Volume 123, Issue 8 p. 6189-6206
Research Article
Free Access

Electron Flux Enhancements at L = 4.2 Observed by Global Positioning System Satellites: Relationship With Solar Wind and Geomagnetic Activity

Xiao-Jia Zhang

Corresponding Author

Xiao-Jia Zhang

Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA, USA

Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA, USA

Correspondence to: X.-J. Zhang,

xjzhang@ucla.edu

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Didier Mourenas

Didier Mourenas

CEA, DAM, DIF, Arpajon, France

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Anton V. Artemyev

Anton V. Artemyev

Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA, USA

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Vassilis Angelopoulos

Vassilis Angelopoulos

Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA, USA

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Richard Mansergh Thorne

Richard Mansergh Thorne

Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA, USA

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First published: 25 June 2018
Citations: 3

Abstract

Determining solar wind and geomagnetic activity parameters most favorable to strong electron flux enhancements is an important step toward forecasting radiation belt dynamics. Using electron flux measurements from Global Positioning System satellites at L = 4.2 in 2009–2016, we seek statistical relationships between flux enhancements at different energies and solar wind dynamic pressure Pdyn, AE, and Kp, from hundreds of events inside and outside the plasmasphere. Most ≥1-MeV electron flux enhancements occur during nonstorm (or weak storm) times. Flux enhancements of 4-MeV electrons outside the plasmasphere occur during periods of low Pdyn and high AE. We perform superposed epoch analyses of Global Positioning System electron fluxes, along with solar wind and geomagnetic indices, 40-keV electron flux, ultralow frequency (ULF) wave index from Geostationary Operational Environmental Satellite, and chorus wave intensity from the Van Allen Probes and Time History of Events and Macroscale Interactions during Substorms mission. We demonstrate that 4-MeV electron flux enhancements outside the plasmasphere start when the interplanetary magnetic field (Bz) reaches a minimum and develop during periods of low Pdyn, high AE, low but increasing Dst, moderate ULF wave index, and intense chorus waves. Flux enhancements at 100 keV occur under conditions with higher Pdyn, higher ULF wave index, and elevated 40-keV electron flux at L = 6.6. Moreover, electron flux enhancements take much more time to develop at higher energies. This suggests that 100-keV flux enhancements are dominated by injections, while MeV electron energization is predominantly induced by chorus waves with further amplification by inward transport.

Key Points

  • Electron flux enhancements at 0.1 − 4 MeV are investigated based on 7-year GPS satellites data at L = 4.2
  • Statistics show electron flux enhancements outside the plasmasphere are likely related to chorus-induced energization
  • Electron flux enhancements generally start after the IMF Bz reaches a minimum

1 Introduction

Electron fluxes are highly variable in the outer radiation belt, located between about L = 3.5 and L = 6.6, with sudden increases or dropouts that can often reach 1 order of magnitude and, in the case of enhancements, represent an important hazard for satellites (e.g., see Baker et al., 2004; Horne et al., 2013; Reeves et al., 2003). Electron flux dropouts have been investigated in various recent works. They are mainly attributed to magnetopause shadowing loss associated with outward radial diffusion, and loss into the atmosphere caused by resonant interaction with electromagnetic ion cyclotron (EMIC) and chorus waves (Boynton et al., 2016, 2017; Gao et al., 2015; Li et al., 2007; Mourenas et al., 2016; Shprits et al., 2006; Summers & Thorne, 2003; Zhang et al., 2017). Atmospheric loss seems to become more important around L = 4.2 than near geosynchronous orbit (Boynton et al., 2017; Gao et al., 2015). The many possible causes of electron flux enhancements have also been examined, with an initial focus on the outer edge of the outer radiation belt based on available data from geosynchronous satellites (e.g., see Borovsky, 2017; Reeves et al., 2003, 2011, and references therein), until recent Van Allen Probes measurements enable further investigations into flux variations between the start and end of storms in the heart of the outer radiation belt (e.g., Moya et al., 2017; Murphy et al., 2018; Turner, O'Brien, et al., 2015).

Various physical processes can contribute to energetic (10–250 keV) and relativistic (>300 keV) electron flux enhancements observed in the outer radiation belt (e.g., Jaynes et al., 2015). Basically, however, all these mechanisms rely on an initial injection of energetic (10–250 keV) electrons from the plasma sheet, which are further transported inward and accelerated by wave-particle interactions (Horne et al., 2005; Jaynes et al., 2015; Ozeke et al., 2014; Su et al., 2015; Tang et al., 2016, 2017). The inward transport may occur through inward radial diffusion by ultralow frequency (ULF) waves, convection by intense dawn-dusk electric fields during extended periods of successive substorms, and effects of substorm-related electric field bursts occurring during dipolarizations (e.g., Elkington et al., 1999; Gabrielse et al., 2012, 2017; Ganushkina et al., 2013; Ozeke et al., 2014; Rodger et al., 2016; Schulz & Lanzerotti, 1974; Sergeev et al., 1998), or via coherent interactions with ULF waves (Mann et al., 2013). As electrons are diffused radially toward lower L shells by ULF waves, or convected inward, conservation of adiabatic invariants leads to their simultaneous acceleration (e.g., Elkington et al., 1999; Schulz & Lanzerotti, 1974). In general, energetic electrons are injected in sufficient numbers to reach observed levels without requiring additional local acceleration mechanisms. In some instances, an additional local acceleration by electrostatic waves resonating with the plasma sheet electrons (e.g., a combination of upper band and lower band oblique chorus waves, or Time Domain Structures, see Ma et al., 2016; Mozer et al., 2016) may speed up the increase of such energetic electron fluxes. Successive injections occurring during prolonged periods of intense substorms can provide a significant seed population of 100- to 250-keV electrons directly at L ∼ 6.6 (Ganushkina et al., 2013; Meredith et al., 2003; Su et al., 2015; Tsurutani et al., 2006) and sometimes down to L ∼ 3–4 (Turner, Claudepierre, et al., 2015; Turner et al., 2017). This seed population of already c particles can be more easily—and rapidly—accelerated to relativistic energies in the heart of the outer radiation belt by chorus waves, which are generated by simultaneously injected anisotropic, hot (10–30 keV) electrons (Baker et al., 2014; Borovsky, 2017; Horne et al., 2005; L. Y. Li et al., 2009; X. Li et al., 2011; W. Li et al., 2010; Meredith et al., 2003; Miyoshi et al., 2013; Tang et al., 2016; Thorne, 2010; Thorne et al., 2013; Tsurutani et al., 2006), and/or by strong ULF waves also observed during intense substorms (O'Brien, Lorentzen, et al., 2003; Ozeke et al., 2014; Rae et al., 2011).

