Global Occurrences of Electrostatic Electron Cyclotron Harmonic Waves Associated With Radiation Belt Electron Distributions

Abstract

Electrostatic electron cyclotron harmonic (ECH) waves can yield diffuse aurora primarily at higher L-shells by driving efficient precipitation loss of plasma sheet electrons. Here using the Van Allen Probes high resolution data, we examine in detail the global occurrences of ECH waves during the period from 1 October 2012 to 30 June 2017 and find that there are totally 419 events of enhanced ECH waves. The statistical results demonstrate that ECH waves can be present over a broad region of L = 4–6 and 00–24 MLT, with a higher occurrence in the region of L = 5–6 and 06–19 MLT. The electron phase space density exhibits a distinct ring distribution (∂f/∂v_⊥ > 0) with the peak energy around a few kiloelectron volts. Both ECH wave events and the electron ring distributions are closely related and tend to be more distinct with increasing geomagnetic activity.

Key Points

• Coordinated observation of electrostatic electron cyclotron harmonic (ECH) waves and electron ring distributions is presented
• ECH waves can be present over a broad region of magnetosphere, with a higher occurrence in the region of L = 5–6 and 06–19 MLT
• Both ECH waves and electron ring distributions are closely related and tend to be more distinct with increasing geomagnetic activity

1 Introduction

Electrostatic electron cyclotron harmonic waves, which have been initially reported by Kennel et al. (1970), propagate at very large angles relative to the ambient magnetic field (Gurnett & Bhattacharjee, 2005). They are considered to be excited by the instability of electrons with loss cone features outside the plasmasphere near the geomagnetic equator (Ashour-Abdalla & Kennel, 1978; Ashour-Abdalla et al., 1979; Horne, 1989; Horne et al., 2003). Those electrons (with the perpendicular velocity v_⊥) can also display a typical ring distribution function (∂f/∂v_⊥ > 0). ECH waves occur in multiple harmonic bands of the electron cyclotron frequency (f_ce) and are usually described as (n + 1/2)f_ce waves (Fredricks & Scarf, 1973; Gurnett et al., 1979; Kennel et al., 1970; Meredith et al., 2009). Recently, Zhou et al. (2017) have provided the observational evidence that ECH waves can be generated in both lower and upper half of harmonic frequency bands. ECH waves can strongly resonate with energetic (approximately kiloelectron volts) electrons and responsible for the precipitation loss of electrons in the diffuse auroral zone (Horne & Thorne, 2000; Horne et al., 2003; Ni et al., 2012; Tao et al., 2011; Zhang et al., 2013). The statistical analysis of ECH waves using Time History of Events and Macroscale Interactions during Substorms data by Ni et al. (2011) shows that ECH waves occur throughout the outer magnetosphere (L> 5), and expand to higher L-shells with enhanced occurrences when geomagnetic activity intensifies. Using the data from the Magnetospheric Multiscale spacecraft, Lou et al. (2018) have found double peaks of ECH wave occurrence zone on the dayside and high occurrence rates of prenoon ECH waves. They further propose that dayside ECH waves can potentially contribute to the formation of dayside diffuse aurora.

In this study, we shall utilize 6 years (from 1 October 2012 to 30 June 2017) of Van Allen Probes data to investigate the global distribution of ECH waves associated with the electron ring distribution under different geomagnetic conditions, which has seldom been reported so far. The wave electric field power spectra (10–500 kHz) are obtained from the high-frequency receiver (HFR) of the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrumentation suite. The electron differential fluxes (15 eV to 50 keV) are measured by the Helium, Oxygen, Proton, and Electron (HOPE) instrument.

2 Coordinated Observation and Analysis

2.1 Case Study

Figure 1 shows dynamic evolution of wave electric spectra and electron differential fluxes during four ECH wave events. Events A and B were observed by Probe A during 23:10–24:00 UT on 22 June 2017 and 06:34–07:02 UT on 17 May 2014, respectively. Events C and D were observed by Probe B during 20:12–20:38 UT on 26 December 2013 and 05:40–06:03 UT on 27 November 2012, respectively. Strong ECH waves exhibited distinct multiple harmonic bands, up to eight harmonic bands in events B and C. The electron differential fluxes for the pitch angle α = 90° were enhanced and displayed peaks roughly in the energy range 3–8 keV.

