Statistical Study on Spatial Distribution of Frequency‐Chirping ECH Elements by Van Allen Probes

Electron cyclotron harmonic (ECH) waves can scatter electrons into the atmosphere causing diffuse aurora with diffusion coefficients depending on the wave frequency. Here we report the Van Allen Probe observations of chirping ECH elements, which are fine structures with a frequency‐chirping rate of ∼kHz/s. 1,834 samples are identified in the 51‐month database and over 93 percent of them exhibit a falling tone pattern. ECH elements cover a broad region from 18 Magnetic Local Time (MLT) through dawn to 14 MLT with L = 4 − 7, and mainly occur in the region of 00–07 MLT with L = 5 − 6. More ECH elements are observed with the occurrence region extending to lower L‐shells during the geomagnetic activity period. Chirping ECH elements can propagate to |MLAT| ∼ 20°, but be confined by the contour of magnetic field strength. The statistical results can be applied on the global simulation of ECH‐induced electron penetration.

can scatter electrons with a pitch angle from loss cone to 60° (Ni et al., 2011a).It means that a rapid change in the frequency of the ECH wave can significantly affect its effect on the magnetospheric electrons.
Frequency-chirping fine structures of chorus (chorus elements) are the most observed (Li et al., 2011;Nunn & Omura, 2012;Santolík et al., 2003Santolík et al., , 2004;;Teng et al., 2017), while the frequency of typical ECH wave barely varies on the time-scale of several seconds in the observations.Chorus elements, of which the duration is about tens to hundreds of milliseconds, can be categorized into rising and falling tones based on the direction of frequency chirping.The frequency chirping rate can be hundreds of Hz to several kHz per second (Li et al., 2011;Teng et al., 2017).Recently, Shen et al. (2021) found 25 events of periodic ECH frequency-chirping in the terrestrial magnetosphere, with 22 (3) of them falling (rising) tones.In their study, the average duration of the ECH frequency-chirping structures is about 40 s with a chirping rate of about 50 Hz/s, which is very different from the chorus waves.In Saturn's magnetosphere, ECH frequency chirping structures can last several minutes with a chirping rate of ∼Hz/s (Teng et al., 2021).Analysis of burst mode data from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) suite (Kletzing et al., 2013) indicates that the duration and chirping rate of ECH rising tones can be comparable with chorus (Gao et al., 2018(Gao et al., , 2020)).Different from the chorus (Omura & Nunn, 2011;Omura et al., 2008;Tao, 2014;Tao et al., 2017Tao et al., , 2020Tao et al., , 2021)), such ECH frequency-chirping structures are suggested to be generated through chorus-ECH interactions (Gao et al., 2018) or the rapid variation of electron loss cone induced by chorus (Gao et al., 2020).Therefore, these ECH frequency chirping structures show an evident correlation or lagged-correlation with the co-existed chorus elements.In this study, based on the Van Allen Probes observations, we report that the ECH frequency-chirping fine structures (also called chirping ECH elements by following the well-known item of chorus elements), with the duration and frequency chirping rate both comparable with chorus, can occasionally occur in the magnetosphere without the presence of correlated chorus.Adopting the database from 1 October 2012 to 31 December 2016, the statistical properties of such chirping ECH elements are studied.

