Volume 46, Issue 5 p. 2328-2336
Research Letter
Free Access

Statistical Occurrence and Distribution of High-Amplitude Whistler Mode Waves in the Outer Radiation Belt

E. Tyler

Corresponding Author

E. Tyler

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA

Correspondence to: E. Tyler,

[email protected]

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A. Breneman

A. Breneman

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA

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C. Cattell

C. Cattell

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA

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J. Wygant

J. Wygant

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA

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S. Thaller

S. Thaller

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA

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D. Malaspina

D. Malaspina

Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, USA

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First published: 13 February 2019
Citations: 31

Abstract

We present the first statistical analysis with continuous data coverage and nonaveraged amplitudes of the prevalence and distribution of high-amplitude (>5 mV/m) whistler mode waves in the outer radiation belt using 5 years of Van Allen Probes data. These waves are most common above L = 3.5 and between magnetic local time of 0–7 where they are present 1–4% of the time. During high geomagnetic activity, high-amplitude whistler mode wave occurrence rises above 30% in some regions. During these active times the plasmasphere erodes to lower L and high-amplitude waves are observed at all L outside of it, with the highest occurrence at low L (3.5–4) in the predawn sector. These results have important implications for modeling radiation belt particle interactions with chorus, as large-amplitude waves interact nonlinearly with electrons. Results also may provide clues regarding the mechanisms which result in growth to large amplitudes.

Key Points

  • High-amplitude whistler mode waves are most prevalent between midnight and dawn and above L of 3.5
  • During active times, high-amplitude waves are present over 30% of the time in some regions
  • Waves greater than 20 mV/m preferentially occur at low L shell in the predawn sector

Plain Language Summary

Our Earth is surrounded by a ring of high-energy electrons, known as the outer radiation belt, which can cause damage to satellites in orbit. These electrons gain such high energy because of a type of electromagnetic waves called “whistler waves,” which exist in the space around Earth. Satellites have recently discovered whistler waves that are tens or hundreds of times as large as the average waves. Such large whistler waves can energize electrons very quickly and also cause electrons to be knocked into our atmosphere, creating aurora. Because these large waves are hard to measure, scientists have not been able to say how often they occur, where they occur, or even how exactly they form. This study uses a unique data set gathered by the Van Allen Probes to find out when and where these very large whistler waves occur. We found that these waves appear mostly in the nightside and morning side of the Earth, and they tend to appear much closer to Earth than smaller whistler waves do. This information offers us clues about how these monster waves form and what impact they might have on the radiation belt and the Earth.

1 Introduction

Since the 1960s, in situ spacecraft measurements of magnetic and electric fields have demonstrated that whistler mode waves are a common feature of the outer radiation belt region (Burtis & Helliwell, 1976). A type of whistler mode wave dubbed “chorus” (due to the frequent rising pitch of the wave packets) are of significant interest due to their interactions with energetic particles. These waves are generated with frequencies below the electron cyclotron frequency (fce), near the magnetic equator, and arise from temperature anisotropies in the electron population (Kennel & Petschek, 1966). Magnetospheric chorus has been shown to be responsible for the acceleration of electrons to highly relativistic energies through resonant interactions (Omura et al., 2015; Summers et al., 1998; Thorne et al., 2013). They also effectively pitch angle scatter electrons into the loss cone (Summers et al., 2007), causing phenomena such as electron microbursts observed in the upper atmosphere (Breneman et al., 2017; Hikishima et al., 2010), pulsating aurora (Sandahl, 1984; Jaynes et al., 2015; Kasahara et al., 2018), and diffuse aurora (Thorne et al., 2010; Villalón & Burke, 1995).

Historically, the amplitudes of whistler mode waves in the radiation belts was known only from time-averaged spectral data, which obscured the true amplitudes of short-lived wave packets. Meredith et al. (2001), using CRRES data, found that mean wave amplitude ranged from less than 0.1 mV/m during quiet times to greater than 0.5 mV/m in active times. Using Time History of Events and Macroscale Interactions during Substorms (THEMIS) electric field data, Cully et al. (2008) observed the highest mean wave amplitude (around 1–2 mV/m) in the prenoon sector for L shell between 5 and 10. However, the distribution of the peak 4-s-averaged amplitudes was much more widely spread across the entire postmidnight and prenoon sectors, and extending in further to L around 3.5. These peak wave amplitudes reached a maximum of around 30 mV/m.