In spite of many past investigations, however, the main governing factors for electron flux enhancements at different energies in the heart of the outer radiation belt have yet to be clearly identified. Various correlations have been found between MeV electron flux enhancements in the outer belt and solar wind pressure, speed, and density, different proxies (AE, Kp) of substorm activity, Dst index, southward interplanetary magnetic field (IMF) orientation, and ULF wave level (Baker et al., 2004; Balikhin et al., 2011; Borovsky, 2017; Kozyreva et al., 2007; W. Li et al., 2015; Mathie & Mann, 2000; Mourenas et al., 2018; O'Brien & Moldwin, 2003; Reeves et al., 2011; Simms et al., 2016; Tang et al., 2017; Zhao, Baker, Jaynes, et al., 2017). However, the degree of correlation is often moderate and exhibits large data scatter (Baker et al., 2004; Reeves et al., 2011). In addition, many of these works mainly considered the geostationary orbit (i.e., the outer edge of the radiation belt) or only examined several years of electron flux data from the Van Allen Probes with a relatively long time step, ∼5–9 hr (Moya et al., 2017; Murphy et al., 2018; Tang et al., 2017; Turner, O'Brien, et al., 2015; Zhao, Baker, Jaynes, et al., 2017). Furthermore, recent studies have shown that the most significant correlations with electron flux increases are found when considering geomagnetic indices (Kp, Dst, or ULF wave index) integrated in time over at least 1 day (during the considered storm or periods of sustained substorms), instead of their hourly or peak value, suggesting the presence of cumulative effects (Borovsky, 2017; Mourenas et al., 2018; Simms et al., 2016). This kind of correlation between a progressive flux increase and an extended period of geomagnetic activity could be easily identified through a superposed epoch analysis over hundreds of events. Examining L shells in the heart of the outer radiation belt with high time resolution data (∼1–3 hr), enabled by Global Positioning System (GPS) satellites, over 2009–2016 also complements previous studies (Balikhin et al., 2011; Borovsky, 2017; Moya et al., 2017; Murphy et al., 2018; Reeves et al., 2003, 2011; Simms et al., 2016; Tang et al., 2017; Turner, O'Brien, et al., 2015; Zhao, Baker, Jaynes, et al., 2017).

Accordingly, we shall hereafter make use of recently available electron flux data from Los Alamos National Laboratory instruments on board GPS satellites to investigate the possible origin of 100-keV, 1-MeV, and 4-MeV electron flux enhancements at L = 4.2. GPS satellites have near-circular orbits at an altitude of 20,200 km, with a 12-hr period and an inclination of 55. They are equipped with a Combined X-ray Dosimeter measuring electron fluxes in 11 successive energy channels over ∼0.14–6 MeV, the final fluxes being recalculated using a sophisticated spectrum fitting procedure after proper subtraction of proton counts (e.g., see Morley et al., 2016, and references therein). We shall first examine separately the occurrence of flux enhancement as a function of different indices in section 2 and then use in section 7 superposed epoch analyses to reveal the most pertinent parameters in the hours leading to flux increases. GOES measurements of 40-keV electron flux and ULF wave power at geosynchronous orbit, and Time History of Events and Macroscale Interactions during Substorm (THEMIS) and Van Allen Probes measurements of chorus waves will also be used. This is expected to help us better identify the main governing factors for these flux enhancements at various energies. Selected events will be discussed in section 10. Note that successive measurements from different GPS satellites (53–61) at the geomagnetic equator were generally available every ∼1–3 hr over 2009–2016, representing a relatively high time resolution data set. These GPS electron flux data have been cross-validated against Van Allen Probes data over 0.1–4 MeV, demonstrating that flux levels are generally within a factor of 2 from Van Allen Probes fluxes (Morley et al., 2016) and have been used in a recent study to infer the main mechanisms leading to electron flux dropouts at L = 4.2 in the same energy range (Boynton et al., 2017).

2 Statistics of Electron Flux Enhancements

2.1 Event Selection

When studying electron flux enhancements detected by GPS satellites at L ∼ 4.2, one must be careful to discard mere oscillations or transient fluctuations of flux that do not represent an actual, sustained increase. A narrow bunch of high electron flux (or a narrow trough with almost no electron flux, related to weak dropout echoes) may simply pass by a certain GPS satellite without representing a sustained, spatially wide flux increase, and is not of interest in our analysis. Drift resonance between electrons and ULF waves can produce such fine-structure modulations in the electron flux, sometimes complicated by the MLT localization of ULF waves and coherent wave-particle interaction (L. Li et al., 2017; Mann et al., 2013; Sarris et al., 2017). Therefore, we used a set of rather restrictive criteria to select flux enhancement events:
  1. For 100-keV, 200-keV, 1-MeV, and 4-MeV electron flux enhancements, the flux must increase by more than a factor of 4 within 3 hr on one satellite, with electron flux measurements available from at least five GPS satellites across four MLT sectors (six in total); events separated by less than 3 hr are combined as a same event, with the start time of the first enhancement, noted T0, corresponding to the time after which the flux starts to increase (by a factor of 4 or more within 3 hr), and the end time Tend being the last point of the flux enhancement; the flux increase ratio is defined as the ratio between the maximum flux during the enhancement event (over t∈[T0,Tend]) and the average flux prior to the event (over t∈[T0−24hr,T0]).
  2. For 100-keV, 200-keV, 1-MeV, and 4-MeV electron flux enhancements, the ratio of maximum electron flux at the time of flux enhancement over the adjacent two time points (prior and after the enhancement, that is, each separated in general by about 1 hr from it) should not exceed a factor of 3, to eliminate single-point increases.
  3. For 100- and 200-keV electron flux enhancements, the maximum ratio of fluxes preceding the event (within 24 hr) over the flux at T0 ( urn:x-wiley:jgra:media:jgra54378:jgra54378-math-0001) should be significantly (i.e., at least 4 times) smaller than the maximum flux increase during the event (over t∈[T0,Tend]), to exclude mere fluctuations (this requirement is not necessary nor applicable for 1- to 4-MeV electron flux enhancements because they occur over much longer time scales than at 100–200 keV).
  4. For all energies, the maximum average flux over three consecutive data points during each event must be greater than the average flux prior to the event (i.e., the average flux J over t∈[T0−24hr,T0]) by at least a factor of 3.5, to exclude transient increases only due to a very localized drop of flux at the single point t = T0.

We used such strict criteria for flux enhancements to better ensure that we do not include artificial data oscillations or bunches of electrons just passing by the satellites. Although this decreases the total number of events, it does provide a more reliable flux enhancement data set. Implementing all the above criteria to the 2009–2016 data set of electron flux measurements from GPS satellites 53–61 at L ∼ 4.0–4.4 (a GPS satellite is always near the magnetic equator, with magnetic latitude ≤5, at such L shells, which happens every 6 hr), we found 131 events of 100-/200-keV electron flux enhancements, 169 events of 1-MeV flux enhancements, and 250 events of 4-MeV electron flux enhancements. Furthermore, we only kept GPS electron flux data above the noise level of 103 electron/cm2/s/MeV for 0.1–1 MeV and above 1 electron/cm2/s/MeV for 4 MeV (e.g., see Figures 8 and 9 from Morley et al., 2016, and references therein).