Figure 1

Coordinated observations of electron cyclotron harmonic wave electric spectra from the high-frequency receiver instrument and the energetic electron differential flux for α = 90° from the Helium, Oxygen, Proton, and Electron instrument onboard (a–d) Probe A in events A–B and (e–h) Probe B in events C–D. The white dashed lines indicate the multiple electron gyrofrequencies obtained from the Ephemeris data of Van Allen Probes.

Using the differential flux j data from the HOPE instrument, we derive the electron phase space density (PSD) f for each event via the standard conversion j = p²f (Xiao et al., 2008). Figures 2a–2d show the electron PSD for the pitch angle α = 90° (PSD₉₀) corresponding to events A–D. The loss cone feature appeared with valleys and peaks at energies between 1 and 10 keV, suggesting that the electron PSD exhibits a ring distribution (∂f/∂v_⊥ > 0) during these ECH wave events. To quantitatively describe the observed ring distribution, we define the peak-to-valley ratio of PSD₉₀ as R_pv in this energy range. In events A, B, C, and D, R_pv respectively equals 2.24, 2.32, 2.16, and 1.52, indicating that there is free energy responsible for generating those ECH waves.

Figure 2

The observed electron phase space density (PSD) for the pitch angle α = 90° measured by the Helium, Oxygen, Proton, and Electron instrument in events A–D.

2.2 Statistical Results

In order to further determine the relationship between ECH waves and electron ring distributions in a global scale, we adopt the data recorded by HFR receivers to screen ECH wave events based on the wave frequency distribution characteristics and calculate R_pv for each ECH wave event. ECH waves are identified based on two conditions: the wave frequency above f_ce and the dominant wave power observed around (n + 1/2)f_ce. We use the time interval to separate different events. We find that there is only one event per day for most of time and the minimum time interval between two adjacent events is about 6 hr. The corresponding values of L and MLT are recorded during each wave event. The HFR data are binned as a function of L in a step of 0.5 L and MLT in an interval of 1 hr. We record the number of ECH wave samples in each bin.

Figure 3a shows the number of ECH wave events per month from 1 October 2012 to 30 June 2017, with totally 419 events during this period. Figure 3b displays statistical results of the global distribution of ECH waves. A total of 1101 wave samples are distributed over a broad region of L = 3–6 and 00–24 MLT. In the region of 3 <L< 4, there are only 22 wave samples. The occurrence rate of ECH wave increases as L increases. ECH waves occur most frequently (totally 645 samples) in the region of L = 5–6 and MLT = 6–19. In this region, the number of samples in the dawn to noon sector (MLT = 6–12) is slightly higher than those in the noon to dusk sector (MLT = 12–18). There are the most samples (48) in the bin at L = 5.5–6, MLT = 7–8. Figure 3c shows the statistical results of R_pv for all the 419 ECH wave events. It is shown that the percentage of R_pv within the region of 1–2, 2–3, and higher than 3 is 62%, 24%, and 14% in all the ECH wave events. Moreover, most of electron ring distributions with R_pv > 2 are present in the region of L = 5–6 and MLT = 6–19.

Figure 3

(a)The number of ECH wave events per month from 1 October 2012 to 30 June 2017. (b) Global occurrences of ECH waves during the period from 1 October 2012 to 30 June 2017. (c) Correlations of R_pv with ECH waves. ECH = electron cyclotron harmonic.

In order to investigate the dependence of ECH wave occurrence rate on the level of geomagnetic activity, we adopt Dst index to separate all identified ECH wave events into three categories: the quiet period (Dst > −10 nT), the weak period (−30 nT <Dst ≤ −10 nT), and the active period (Dst≤ − 30 nT). Figures 4a–4c show the number of ECH wave samples in each bin as a function of L-shell and MLT for various geomagnetic periods. During the period Dst > −10 nT, most (535 of the 749 samples) ECH waves occur in the dayside region of L = 5–6 and 4–19 MLT, and the region with the most samples (32) is L = 5.5–6 and MLT = 7–8. ECH waves can extend to lower L-shells during enhanced geomagnetic activity while the highest occurrences of ECH wave events are still located in L = 5.5–6. The most wave samples occur between the location L = 5.5–6 in the 15–21 (or 6–9) MLT sector during the period −30 nT <Dst≤ − 10 nT (or Dst ≤ −30 nT). Figures 4d–4f show the percentage of R_pv in different ranges during ECH wave events under different geomagnetic conditions. The percentage of ECH events with R_pv > 3 is 12% during the quiet period Dst > −10 nT and becomes 19% during the disturbed period Dst ≤ −30 nT. This indicates that during active geomagnetic storms, the electron ring distributions become more distinct and consequently more strong ECH waves can be excited.