Burst capture data expanded our understanding of whistler mode waves by enabling us to observe their true amplitudes. Santolík et al. (1278), utilizing Cluster's wide-band waveform electric field data, observed chorus packets with 30 mV/m amplitudes. Cattell et al. (2008) observed whistler mode waves up to 240 mV/m from waveform capture data on the STEREO B satellite. Large-amplitude waves have now also been observed and studied with THEMIS, Wind, and the Van Allen Probes (e.g., Cully et al., 2008; Kellogg et al., 2010; Li et al., 2011, 2013; Wilson et al., 2011). These large-amplitude whistler mode waves interact differently with electrons than their lower-amplitude counterparts, potentially resulting in trapping, rapid energization or de-energization, and pitch angle scattering (Bortnik et al., 2008; Cattell et al., 2008; Kellogg et al., 2010; Kersten et al., 2011; Omura et al., 2008, 2013; Summers & Omura, 2007). Malaspina et al. (2018) showed that even moderate-amplitude whistler mode waves could demonstrate nonlinear distortions in their waveforms, and the relative magnitude of this distortion is amplitude dependent.

However, statistically, studying large-amplitude waves has remained a challenge due to the low-duty cycle of burst capture data. The Electric Field and Waves (EFWs) filter bank data set from the Van Allen Probes (Wygant et al., 2013) offers the first opportunity to determine the prevalence, location, and distribution of these high-amplitude whistler mode waves in the radiation belt region with 100% duty cycle and without time averaging the amplitudes. We have performed a statistical analysis of 5 years of continuous Van Allen Probe B data covering all magnetic local time (MLT) and a range of L from 3 to 6 to map the distribution of high-amplitude chorus waves in the outer radiation belt. By selecting waves with an amplitude greater than 5 mV/m, we can study whistler mode waves with peaks approximately 1 to 2 orders of magnitude larger than the reported average chorus amplitude.

2 Data and Methodology

The Van Allen Probes are in a 9-hr elliptical orbit, with perigee around 600 km and apogee around 6 Re, covering much of the radiation belts region. The spacecraft orbit remains within 20° of the equatorial plane and precesses around the earth over the course of around 22 months. During the 5-year FBK7 collection phase, all MLT sectors below L = 6 are covered multiple times, giving robust statistical results throughout most of the declining phase of the solar cycle.

We use the filter bank data product produced by the EFW instrument on Van Allen Probe B for our statistical analysis. This product takes wave data measured at 16,384 samples per second and records the maximum and average wave amplitude every 1/8 s in a frequency range from 0.8 to 6500 Hz. No time averaging is performed on the peak amplitudes, thus preserving the observed amplitude of the wave without the constraint of storing and telemetering high-cadence burst data. The EFW filter bank data product operates in two modes—FBK13 and FBK7. FBK13 collects only electric field data in 13 logarithmic-spaced frequency bins, while FBK7 collects both electric and magnetic field data in seven frequency bins. This study will focus on electric field results from the FBK7 mode spanning 5 years from 16 March 2013 to 28 February 2018.

The EFW filter bank is able to provide this continuous, high-cadence data product because of its limited frequency resolution. However, due to the design of the instrument, we can improve both the frequency resolution and amplitude accuracy of the filter bank data by interpolating between the different frequency channels. Much like the human brain receives signals from three types of color-sensing cells in the eye and recreates the full spectrum of visible color from that data, we use the data from each frequency channel to reconstruct the original wave frequency observed by the instrument.