To better assess the main governing factors for electron flux enhancements at L ∼ 4.2, we first consider the events outside or inside the plasmasphere separately, because they are likely caused by different physical processes. For instance, chorus wave-induced electron acceleration occurs only outside the plasmasphere (e.g., Agapitov et al., 2018; Horne et al., 2005; Thorne, 2010). Therefore, the events have been split into two categories with respect to the plasmapause position: Lpp<4.2 (events outside the plasmasphere) and Lpp>4.2 (events inside the plasmasphere), where Lpp was estimated based on the statistical empirical plasmapause location models from O'Brien and Moldwin (2003). To select events inside/outside the plasmasphere, we used the minimum Lpp(AE) value over the period from 36 hr before T0 until the end of the event. To demonstrate that this separation is correctly performed, we also consider two additional data sets obtained using stricter criteria: Lpp+0.3 < 4.2 (events outside the plasmasphere) and Lpp−0.3 > 4.2 (events inside the plasmasphere). The additional ±0.3 terms have been added to take into account the standard deviation of Lpp values measured by CRRES around the Lpp(AE) estimate from O'Brien and Moldwin (2003). We further checked that only a small percentage (always <18%) of events would not be located in the same category when requiring that the same condition on Lpp be satisfied for all three Lpp estimates inferred from maximum Kp, maximum Dst, or maximum AE (see O'Brien & Moldwin, 2003). Note, however, that we cannot exclude the possibility that during some of these events, the electrons spent some time on the other side of the plasmapause over some limited MLT sector, due to our use of a statistical Lpp location and to the variation of the plasmapause location with MLT during disturbed periods. Nevertheless, an MLT-averaged Lpp model is more appropriate for our study, because the duration of flux enhancement events is sufficiently long, in general, for electrons to perform at least one azimuthal drift around the Earth (the distribution of flux enhancement event duration peaks at ∼100–200 min for all investigated energies—not shown).

One important characteristic of the present statistics of collected events is that the overwhelming majority of ≥1-MeV electron enhancements are observed during periods of not too deep Dst minima. To examine the possible relationship of ≥1-MeV electron enhancements with geomagnetic storms, we checked the minimum value of Dst measured during the 2 days preceding each enhancement. We found that urn:x-wiley:jgra:media:jgra54378:jgra54378-math-0002 nT in only ∼11% of these events (45 out of 419) and urn:x-wiley:jgra:media:jgra54378:jgra54378-math-0003 nT in half of the events. Thus, the present statistics contains electron flux enhancements that occurred mainly during weak storms or nonstorm times, or during the late recovery phase of some strong storms.

2.2 Flux Enhancements as a Function of Solar Wind and Geomagnetic Indices: Outside the Plasmasphere

We only focus here on two very different populations, the seed population of 100s of keV electrons and the most significantly increased (during enhancements) population at 4 MeV, to better highlight their differences (the flux of 1-MeV population is increased by acceleration mechanisms like the 4-MeV population, but it is increased to a lesser extent in general, because of an initially higher background level, explaining the smaller number of strong enhancements found at 1 MeV).

When GPS satellites (at L ∼ 4.2) are located outside the plasmasphere, we found 181 flux enhancements events at 4 MeV, and 61 events at 100 and 200 keV. The occurrence rate of such events is displayed in Figure 1a, as a function of AE (calculated here as the maximum AE between T0 and T0+3 hr) and solar wind dynamic pressure Pdyn (calculated as the maximum Pdyn between T0−3 hr and T0+3 hr) during the considered events. There are clearly many more flux enhancements for AE > 500 nT and low Pdyn (<5–7 nPa), for both 100-keV and 4-MeV electrons.

Details are in the caption following the image
Occurrence rates of electron flux enhancement event at L ∼ 4.2 (a) outside and (b) inside the plasmasphere at different energies (top for 100 and 200 keV, bottom for 4 MeV) as a function of solar wind dynamic pressure Pdyn and AE or Kp. The right panels also show enhancement occurrences as a function of AE for the subset of Pdyn<2 nPa events. Black lines show results using the inside/outside plasmapause criteria of Lpp<4.2/Lpp>4.2 and blue lines show results for stricter criteria of Lpp<4.2 − 0.3/Lpp>4.2 + 0.3.

Moreover, Figure 2a shows an augmentation with AE of both the median and mean values of maximum flux increases at 4 MeV (for all events as well as for the low-Pdyn subset), which is fully consistent with the increase of 4-MeV event occurrences with AE in Figure 1a. Thus, there is a clear augmentation of both the magnitude and occurrence rate of 4-MeV flux enhancements as AE increases. It is well known that high AE (or high Kp) can lead to more intense whistler mode chorus waves at L = 4–6 (Agapitov et al., 2018; L. Y. Li et al., 2009; Meredith et al., 2003). Thus, electron flux enhancements at high energy (∼4 MeV) observed by GPS satellites in the heart of the outer radiation belt are consistent with a stronger effect of quasi-linear energization or nonlinear trapping acceleration of seed electrons from 0.2–1 MeV to 4 MeV by intense chorus waves (e.g., see Agapitov et al., 2018; Artemyev et al., 2016; Foster et al., 2017; Horne et al., 2005; L. Y. Li et al., 2009; W. Li et al., 2015; Meredith et al., 2003; Mourenas et al., 2014, 2015; Omura et al., 2015; Tang et al., 2017; Thorne et al., 2013). The present results agree with previous results from W. Li et al. (2015), which were based on a superposed epoch analysis of Van Allen Probes observations of 1-MeV acceleration events from October 2012 to March 2015, as well as with the work from Pinto et al. (2018) who found a high AE (>250 nT) during 90% of 2-MeV flux enhancements at L = 6.6 in 1996–2006. The prevalence of nonlinear or quasi-linear electron acceleration processes depends on the relative occurrence of high-intensity (>500 pT) chorus waves versus ∼100 pT waves, on the fine details of the wave distribution that determine the probability of trapping and acceleration of seed electrons (Artemyev, Vasiliev, et al., 2015; Foster et al., 2017), as well as on the presence of effects restraining nonlinear acceleration, such as fast modulations of wave amplitudes or the additional presence of other, weaker waves (e.g., see Artemyev, Mourenas, et al., 2015; Tao et al., 2013, and references therein).

Details are in the caption following the image
Distribution of maximum electron flux increase at different energies (top for 100 and 200 keV, bottom for 4 MeV) as a function of solar wind dynamic pressure Pdyn and AE or Kp, for the same events as in Figure 1 at L ∼ 4.2 (a) outside and (b) inside the plasmasphere. The right panels also display maximum flux increases as a function of AE for the subset of Pdyn<2 nPa events. Median maximum flux increases are shown in black (in green for stricter plasmapause criterion) and mean values in blue (in red for stricter plasmapause criterion).

