrons decay faster and higher-energy electron fluxes gradually enhance.
For the power law spectra j = j₀E^−α, the coefficient α generally ranges from ~2 to 6 in the outer belt. In the high L region, α generally decreases as L decreases, which is likely due to the limited injections of lower-energy electrons into the lower L during active times and higher fluxes of high-energy electrons in the center of the outer belt.
Combining observations and fitting results of BOT energy spectra, during relatively quiet times, we find that the BOT energy spectra dominate inside the plasmasphere at L>2.5, with the energy of flux maximum ranging from approximately hundreds of keV to several MeV and the energy of flux minimum varying from ~100 keV to ~MeV, both increasing as L-shell decreases. The ratio of flux maximum to minimum generally ranges ~1 – 2 orders of magnitude. These results are consistent with the observed S-shaped spectral features of Reeves et al. (2016), which have been demonstrated to be caused by hiss wave scattering by Ripoll, Loridan, et al. (2016), Ripoll, Reeves, et al. (2016), Ripoll et al. (2019), and further confirm the critical role of hiss wave scattering in the formation and evolution of BOT energy spectra.
Comparing the energy spectrum types to the plasmapause location, statistically, the peak location of BOT energy spectra is ~1 L-shell inside the minimum plasmapause, where over 70% of energy spectra are BOT energy spectra; exponential energy spectra peak at ~2 L above the minimum plasmapause, where ~85% of energy spectra are exponential spectra; power law energy spectra peak further away from the plasmapause during active times. Statistical results also suggest that BOT energy spectra mostly form in ~1 – 2 days as a result of hiss wave scattering inside the plasmasphere, consistent with the results from Reeves et al. (2016) and Ripoll, Loridan, et al. (2016), Ripoll, Reeves, et al. (2016), Ripoll et al. (2019).

Acknowledgments

The research presented here was supported by RBSP-ECT funding through JHU/APL contract 967399 (under prime NASA contract NAS5-01072). Van Allen Probes MagEIS and REPT data used in this paper are available from the ECT Science Operations and Data Center (http://www.rbsp-ect.lanl.gov). The Dst and AE indices are available at OMNIWeb (http://omniweb.gsfc.nasa.gov/). B. Ni thanks the support from the NSFC grants 41674163 and 41474141 and the Hubei Province Natural Science Excellent Youth Foundation (2016CFA044).

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Volume124, Issue6

June 2019

Pages 4217-4232

Characterization and Evolution of Radiation Belt Electron Energy Spectra Based on the Van Allen Probes Measurements

Abstract

Key Points

1 Introduction

2 Radiation Belt Electron Energy Spectrum Evolution During Two Storms

3 Radiation Belt Electron Energy Spectra Categorization and Characterization During Two Storms

4 Statistical Results of Radiation Belt Electron Energy Spectra

5 Summary

Acknowledgments

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Characterization and Evolution of Radiation Belt Electron Energy Spectra Based on the Van Allen Probes Measurements

Abstract

Key Points

1 Introduction

2 Radiation Belt Electron Energy Spectrum Evolution During Two Storms

3 Radiation Belt Electron Energy Spectra Categorization and Characterization During Two Storms

4 Statistical Results of Radiation Belt Electron Energy Spectra

5 Summary

Acknowledgments

References

Citing Literature

Figures

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