This reconstruction was done in two steps: first, a frequency interpolation and then an amplitude interpolation. The instrument was designed so that the gain curves of each frequency channel would overlap, allowing a narrowband wave with a frequency between the peaks of two gain curves to be observed in both channels simultaneously. To reconstruct the correct frequency of the wave, we measure the level of attenuation between the peak amplitude measured in one channel to the amplitude measured in the other. Given the assumption that the two peaks recorded are the result of a single, narrowband wave, we can determine the actual frequency of the observed wave. Once the frequency has been corrected, we can use the shape of the gain curves to reconstruct the correct amplitude of the narrowband wave. The corrected amplitude of a wave will always be equal to or larger than the measured amplitude.

Figure 1 demonstrates the ability of this interpolation method to reconstruct the frequencies and amplitudes of chorus waves observed by Van Allen Probes B during a 4-hr period on 16 April 2015. Panels (a) and (b) compare wave frequencies from the time-averaged spectral data in color with the interpolated filter bank data in black. It is apparent that the interpolated values greatly improve the frequency resolution of the filter bank data, and the black squares are largely in agreement with the time-averaged spectral data. Panels (c) and (d) show the original amplitude measurements from the filter bank data plotted in blue (with cyan dots in panel d) and the corrected amplitudes plotted in red (with yellow dots in panel d). Panel (d) also compares full waveform data from a period of burst capture on the E12 axis to the original and interpolated filter bank amplitudes. These comparisons indicate that the amplitude interpolation improves the filter bank accuracy, but it still underestimates the true amplitude of the waveforms.

Details are in the caption following the image
A comparison of the interpolated frequencies and amplitudes to time-averaged spectral data and original filter bank data. (a) The time-averaged spectrogram for the electric field during the first orbit of Van Allen Probes B on 16 April 2015; (b) the same spectrogram with the interpolated frequencies of filter bank peaks overplotted in black squares. The original filter bank frequencies are shown by the pink lines. (c) The original filter bank amplitudes in blue and interpolated amplitudes in red. (d) A segment of burst data in black with blue/cyan indicating filter bank amplitudes before interpolation and red/yellow indicating filter bank amplitudes after interpolation.

Although interpolation is a powerful method by which we can improve the quality of our data, there is the potential of introducing errors. To mitigate this, we placed upper and lower limits on the ratio of amplitudes observed in adjacent frequency bins. If adjacent amplitude ratios were either too high or too low, interpolation was not permitted and the original filter bank results were preserved. The lower limit is set due to the nature of the overlap of the filter bank gain curves; the upper limit is a condition of the narrowband assumption for observed waves. We also limited the allowed amplitude adjustment to a factor of 2 times increase from the original data in order to avoid introducing large errors in cases where waves are not narrow band. This limit generally prevented overestimation errors but causes some amplitudes to be underestimated, which was deemed an acceptable compromise to avoid introducing spurious high-amplitude events into the statistics. Finally, in order to filter out broadband time domain structures, we flagged and removed any data in which the 12- to 24- and the 50- to 100-Hz frequency bands simultaneously observed peaks greater than 0.4 mV/m. These two bands consistently responded with such high amplitudes simultaneously only if time domain structures were present. All limits were chosen based on quality testing as in Figure 1 and the shape and overlap of the instrument gain curves. A more in-depth discussion of the interpolation and filtering performed on the filter bank data can be found in Tyler (2018).

After the interpolation and filtering, we selected only waves with frequencies between 0.1 and 1 fce with amplitudes greater than 5 mV/m. These waves constitute our high-amplitude whistler mode wave data set. Our frequency and amplitude limits eliminate most plasmaspheric hiss from our data set (Hartley et al., 2018; Meredith et al., 2018), leaving primarily magnetospheric chorus waves, with the exception of unusually low frequency “cernuous” chorus (Cattell et al., 2015). However, we will refer to the observed waves herein as whistler mode waves to reflect the possibility that we may include a small population of hiss or other whistler mode waves besides chorus. We also include a very small population of electron cyclotron waves, but these waves tend to be less common and lower in amplitude than whistler mode waves. Comparison to time-averaged data indicated that electron cyclotron wave contamination is insignificant. Due to limitations in the interpolation method discussed above and the fact that the filter bank data are collected on one spacecraft axis only, all amplitude results given here are still underestimates of the true wave amplitudes and statistical results should thus be seen as lower limits.