Additionally, 90% of 4-MeV electron flux enhancements occur during low Pdyn (<5 nPa) periods, whereas only 10% occur when Pdyn>5 nPa (see Figure 1a). One might conclude from this that high Pdyn periods are less conducive to 4-MeV flux enhancements, possibly due to stronger magnetopause shadowing losses when an increased solar wind pressure pushes the magnetopause closer to the Earth. However, the maximum flux increases during high Pdyn (>5–10 nPa) periods in Figure 2a are similar to, or even higher than during low Pdyn periods. Thus, the higher occurrences of 4-MeV flux enhancements when Pdyn<5 nPa may be simply due to the fact that statistically there are longer intervals with low Pdyn than high Pdyn (with or without flux enhancements). Moreover, intense chorus waves are mainly generated during the main and recovery phases of storms as well as during strong substorms, that is, after the storm commencement during which strong increases of Pdyn are often observed. This agrees with superposed epoch analysis results from W. Li et al. (2015), which showed similarly low levels of Pdyn during efficient MeV electron acceleration events, and an increase of Pdyn just before the flux enhancements. The events of strongest flux increases at Pdyn>10 nPa in Figure 2a may be a result of significant dropouts related to magnetopause shadowing (Shprits et al., 2006) or losses induced by EMIC waves (generated by magnetosphere compression; Gao et al., 2015; W. Li et al., 2007; Mourenas et al., 2016) just before the enhancements, favoring a higher flux enhancement compared to the initial flux level—or they may be caused by strong shock-induced fast acceleration up to a few MeVs (X. Li et al., 1993; Zong et al., 2009).

Interestingly, during low Pdyn (<2 nPa) periods, there are twice more 4-MeV flux enhancements for AE < 300 nT than for higher AE, although the mean and median values of maximum flux increases for AE > 550 nT are similar or larger than over the 100 nT <AE < 550 nT range (see Figures 1a and 2a). This seems to indicate that during low Pdyn<2 nPa periods, electron flux enhancements at 4 MeV do not necessarily require strong and deep injections of hot electrons from the plasma sheet (that may be needed to replace lost particles during magnetopause shadowing), but rather prolonged periods of moderate, steady activity allowing a progressive acceleration of the already sufficiently dense lower-energy electron population. However, the similar or larger flux increases during AE > 550 nT periods suggest that the higher occurrence rate at low AE could also be attributed to a higher probability of having lower AE during periods of low Pdyn (<2 nPa).

Considering now 100-keV flux enhancement occurrences and maximum flux increases from Figures 1a and 2a, the results are less clear than at 4 MeV. There are twice as many electron flux enhancements for Pdyn<8 nPa than in the complementary parameter range, whereas the maximum flux increase at Pdyn<8 nPa is smaller when considering median values but larger when considering mean values, compared to the range 8 nPa <Pdyn<16 nPa. The mean of maximum flux increases is also higher for Pdyn>16 nPa, which could be related to shock-induced acceleration, as for 4-MeV flux enhancements, but this category has a very small number (4) of events. Actually, there are fewer events in general at 100 keV than at 4 MeV, with only seven events at Pdyn<2 nPa, which could explain the less clear statistical results at 100 keV than at 4 MeV. The strong differences between mean and median values of flux increases in some parameter domains are due to the presence of several events with very large flux increases. In such a situation, the median is statistically more reliable than the mean and could indicate an augmentation of maximum flux increases with both Pdyn and AE (except at low Pdyn<2 nPa). Statistically, we found that the average solar wind dynamic pressure Pdyn was indeed ∼3.23 nPa during 100- to 200-keV electron enhancement events in 2009–2016, while it was a factor of 2 smaller (Pdyn∼1.84 nPa) during nonenhancement times. Therefore, the probability to get an enhancement of 100- to 200-keV flux at GPS orbit is higher during periods of higher Pdyn. However, the pertinent threshold is very low, somewhere between Pdyn=2 nPa and Pdyn=3 nPa, implying that a large Pdyn (>8 nPa) does not necessarily lead to a strong 100-keV flux enhancement, in agreement with lower occurrences of such flux enhancements at Pdyn>8 nPa in Figure 1a. In summary, we interpret these results to suggest that 100-keV flux enhancements occur more often for 2 nPa <Pdyn<7 nPa simply because the presence of some substorm or storm disturbance is needed to produce them, whereas they occur less often at Pdyn>7 nPa probably because increases of solar wind pressure can lead to drift loss of energetic particles and thus mitigate the impact of electron injections during substorms.

With regard to the variation of 100-keV flux enhancements with AE, there are 2.3 times more events for AE > 550 nT than in the complementary parameter range, with higher mean and median values of maximum flux increases for AE > 550 nT than over the 100 nT <AE < 550 nT range (Figure 2a). Although the highest mean maximum flux increase occurs for AE < 100 nT, this category only contains three events and the median maximum flux increase in this low AE range remains much smaller than at AE > 550 nT, meaning that the high mean value is merely due to a few very large flux increases. Thus, 100-keV electron flux enhancements are both more frequent and stronger at AE > 550 nT, which is very likely related to stronger injections of 30- to 200-keV electrons from the plasma sheet, as well as to their stronger inward convection and radial diffusion during periods of higher AE (Ganushkina et al., 2013; Meredith et al., 2003; Ozeke et al., 2014; Rodger et al., 2016; Sergeev et al., 1998; Su et al., 2015; Tsurutani et al., 2006; Turner, Claudepierre, et al., 2015; Turner et al., 2017). When considering only events during low Pdyn (<2 nPa) periods, however, the trends with AE are reversed, with both fewer events and smaller mean flux increases at AE > 100 nT than at AE < 100 nT. Nevertheless, for Pdyn<2 nPa, the AE < 100 nT bin is composed of only one event and all the AE > 100 nT bins only six events. Still, these results show the presence of several significant 100-keV electron injections down to L = 4.2 during periods of both low Pdyn and low AE, indicating that the level of the global AE index may sometimes underestimate the effects of some very localized injections.

2.3 Flux Enhancements as a Function of Solar Wind and Geomagnetic Indices: Inside the Plasmasphere

When examining events inside the plasmasphere, we used the Kp index (obtained from midlatitude magnetometer stations, and calculated here as the maximum Kp between T0 and T0+3 hr), as opposed to the AE index (obtained from high-latitude stations) for events outside the plasmasphere. The AE index is a good proxy of both electron injections (Gabrielse et al., 2014; Ganushkina et al., 2013) and chorus wave intensity outside the plasmapause, where chorus-induced electron acceleration is more efficient in regions of low electron plasma frequency to gyrofrequency ratio (Meredith et al., 2003). The Kp index, on the other hand, is a good measure of injections and chorus wave intensity but also of ULF wave intensity and, therefore, of inward radial diffusion (e.g., Agapitov et al., 2018; Ganushkina et al., 2013; Ozeke et al., 2014). When the empirical plasmapause (O'Brien & Moldwin, 2003) is situated above the GPS observation zone at L = 4.2, electron fluxes cannot be directly increased there by local chorus-induced energization, since chorus waves are absent and replaced by hiss waves leading preferentially to atmospheric losses (e.g., Thorne, 2010), while the high electron plasma frequency to gyrofrequency ratio can lead to even faster losses in the simultaneous presence of EMIC waves (Mourenas et al., 2016; Zhang et al., 2017). Instead, electron fluxes can be increased by inward convection (at low energy <250 keV) or radial diffusion (at all energies) from regions outside the plasmasphere, where chorus-induced energization may still take place, or by localized electric field impulses leading to fast inward transport and acceleration (X. Li et al., 1993; Ozeke et al., 2014; Rodger et al., 2016; Turner, Claudepierre, et al., 2015; Turner et al., 2017; Zhao, Baker, Califf, et al., 2017; Zong et al., 2009). Therefore, Kp appears to be more appropriate for parameterizing both radial diffusion and fast transport inside the plasmasphere, and electron injections and chorus-induced energization outside the plasmasphere.