Figure 4

(a–c) Global occurrences of ECH waves for different storm index Dst during the period from 1 October 2012 to 30 June 2017. (d–f) Correlations of R_pv with ECH waves under different storm index Dst. ECH = electron cyclotron harmonic.

In Figure 5, we similarly use AE index to separate ECH wave events into three geomagnetic periods: the quiet period (AE< 100 nT), the weak period (100 nT ≤AE< 200 nT), and the active period (AE≥ 200 nT). Clearly, most ECH wave samples occur in the dayside region of L = 5.5–6 for different AE indexes (Figures 5a–5c). Specifically, the highest occurrences of wave samples are located in the location L = 5.5–6 in the 17–18, 7–8, and 11–13 MLT sectors during AE < 100 nT, 100 nT ≤AE< 200 nT, and AE ≥ 200 nT, respectively. Figures 5d–5f show that the value of R_pv is sensitively dependent on AE index. When AE index varies from <100 to ≥200 nT, the percentage of 1 < R_pv < 2 decreases from 72% to 30%, while the percentage of R_pv > 3 increases from 10% to 34%. The favorable conditions for ECH wave growth are that there are sufficient resonant electrons and the ring distribution or loss cone features (Ashour-Abdalla & Kennel, 1978; Ashour-Abdalla et al., 1979; Horne et al., 2003; Zhou et al., 2017). The basic reason for the results above lie in that the strong geomagnetic activities can maintain an strong injection of plasma sheet electrons into the inner magnetosphere under enhanced magmetoshperic convection. Meanwhile, the electron perpendicular velocity increases faster than parallel velocity due to the first and second adiabatic invariants. This is tempting to form ring distributions with sufficient resonant electrons during high geomagnetic activities.

Figure 5

The same as Figure 4 but under different substorm index AE.

To support the results above, following the methods in the previous works (Marquardt, 1963; Moré, 1978; Zhou et al., 2017), we have calculated ECH wave growth rate using the data from Van Allen Probe B at 20:34:58 UT on 26 December 2013 (please see supporting information). We find that the observed electron ring distribution can indeed produce distinct ECH waves (see Figure S1). In particular, the wave growth occurs in six harmonic bands, and is stronger in the first four harmonic bands, but weaker in the fifth and sixth harmonic bands. This is consistent with the observation (Figure 1e). Calculations for different cases indeed show similar results (not shown for brevity). This tends to support the current conclusions about the relation between electron distributions and ECH waves though it is not feasible to present calculations of ECH wave growth rates for all the events.

3 Summary

We present the global distributions of ECH wave events associated with electron ring distributions based on the statistical study of the measurements from Van Allen Probes from 1 October 2012 to 30 June 2017. The peak-to-valley ratio (R_pv) of the electron PSD for the pitch angle α = 90° at energies between 1 and 10 keV during ECH wave events is calculated. The statistical database spans a broad radial L range of 3 to 6 and all magnetic local times for quiet and active geomagnetic conditions. The main results are summarized as follows:

1. ECH waves are observed in a abroad region of L = 3–6 and 00–24 MLT and values of R_pv are mostly between 1 and 3 during ECH wave events. Most of wave samples and electron ring distributions with R_pv > 2 are present within the region of L = 5–6 and 6–19 MLT, suggesting that ECH waves are closely related to electron ring distributions.
2. ECH waves can extend to lower L-shells during enhanced geomagnetic activity. The ratio R_pv tends to increase with increasing geomagnetic indexes Dst and AE. This is reasonable because enhanced geomagnetic activity can sustain a prolonged plasma sheet electron injection and consequently an intensified electron distribution. The current results firstly associate ECH waves with the electron ring distribution and provide an important basis for establishing the global model of ECH waves under different geomagnetic conditions in the Van Allen radiation belts.

Acknowledgments

This work is supported by the National Natural Science Foundation of China grants 41531072, 41674166, 41774194, and 41804171 and Scientific Research Fund of Hunan Provincial Education Department under Grant 16K003. All the Van Allen Probes data are publicly available at http://emfisis.physics.uiowa.edu/data/index by the EMFISIS instrument and at https://www.rbsp-ect.lanl.gov/data_pub/ by the HOPE instrument.