We have included the average plasmapause location in our analysis. The average locations plotted in Figure 3 are derived from estimates of the cold plasma density, calculated from the spacecraft potential and calibrated by comparison to the upper hybrid resonance line in the electric field spectra from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) High-Frequency Receiver (Kletzing et al., 2013; Kurth et al., 2015; Thaller et al., 2015; Wygant et al., 2013). We denote the average plasmapause location to be the L value where the average density falls below 100 cm−3 as discussed in Thaller et al. (2015).

3 Statistical Results

Figure 2 shows the occurrence of high-amplitude whistler mode waves binned by 0.5 L shell and 0.5 MLT. Panel (a) represents all waves >5 mV/m, and panels (b)–(d) respectively show waves within 5–20, 20–50, and >50 mV/m. Each panel represents the percentage of time in each spatial bin when high-amplitude waves were observed, with white bins indicating percentages which fall below the lowest value shown on the color bar. Note that the color bars differ between panels.

Details are in the caption following the image
The percent occurrence of whistler mode waves with (a) amplitudes >5 mV/m, (b) amplitudes between 5 and 20 mV/m, (c) amplitudes between 20 and 50 mV/m, and (d) amplitudes greater than 50 mV/m. Note that the color bars differ between panels.

Whistler mode waves above 5 mV/m are present across the night and morning sectors, extending up to noon, but are largely absent in the postnoon to dusk region. They are observed at all L above 3.5. These waves are most prevalent in the region between midnight and 7 MLT, with peak occurrence of 4.1%. The majority of the waves are observed within 5° of the magnetic equator in all regions except at low L near dawn. The MLT distribution of the occurrence of the highest-amplitude waves is clearly different than the distribution of mean chorus wave amplitude and power, which is maximum from dawn to noon in for higher L (Cully et al., 2008), and across the entire midnight-to-noon span in for lower L (Aryan et al., 2016).

Waves with amplitudes between 5 and 20 mV/m occur a few percent of the time throughout the nightside and morning side, with more common occurrence between 0 and 7 MLT and a preference for L > 5. The peak occurrence of 3.8% is seen around an MLT of 3 and L between 5 and 5.5. Waves with amplitudes 20–50 mV/m in contrast have a more restricted spatial extent, vanishing almost entirely past MLT of 7. Occurrence in the postmidnight to dawn sector in most spatial bins is around a tenth of a percent. Occurrence between MLT of 0 and 3 is highest at L > 5 and shifts to lower L shell between MLT of 3 and 7. The distribution peaks around MLT 4 and 5 where the occurrence of waves between 20 and 50 mV/m reaches 0.59%. Panel (d) shows that the occurrence of waves greater than 50 mV/m rose above 0.01% in only a few regions. These extremely high amplitude events occur primarily at low L shell, between L = 3.5 and 4 and MLT = 3–7. The peak occurrence rate was 0.15% around MLT = 4. A comparison of these panels demonstrates that, while whistler mode waves greater than 5 mV/m populate much of the chorus source region, the largest of these waves are preferentially generated at low L and in the predawn sector.

The prevalence and location of high-amplitude waves changes dramatically with geomagnetic activity as quantified by the Auroral Electrojet Index (AE). We define three levels of geomagnetic activity, with AE < 300 nT indicating “quiet” times, AE between 300 and 600 nT indicating moderate activity, and AE > 600 nT indicating active times. The occurrence of large-amplitude whistler mode waves increases with increasing geomagnetic activity. For all waves >5 mV/m, peak occurrence in any spatial bin is 1.8% for quiet activity, rises to 13% for moderate activity, and reaches 31% for high activity.