For both 100 keV (70 events) and 4 MeV (69 events), most GPS electron flux enhancements inside the plasmapause occur during low Kp (<2) and low Pdyn (<5 nPa) periods, as shown in Figure 1b. The maximum flux enhancement at 4 MeV (both the mean and median values) increases as Kp increases (Figure 2b), reaching levels similar to maximum flux enhancements outside the plasmasphere, except that the latter attain higher mean levels when AE > 550 nT. However, there is no clear variation of maximum flux increase with Pdyn. These results suggest that 4-MeV electron flux enhancements inside the plasmasphere mainly arise from chorus-induced energization outside the plasmasphere followed by inward transport of a small fraction of this increased flux. The higher increases during higher Kp intervals likely result from both more intense chorus waves outside the plasmapause and more efficient subsequent inward radial diffusion. The higher occurrence at low Kp < 2 is likely because statistically there are more frequent periods (with or without enhancements) with Kp < 2 during 2009–2016 and may also stem from the finite amount of time needed for MeV fluxes to reach the plasmasphere after being produced outside it, allowing Kp to relax to lower (more common) values than during their initial production. Nevertheless, the distribution of events with Kp is probably somewhat influenced also by our separation of events into two groups, inside and outside the plasmapause, because events at L = 4.2 are mainly located inside the plasmapause following lower Kp periods (O'Brien & Moldwin, 2003). Pdyn has apparently little effect (higher event occurrences at low Pdyn are probably due only to the higher global occurrence of such periods for both event and non-event times), probably because at L = 4.2 inside the plasmasphere, the variation of the magnetopause position has a much lower impact on electron flux variations than at higher L outside of the plasmasphere.

Similarly, 100-keV electron flux enhancements inside the plasmapause mostly take place when Kp < 2 and Pdyn<5 nPa. However, in contrast to the increase of maximum flux enhancement with Kp at 4 MeV and contrary to the increase of maximum flux enhancement with AE at 100 keV outside the plasmasphere, the maximum flux enhancements at 100 keV inside the plasmasphere remain roughly the same as Kp increases. This suggests that 100-keV flux enhancements inside the plasmasphere might not proceed from earlier flux enhancements outside the plasmasphere (due to chorus-induced acceleration) nor from radial diffusion, but rather from a fast inward transport that is less dependent on Kp (Turner, Claudepierre, et al., 2015; Turner et al., 2017)—the higher occurrences at Kp < 2 being simply due to the statistical peak in the global distribution of Kp occurrences at low values (<2) during 2009–2016.

2.4 Time Delays Between 100 keV and 1- or 4-MeV Electron Flux Enhancements During the Same Events

Interestingly, during four events inside the plasmasphere and seven events outside it (based on our most strict plasmapause criteria), increases of 1- or 4-MeV electron fluxes were observed by GPS satellites at L = 4.2 simultaneously or following 100-keV electron flux enhancements. Although 11 events are obviously not sufficient for a statistical study, it may be instructive to examine such events in details. The time delays between 100-keV flux enhancements and 1- or 4-MeV flux enhancements are plotted in Figure 3. During five out of seven events outside the plasmasphere, the time delay between 100-keV and MeV flux enhancements was ∼2–4 hr, consistent with the scenario of a quasi-linear energization of electrons by chorus waves which occurs at progressively higher electron energies (Horne et al., 2005; Mourenas et al., 2015; Thorne et al., 2013). However, during two out of seven events, the flux enhancements happened nearly simultaneously at 100 keV and 1 MeV. Since these events mostly occur during low Pdyn (1.0–4.5 nPa) and high AE (>400 nT) intervals, it is likely that they result either from a fast inward radial diffusion (independent of energy for a roughly constant ULF wave intensity over ∼2–10 mHz, see Ozeke et al., 2014) or from ∼100- to 300-keV electron injection (or inward radial diffusion) immediately followed by a rapid (over ∼10 min) nonlinear acceleration by intense chorus waves up to MeVs (Artemyev, Vasiliev, et al., 2015; Foster et al., 2017; Omura et al., 2015), consistent with our previous discussions.

Details are in the caption following the image
Time delays between 100 keV and 1 MeV (black symbols) or 4 MeV (red symbols) or both (green symbols) electron flux enhancements during the same events, seven events observed at L = 4.2 outside the plasmasphere as a function of Pdyn (left) and AE (center), and four events observed at L = 4.2 inside the plasmasphere as a function of Kp (right).

The four events inside the plasmasphere happen when Pdyn<6 nPa. Figure 3 demonstrates that for most cases, flux enhancements at 100 keV and 1 or 4 MeV occurred within less than 40 min, with only one event for which the time delay reached 3 hr. Moreover, three out of four events occur when Kp < 1. Although the number of such events is very limited, these observations contrast with flux enhancements outside the plasmasphere. This agrees with our previous conjecture that most MeV electron flux enhancements inside the plasmasphere might be produced by inward radial diffusion from regions located outside the plasmasphere, where chorus-induced energization takes place earlier (when Kp is still >3), or by localized electric field impulses leading to fast inward transport and acceleration (Ozeke et al., 2014; Turner, Claudepierre, et al., 2015; Turner et al., 2017; Zong et al., 2009).

3 Superposed Epoch Analysis of Electron Flux Enhancements

Additional insight into the possible origin of flux enhancement events can be gained from a superposed epoch analysis of different events, because it can reveal long-term correlations with various indices or physical quantities (e.g., W. Li et al., 2015). To this aim, we have used even more restrictive conditions to separate events outside and inside the plasmasphere, requiring for events outside the plasmasphere that all three empirical statistical plasmapause location models (O'Brien & Moldwin, 2003) based on AE, Kp, and Dst give Lpp<4.2, and for events inside the plasmasphere that all models give Lpp>4.2. This gave 200 events outside of the plasmasphere at 4 MeV, 110 events at 1 MeV, and 38 events at 100 keV.

In addition to AE and Pdyn, we further considered here IMF Bz(GSM), Dst (or Kp inside the plasmasphere), the GOES ULF wave index, as well as the 40-keV average electron flux at L = 6.6 from GOES for 100-keV flux enhancement events, and lower-band chorus intensity at L = 4–5 from THEMIS spacecraft and the Van Allen Probes (when the latter were available after October 2012) for 4-MeV events. The ULF index is the root-mean-square (RMS) wave power measured by GOES magnetometer within the frequency range of ∈[1,8] mHz, corresponding to Pc5 pulsations (see details on ULF index calculations in ; Kozyreva et al., 2007, and link to ULF index database in the Acknowledgments). The 40-keV electron fluxes measured by GOES at L = 6.6 should be useful for comparisons with 100-keV electron fluxes from GPS satellites at L = 4.2, because when keeping the first adiabatic invariant fixed, 100-keV electrons at L = 4.2 would correspond to ∼30-keV electrons at L = 6.6. This enables us to check whether significant injections from the plasma sheet occur only just before the 100-keV electron flux enhancement at L = 4.2 (related to fast injections down to L = 4.2) or somewhere else at earlier times (related to the more progressive radial diffusion or convection to lower L).

The superposed epoch analyses of different GPS electron flux enhancement events are shown in Figures 4 and 5, separately for cases outside and inside the plasmasphere, as a function of tTend, where Tend denotes the time when the measured electron flux reaches its maximum level.

Details are in the caption following the image
Superposed epoch analysis of electron flux enhancements at L = 4.2 from Global Positioning System (GPS) satellites outside the plasmasphere. From left to right: For 100 keV, 1 MeV, and 4 MeV GPS electron flux enhancements. Top to bottom panels show, respectively, the solar wind dynamic pressure Pdyn, interplanetary magnetic field (IMF) Bz, AE, ULF wave index from Geostationary Operational Environmental Satellite (GOES) at L = 6.6 (Kozyreva et al., 2007), averaged lower-band chorus wave intensity (from THEMIS and the Van Allen Probes) or average 40-keV electron flux from GOES, SYMH index, and GPS electron flux at the considered energy. Black curves show the median values obtained using the stricter criterion for the plasmapause location.
Details are in the caption following the image
Superposed epoch analysis of electron flux enhancements at L = 4.2 from Global Positioning System (GPS) satellites inside the plasmasphere. From left to right: For 100 keV, 1 MeV, and 4 MeV GPS electron flux enhancements. Top to bottom panels show, respectively, the solar wind dynamic pressure Pdyn, interplanetary magnetic field (IMF) Bz, AE, ULF wave index from Geostationary Operational Environmental Satellite (GOES) at L = 6.6 (Kozyreva et al., 2007), average 40-keV electron flux from GOES, Kp index, and GPS electron flux at the considered energy. Black curves show median values obtained using the stricter criterion for the plasmapause location.

3.1 Flux Enhancements Outside the Plasmasphere

At L = 4.2 outside the plasmasphere, one can clearly see from Figure 4 that
  1. 100-keV electron flux enhancements (reaching generally a factor of ∼10) develop in 2–3 hr during periods with AE peaking at 200–800 nT, continuously low Dst (<−20 nT), and moderate Pdyn (∼2–6 nPa); the start of such 100-keV flux enhancements coincides with a minimum of IMF Bz (∼−5 nT); over the 100-keV flux enhancement period, the ULF wave index inferred from GOES measurements at L = 6.6 (Kozyreva et al., 2007) is elevated, varying between 1 and 4 (with a median of 2), and the average 40-keV electron flux from GOES at L = 6.6 also remains continuously high, above 105 e/s/cm2/str/eV, during more than 9 hr before the peak of 100-keV flux enhancement at L = 4.2.
  2. 1-MeV electron flux enhancements (reaching generally a factor of ∼5–10) develop in 6–7 hr during periods of continuously high AE (∼200–800 nT), with continuously low Dst (<−20 nT), and moderate Pdyn (∼2–4 nPa); the start of 1-MeV flux enhancements coincides with a minimum of IMF Bz (∼−3 nT); over the 1-MeV flux enhancement period, the ULF wave index inferred from GOES measurements at L = 6.6 is significant, varying between 0.7 and 2.8 nT (with a median of 1.5 nT), and lower-band chorus wave RMS amplitudes measured by THEMIS and the Van Allen Probes at L = 4–5 remain consistently ≥100 pT.
  3. 4-MeV electron flux enhancements (reaching generally a factor of ∼5–10) develop in 10–14 hr during periods of significant but temporally decreasing AE (∼150–600 nT), low but temporally increasing Dst (<−20 nT), and low Pdyn (∼1–3 nPa); the start of 4-MeV flux enhancements coincides with a minimum of IMF Bz (∼−2 nT; although Figure 4 only shows Tend−15 hr <t < Tend+1 hr, we checked that the minimum of Bz really occurs between Tend−14 hr and Tend−10 hr); over the 4-MeV flux enhancement period, the ULF wave index inferred from GOES measurements at L = 6.6 varies between 0.5 and 2 nT (with a median of 0.9 nT), and lower-band chorus wave RMS amplitudes measured by THEMIS and the Van Allen Probes at L = 4–5 remain consistently ≥100 pT.

The above results indicate that electron flux enhancements at L = 4.2 outside the plasmasphere definitely take more and more time at higher energies (from 2 hr at 100 keV to 7 hr at 1 MeV and 14 hr at 4 MeV). Are these results more indicative of ULF wave-driven radial diffusion and acceleration, or of local accelerations by chorus waves?

The median GOES ULF wave index (the square root of ULF wave power) decreases from 2 to 1.5 to 0.9 for 100-keV, 1-MeV, and 4-MeV events, corresponding to ≈5 (≈2.5) times more Pc5 ULF wave power during 100-keV (1 MeV) events than during 4-MeV events, which should lead to a faster radial diffusion during lower-energy events. The resultant stochastic radial displacement is urn:x-wiley:jgra:media:jgra54378:jgra54378-math-0004 (with the radial diffusion coefficient, DLL, proportional to Pc5 ULF wave power and the available time, Δt), which leads to simultaneous inward electron transport and acceleration provided that the electron phase space density (PSD) gradient is positive toward larger L shells (e.g., Green & Kivelson, 2004; Mourenas et al., 2017; Schulz & Lanzerotti, 1974). Based on the higher median value of the measured GOES ULF wave index during flux enhancement events at lower electron energy, 4-MeV electrons can then take 2.5 (5) times more hours to reach L = 4.2 than 1-MeV (100-keV) electrons when originating from the same, higher L shells. Thus, inward radial diffusion by ULF waves could, in principle, explain the observed longer time scales of flux enhancements at MeV energies. However, this further requires either that such MeV flux enhancement intervals do not overlap at all with time intervals of 100-keV flux enhancements or that the positive electron PSD gradient toward higher L shells be weaker at MeVs than at 100 keV just above L = 4.2. Otherwise, the same ULF wave power should lead to an inward diffusion as fast as for 100-keV electrons over the same time interval. In our data set of flux enhancements, 100-keV electron flux enhancements took place within the 20 hr preceding 35% of the MeV flux enhancement peaks, and 80% of these 100-keV flux enhancements occurred more than 5 hr before MeV flux enhancement peaks. A weaker positive electron PSD gradient toward higher L shells at MeVs than at 100 keV just above L = 4.2 would be needed to account for the observed acceleration via radial diffusion by ULF waves alone. This situation is not unrealistic at all, because observations have shown a usually steeper positive electron PSD gradient toward higher L shells for magnetic moments below 200 MeV/G (i.e., energies below 600 keV at L = 4.2) in the outer belt (e.g., Turner et al., 2012).