Figure 3 shows the three amplitude ranges separated by geomagnetic activity. Panels (a)–(c) show the percent occurrence of 5- to 20-mV/m whistler mode waves in quiet, moderate, and active times respectively; panels (d)–(f) show the same quantities for 20- to 50-mV/m waves; and panels (g) and (h) for amplitudes greater than 50 mV/m. The average plasmapause location is overplotted for each AE range with a pink line. As geomagnetic activity increases, the average location of the plasmapause in the postmidnight to dawnside moves to lower L shell as expected due to erosion by enhanced electric fields (Grebowsky, 1970; Thaller et al., 2015). For moderate geomagnetic activity, the average location is approximately L = 4, and for high activity it is around L = 3.5 in this sector.

Details are in the caption following the image
The percent occurrence of whistler mode waves separated by geomagnetic activity for amplitudes between 5 and 20 mV/m (a–c), amplitudes between 20 and 50 mV/m (d–f), and amplitudes greater than 50 mV/m (g and h). Average plasmapause location for each range of geomagnetic activity is indicated by the pink line. No spatial bin observed >50 mV/m waves more than 0.01% of the time during quiet times, so no results are displayed at that panel. Color bars vary between panels.

For all amplitude ranges, higher activity correlates with increasing wave occurrence at low L shell in the predawn sector. For waves greater than 20 mV/m this increase in low-L whistler mode waves occurs inside the average position of the plasmapause for moderate storm activity (panels e and g). However, because the plots show only the average plasmapause location rather than the instantaneous location, these extremely high-amplitude events likely still occur outside of the plasmapause, at times when the plasmasphere configuration is more eroded than is typical for the given AE range. Because the majority of high-amplitude waves fall between 5 and 20 mV/m, the occurrence pattern for waves in this amplitude bin are very similar to the occurrence for all waves >5 mV/m. Peak occurrence is 1.8% for quiet activity, 12% for moderate activity, and 25% for high activity in the 5- to 20-mV/m bin. Waves with amplitudes between 20 and 50 mV/m peak at 0.11% occurrence in quiet conditions, reach up to 1.5% during moderate activity, and 6.6% during high activity. Waves greater than 50 mV/m do not exceed 0.01% in any spatial bin for quiet conditions, peaks at 0.18% of the time for moderate conditions, and reaches 2.1% of the time for active conditions, particularly in the predawn, low-L sector.

4 Discussion and Conclusions

We have presented the first statistical maps of the occurrence of whistler mode waves with amplitudes from approximately 10 to more than 100 times the reported average amplitudes. Because electrons in the radiation belt are expected to interact strongly with these high-amplitude waves, understanding their true prevalence and spatial distribution is vital for accurate modeling of radiation belt dynamics. Using 5 years of Van Allen Probes EFW filter bank data, we have demonstrated occurrence patterns for these waves, which have not been previously described and are distinct from the statistical patterns of mean-amplitude chorus.

High-amplitude whistler mode waves >5 mV/m are observed throughout the premidnight to early-afternoon sector, but particularly above L of 3.5 and MLT from 0 to 7 and within 5° of the magnetic equator. Within this region, chorus with amplitudes greater than 5 mV/m are seen a few percent of the total time, peaking at 4.1% occurrence. Most of these high-amplitude whistler mode waves fall between 5 and 20 mV/m. Waves greater than 50 mV/m are largely restricted to low L shell between MLT = 4 and 7. We note that these amplitudes are still underestimates of the actual wave amplitudes and the occurrence is thus a lower limit.

Occurrence rate increases dramatically with geomagnetic activity. During low activity (AE < 300 nT) the maximum occurrence rate observed in any spatial bin for waves greater than 5 mV/m is 1.9%. That rises to 13% for moderate geomagnetic activity (AE = 300–600 nT) and 31% for high geomagnetic activity (AE > 600 nT). Peak occurrence for waves between 20 and 50 mV/m reach 6.6% for high activity and waves greater than 50 mV/m are seen up to 2.1% of the time for high activity in some regions.