However, it is worth noting that the GOES ULF wave index (i.e., the square root of ULF wave power) is moderate and steadily decreasing over 4-MeV flux enhancement events (contrary to 0.1- to 1-MeV events) in Figure 4, especially during the last 4 hr when the flux increases the most. Furthermore, DLL varies faster than L6 over L = 4–6.6, leading to a much weaker radial diffusion at low L shells (<4.5–5) than at L ∼ 6.6 (Ozeke et al., 2014). These two facts suggest that radial diffusion may not be the dominant mechanism in the 4-MeV flux enhancement events displayed in Figure 4. In contrast, the simultaneously measured lower-band chorus waves are sufficiently intense, >100 pT (see Figure 5 from W. Li et al., 2015; our Figure 4), to account for both the observed multi-MeV electron flux enhancements at L = 4.2 and the longer acceleration time scales at higher energies—Fokker-Planck simulations have indeed demonstrated that such intense chorus waves can locally accelerate 30–300 keV injected electrons up to progressively higher energies with typical time scales of ∼10–20 hr for multi-MeV electron energization (Horne et al., 2005; Mourenas et al., 2015; Thorne et al., 2013). Consequently, this local mechanism seems more likely to be the dominant one in general at L < 4.5–5—although probably with some help from fast acceleration near injection fronts, or Time Domain Structures and upper band chorus acceleration, and subsequent inward radial diffusion to get a sufficient seed population of 100- to 500-keV electrons ready for a final chorus-induced acceleration up to MeVs (Gabrielse et al., 2014, 2017; Ganushkina et al., 2013; Jaynes et al., 2015; Ma et al., 2016; Tang et al., 2016, 2017).

The 1-MeV electron flux enhancements develop during intervals of continuously high AE (∼200–800 nT) and continuously low Dst (<−20 nT). They begin just after the IMF Bz reaches a minimum (Bz∼−3 nT), which is likely related to the start of 30- to 100-keV electron injections. Thus, 1-MeV flux enhancements occur during continuous periods of successive substorms with high AE and just after injections, during circumstances usually conducive to strong chorus wave generation (W. Li et al., 2010; Meredith et al., 2003; Miyoshi et al., 2013; Tsurutani et al., 2006), and probably often during the main or early recovery phase of storms. The 4-MeV electron flux enhancements also start just after the IMF Bz reaches a minimum (Bz∼−2 nT) and develop during periods of temporally decreasing but still elevated AE (∼150–600 nT) and increasing Dst (<−20 nT), when intense (≥100 pT) chorus waves are continuously measured. This suggests that the increases in 4-MeV electron flux at L = 4.2 outside the plasmasphere occur during circumstances similar to the 1-MeV flux enhancements but at later times than 1-MeV flux enhancements—that is, when the disturbances start to subside, as during the late part of the storm recovery phase, or during the ending of an especially prolonged period of sustained substorms. Although the ULF wave index from GOES (at L = 6.6) is significant during 1-MeV events, it is smaller than during 100-keV electron flux enhancements. This seems to imply that inward radial diffusion can have some effect in the observed 1-MeV flux enhancements at L = 4.2 but less significant than for 100-keV events.

The 100-keV electron flux enhancements occur within short time periods (∼2–3 hr) when AE is clearly peaking around 400–800 nT. They begin just after IMF Bz reaches a minimum, lower than for MeV flux enhancements, and develop during periods of higher Pdyn and lower Dst than for MeV events. This suggests that 100-keV events at L = 4.2 generally occur earlier than MeV events—during an earlier part of a storm, or of a period of successive substorms, following an increase in solar wind dynamic pressure. Moreover, the ULF wave index is significantly higher than for MeV events and the 40-keV electron flux from GOES at L = 6.6 remains elevated for hours before the enhancement at L = 4.2, indicating the probable importance of inward radial diffusion after initial injections from the plasma sheet. Interestingly, the IMF Bz turns slightly positive within ±1 hr of the maximum 100-keV flux enhancement during half of the events, showing that such events often proceed very quickly from short-lived injections.

The relationships found here between MeV electron flux enhancements and AE, Pdyn, Dst, and IMF Bz based on 7 years of GPS satellite data at L = 4.2 outside the plasmasphere are in good agreement with the superposed epoch analysis from W. Li et al. (2015), which considered efficient MeV electron acceleration events between October 2012 and March 2015 based on Van Allen Probes measurements. W. Li et al. (2015) found that efficient MeV electron acceleration at L = 4–5.5 mostly occurs during periods of AL =− 200 to −400 nT, SYMH =− 60 to −25 nT, IMF Bz between −4 and −2 nT, Pdyn∼1.8–3.5, and the presence of intense chorus waves at L = 4–5.5. In contrast with the present GPS results, however, they did not find a minimum of IMF Bz at the beginning of electron flux increases, maybe because they considered the PSD maximum (which may be at different Ls as a function of time) instead of the flux at a fixed L as in the present analysis, or maybe due to the much smaller number of events (16) in their data set. But at least one of their events (in their Figure 1) shows the same behavior with IMF Bz as in our Figure 4.

Let us finally note that during the considered flux enhancements, SYMH generally only varies slightly (by less than 10 nT, as shown in Figure 4, compared to a background magnetic field magnitude of 400 nT at L = 4.2), implying that purely adiabatic flux increases related to the Dst effect (e.g., see Kim & Chan, 1997) should remain moderate during such flux enhancements, except maybe during some strong storms.

3.2 Flux Enhancements Inside the Plasmasphere

Electron flux enhancements inside the plasmasphere at L = 4.2 occur during completely different circumstances compared to those outside the plasmasphere. Figure 5 shows that at all energies, the flux increase takes place in less than 1 hr, with a smaller magnitude than outside the plasmasphere (only a factor of 3–5 at 1–4 MeV). Moreover, the flux decreases to its initial level within the next hour. Furthermore, during these events, IMF Bz∼0, AE < 100 nT, and GOES ULF wave index is smaller than 0.8 (i.e., low disturbances). However, during about 25% of such flux enhancements, Pdyn simultaneously increases above 3–4 nPa, Kp increases to 1.7–3.0, and GOES ULF wave index increases.

All these results seem to indicate that such electron flux enhancements are not produced locally but rather from a fast inward transport (through radial diffusion, convection, or coherent interaction with some waves) of some elevated flux originating at higher L above the plasmapause. The rapid decrease of flux 1 hr after the enhancement may come in part from losses into the atmosphere induced by resonant interaction with hiss waves, possibly combined with resonant interaction with EMIC waves at high energies above 4 MeV, but such losses should usually lead to a reduction of 100-keV to 4-MeV electron flux at L = 4.2 inside the plasmasphere by less than 10% over 1 hr for typical wave amplitudes when Kp ∼ 2 (e.g., see Mourenas et al., 2016, 2017, and references therein). Thus, the rapid flux decrease should probably result from the limited duration of a fast injection and inward transport of a wide but limited bunch of high electron flux (Turner, Claudepierre, et al., 2015; Turner et al., 2017), leading to the limited duration of the flux increase captured at a given L shell (∼3.5–5). This interpretation is supported by two facts: (1) the average 40-keV electron flux measured by GOES at L = 6.6 reaches high levels (>2 × 104 e/s/cm2/str/eV) over 1 hr preceding these 100-keV flux increases in Figure 5 and (2) there are as many similar flux increases at 100 keV but 3 times fewer increases at 4 MeV, than outside the plasmasphere, in agreement with the much higher occurrence of fast electron injections to L < 4.5 at energies <300 keV (e.g., Turner et al., 2017).

4 A Typical GPS Electron Flux Enhancement Outside the Plasmasphere

One typical event of multi-MeV electron flux enhancement at L = 4.2 outside the plasmasphere, observed on 28 September 2016 by GPS satellites when IMF Bz was increasing and AE was steady before decreasing, is shown in Figure 6. During this event, electron fluxes increased significantly at 0.1–5 MeV, by a considerably larger amount and much more rapidly at lower energies. Due to much higher initial fluxes at lower energy, however, the flux enhancement ratio (compared to the initial value) is smaller (Figure 7). At 3–5 MeV, fluxes increased by a factor of 5–10 over 8–9 hr. Such characteristic behaviors are expected in the case of quasi-linear energization by chorus waves from an initially narrow energy distribution, leading to a progressive energy broadening of this distribution (Horne et al., 2005; Mourenas et al., 2015; Thorne et al., 2013). Then, Kp was around 4–5 and AE ∼ 1,000–1,500 nT, SYMH decreased from −30 to −49 nT before recovering, and Pdyn remained stable at ∼3.5–4. During this event, the Van Allen Probes measured lower-band chorus waves with RMS amplitudes Bw∼50–100 pT (and a large variance δBw∼50 pT) at a frequency ∼0.35 times the electron gyrofrequency over L ∼ 4.5–5.8, during at least 2 hr over 0–3 MLT. Intense chorus waves may also be present at other MLTs at L ∼ 4.2 during this event, but the orbital coverage of the Van Allen Probes did not allow us to confirm this. Such high chorus amplitudes are similar to chorus amplitudes measured during the strong storm on 17 March 2013 at L ∼ 4.25, when ∼100 pT chorus waves, present over 8–10 hr in MLT, were measured and were sufficient to account for the observed increase of 1- to 5-MeV electron fluxes over a 10-hr period through chorus-induced energization alone, provided that the local electron plasma density was sufficiently small, <13 cm−3 (W. Li et al., 2014; Mourenas et al., 2015). During our event on 28 September 2016, the density inferred from spacecraft potential measurements of the Van Allen Probes at L = 4.2–4.6 was roughly ∼10–20 cm−3.

Details are in the caption following the image
A typical event of multi-MeV electron flux enhancement at L = 4.2 outside the plasmasphere on 28 September 2016. The variations of interplanetary magnetic field (IMF) components, Pdyn, solar wind velocity Vs, Kp, AE, SYMH, measured lower-band chorus RMS amplitudes along with their standard deviation from the Van Allen Probes at L = 4.6–5, and the 0.12, 1, and 4 MeV fluxes from Global Positioning System satellites are displayed.
Details are in the caption following the image
The initial and final Global Positioning System electron distributions for the same event as in Figure 6.

Further assuming that a peak of electron PSD formed at L = 4.5–5.5 through chorus-induced energization and using the radial diffusion coefficient DLL from (Ozeke et al., 2014) for Kp ∼ 5 and L ∼ 4.5, an inward radial diffusion of urn:x-wiley:jgra:media:jgra54378:jgra54378-math-0005 from L = 4.5 to L = 4.2 may have occurred over Δt≤6 hr (Mourenas et al., 2017). Thus, the 28 September 2016 energization event at L = 4.2 may be explained by 30- to 200-keV electron injections, followed by chorus-induced quasi-linear electron energization around L = 4.5–5.5, and further inward radial diffusion by intense ULF waves from this flux peak, although it occurred during a much weaker storm than the one on 17 March 2013.

5 Conclusions

The statistical results presented in this paper demonstrate the main solar wind and geomagnetic activity parameters most favorable to strong electron flux enhancements, confirming or supplementing findings from other similar studies (e.g., Kim et al., 2015; Murphy et al., 2018, and references therein). This is an important step toward accurate forecasts of the dynamics in the outer radiation belt. First, we examined hundreds of electron flux enhancements (between 100 keV and 4 MeV) observed by GPS satellites at L = 4.2 (inside or outside the plasmasphere) from 2009 to 2016, looking for statistical relationships between flux enhancements at different energies and solar wind dynamic pressure Pdyn, AE, and Kp indices. We have found that multi-MeV electron flux enhancements outside the plasmasphere occur during intervals of low Pdyn and high AE, with increasing enhancements at higher AE, whereas 100-keV enhancements occur during moderately elevated Pdyn periods and preferentially with higher AE.

A superposed epoch analysis of GPS electron flux enhancements and solar wind and geomagnetic indices, as well as 40-keV electron flux and ULF wave index obtained from GOES at geosynchronous orbit, and chorus wave intensity measured by THEMIS and Van Allen Probes at L = 4−5, further demonstrated that 4-MeV electron flux enhancements outside the plasmasphere start when the IMF Bz attains a (generally negative) minimum value and that they develop during intervals of low Pdyn, high AE, low but temporally increasing Dst <− 20 nT, moderate GOES ULF wave index, and high-amplitude (>100 pT) lower-band chorus waves. The 100-keV electron flux enhancements occur during times of higher (but still moderate) Pdyn, high AE, elevated GOES ULF wave index, and high 40-keV electron fluxes at geosynchronous orbit. Moreover, electron flux enhancements outside the plasmasphere clearly take more time to develop at higher energies: 100-keV events take 2 hr, 1-MeV events take 7 hr, and 4-MeV events develop over 14 hr. These results suggest that flux enhancements at 100 keV are dominated by injections and that electron energization up to a few MeVs is induced predominantly by chorus waves, with further amplification by inward radial diffusion or fast transport.

Inside the plasmasphere, electron flux enhancements are generally weaker than outside the plasmasphere and last less than 1 hr; there are 3 times fewer electron flux enhancements at 1 or 4 MeV but just as numerous flux enhancements at 100 keV as outside the plasmasphere. Such flux enhancements inside the plasmasphere are likely the result of intense injections from the plasma sheet followed by a fast inward transport of limited duration.

Acknowledgments

We gratefully acknowledge the NOAA GOES teams for online data access, the CXD team at LANL for GPS electron flux measurements available from NOAA at https://www.ngdc.noaa.gov/stp/space-weather/satellite-data/satellite-systems/gps/, and the Van Allen Probes EMFISIS data obtained from https://emfisis.physics.uiowa.edu/data/index. X. J. Z. acknowledges the support from RBSP-EMFISIS funding 443956-TH-81074 under NASA's prime contract NNN06AA01C and NASA contract NAS5-02099 for the use of data from the THEMIS Mission accessible from http://themis.ssl.berkeley.edu/, specifically J. W. Bonnell and F. S. Mozer for use of EFI data, A. Roux and O. LeContel for use of SCM data, and K. H. Glassmeier, U. Auster and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC 0302. We also thank the World Data Center for Geomagnetism, Kyoto, for providing the AE, Kp, Dst indexes, and the Space Physics Data Facility at the NASA Goddard Space Flight Center for providing the OMNI data used in this study.