Geomagnetic activity also changes the spatial distribution of the waves. As increased activity causes erosion of the plasmasphere, high-amplitude whistler mode waves are observed at lower L, particularly between MLT of 4 and 7 and L between 3.5 and 4. The increase in wave occurrence in this sector is more prominent with higher geomagnetic activity and with higher amplitude waves, with waves greater than 50 mV/m occurring almost exclusively in this region. The high occurrence of these very large waves at low L in the predawn sector may provide important clues to the mechanism by which whistler mode waves reach such high amplitudes. Wave occurrence, particularly during moderate or high activity, peaks at higher L near midnight and lower L in the predawn to dawn sector, following the drift pattern of electron injections from the tail. However, occurrence of high-amplitude waves does not decrease along this drift path as one might expect as drifting electrons gradually lose their free energy. High-amplitude waves actually become more prevalent in the low-L morning sector. One possible reason for these observations is that, when the plasmasphere is highly eroded, the low-density and high magnetic field strength in this inner region may enhance the growth of whistler mode wave amplitudes (Omura et al., 2009).

Comparison with previous studies on chorus wave statistics shows that the high-amplitude wave distribution patterns are distinctly different from the average wave distribution. Agapitov et al. (2013) used 10 years of Cluster data to demonstrate that the occurrence rate of >1 pT, near-equatorial chorus waves between L = 3 and 6 was spread across the morning, day, and afternoon sectors, with greater occurrence in the afternoon region. During high geomagnetic activity (which they defined as Kp > 3) an increase in low-L shell occurrence was observed primarily on the dayside. Li et al. (2011) reached similar conclusions using THEMIS spectral and burst data between an L of 5 and 10. They found the highest 10- to 50-pT chorus occurrence across the entire dayside in this L range. However, they also binned the burst-capture chorus results by amplitude and found that chorus amplitudes greater than 300 pT occurred preferentially (up to a few percent of the time) in the premidnight to postdawn sector, similar to our electric field results. Our Van Allen Probe statistics expand this view down to lower L and with higher spatial resolution and more complete coverage, demonstrating that the pattern observed in Li et al. (2011) extends down to L of 3.5 during times of plasmasphere erosion.

Previous studies have observed that many high-amplitude whistler mode waves are obliquely propagating and quasi-electrostatic (Cattell et al., 2008; Wilson et al., 2011). Comparison of our results to Li et al. (2016) shows that the MLT and L shell range of high-amplitude events matches well with the location of quasi-oblique lower-band chorus observed using EMFISIS data. This suggests that the high-amplitude waves may be an important constituent of this quasi-obliquely propagating population. A similarly located oblique and electrostatic population was observed in plasmaspheric hiss by Hartley et al. (2018) below L of 3, which was suggested to be generated by chorus waves penetrating into the plasmasphere. However, both the quasi-oblique chorus and oblique hiss populations were shown to be more prevalent during geomagnetic quiet conditions, while high-amplitude waves in our sample are much more prevalent in active conditions. Our sample may also contribute to the highly oblique chorus population reported in Agapitov et al. (2018) observed on the nightside and at L < 5. These waves were reported to occur during active times and could have very high electric to magnetic field ratios.

An open question suggested by our results is whether large-amplitude chorus waves are preferentially generated very close to the plasmapause boundary or whether they are generated at all L outside of the plasmasphere. To investigate this, future work will examine the chorus wave standoff distance from the plasmapause, using real-time modeled and measured plasmapause locations rather than the average plasmapause location. Additionally, our study has provided a large data set of high-amplitude wave events from which we can select specific case studies based on geomagnetic activity or location in order to examine their burst waveform data. Comparative case studies of whistler mode waves observed in the region of low-L-enhanced wave power and those elsewhere in the magnetosphere may provide a clearer picture of why high-amplitude waves occur preferentially in this region during high geomagnetic activity.

Acknowledgments

This study was supported by NASA contract NNN06AA01C at the University of Minnesota. Van Allen Probes EFW data may be accessed at http://www.space.umn.edu/rbspefw-data website. Van Allen Probes EMFISIS data may be accessed at https://emfisis.physics.uiowa.edu website. The Auroral Electrojet Index may be accessed at http://wdc.kugi.kyoto-u.ac.jp/aedir/index.html website.