Rising Tone ECH
The wave instrument onboard Van Allen Probes provides magnetic spectral matrices with a frequency range up to 12 kHz and electric spectral matrices up to 500 kHz, which are widely adopted to capture the ECH emissions in the inner magnetosphere (Chen et al., 2019).Especially, the Waveform Receiver (WFR) collects a set of six phase-matched continuous waveform data (three-axis magnetic and electric components, respectively) with sampling rate of 35 kHz (burst mode data) (Kletzing et al., 2013), providing us a great opportunity to analyze the fine structures of low harmonic ECH waves.The High Frequency Receiver (HFR) measures the electric field power in the frequency range of 10-500 kHz (Kletzing et al., 2013).To obtain the magnetic and electric spectra, the fast Fourier transform is applied to the 6-s burst mode data set.
Figure 1 shows an observation of ECH rising tone, which was observed by Van Allen Probe A on 8 January 2015.Figures 1a and 1b exhibit the magnetic (Figure 1a) and electric (Figure 1b) spectral intensities from 06:00 to 09:00 UT, when the spacecraft traveled from L = 4.4 to 6.4 in the midnight with Magnetic Local Time (MLT) of 22.7 − 1.5.The red solid lines represent the harmonics of the local electron gyrofrequency f ce , which is calculated using the measured ambient magnetic field.During 06:24-07:30 UT, pronounced electrostatic emissions were observed in the equatorial region with L = 5.0 − 6.1, showing clear harmonic structures, which is consistent with the characteristics of ECH waves.The first harmonic was the strongest band with the intensity approaching 10 −3 mV 2 m −2 Hz −1 .The electromagnetic emissions below f ce were identified as whistler mode waves.Figures 1c  and 1d display the magnetic and electric spectra around 07:23:54 to 07:23:56 UT, which are obtained by performing a fast Fourier transform on the continuous waveform samples.Obviously, a distinct ECH element, showing a clear rising tone pattern in the frequency spectrum, occurred around 07:23:54.500 to 07:23:54.720UT in the first harmonic band.In comparison, the simultaneously observed whistler mode waves exhibit a hiss-like feature (Li et al., 2012), showing little correlation to the ECH element.We apply a 4-6 kHz band-pass filter on the data to obtain the ECH waveform (Figure 1f).Then the Hilbert transform is adopted to estimate the instantaneous frequency of the ECH rising tone.As shown in Figure 1g, the wave frequency gradually increases from ∼5.67 to ∼5.75 kHz in 30 milliseconds, corresponding to a chirping rate of 2.8 kHz/s.The waveform of the whistler mode waves in Figure 1h further illustrates the uncorrelation between these two waves.2a and 2b, distinct ECH waves were detected in the region of magnetic latitude (MLAT) = 13.3°-14.8°at nightside with MLT = 0.9-1.6 and L = 6.3 − 6.8.The signals with a constant frequency below f ce may be noises from the instrument.It's worthwhile to note that there is no detectable chorus waves during the ECH event, suggesting that the ECH falling tones are independent on the chorus elements here.The electric frequency spectrum (Figure 2d) of burst mode data measured at 03:46:28 to 03:46:34 UT presents that successive ECH falling tone elements occurred with duration ∼400 milliseconds.The instantaneous frequency analysis of the waveform (Figures 2f and 2g) shows that the wave frequency gradually decreases from 5.33 to 5.10 kHz in 30 milliseconds, corresponding to a chirping rate of −7.7 kHz/s.

Statistical Analysis
In order to investigate the statistical characteristics of the ECH frequency-chirping fine structures, all available wave burst data from 1 October 2012 to 31 December 2016 of Van Allen Probes are visually checked, and the following criteria are implemented to identify the ECH elements: 1.The magnetic spectral intensities should be lower than 10 −8 nT 2 /Hz, due to the electrostatic feature of ECH waves.2. The electrostatic emissions should occur higher than the electron gyrofrequency and between the harmonics of electron gyrofrequency.The instantaneous frequency analysis result of the waveform in Figure 2f.Li et al., 2011).It also should be mentioned here that all the chirping ECH elements occur in the first harmonic band, and few of them show correlations with chorus, implying that the generation of such frequency chirping structures is independent on chorus waves.
The corresponding values of L, MLT, and MLAT are calculated by adopting the TS04 magnetic field model (Tsyganenko & Sitnov, 2005) for each sample.The rising (Figure 3a) and falling (Figure 3b) tones are respectively binned in a step of 1 hr in MLT and per half L-shell as displayed in Figure 3.Although the rising tones are much less observed than the falling tones, the ECH elements, regardless the frequency chirping direction, occur in the region from 18 MLT through dawn to 14 MLT with L = 4 − 7, and they are predominantly observed from the midnight to dawn (00-07 MLT) in the range of L = 5 − 6.The preferential MLT region of the chirping ECH elements is very similar to that of the distinct ECH waves observed by THEMIS (Ni et al., 2017), but different from the slow chirping structures which mainly occur in the dusk sector (Shen et al., 2021).Figures 3c-3h illustrate the spatial distribution of ECH elements with respect to three different levels of geomagnetic activity, that is quiet (AE ≤ 100 nT), moderate (100 < AE < 300 nT), and disturbed (AE ≥300 nT).During the quiet period, most of the ECH elements (103 of 112) are found in the region 5 < L < 7. The number of rising tone samples is 39 during the moderate storms and 49 during the disturbed period.For the falling tones, the number of samples is 497 and 1,137, respectively.This suggests that the occurrence rate of ECH frequency-chirping structures becomes higher when the geomagnetic activity is more intense.Moreover, as the AE index increases, the presence of ECH frequency chirping structures extends to lower L-shells.It is probably because the location of plasmapause is compressed to lower L-shells during the disturbed period, and the ECH is excited outside the plasmasphere.
Figures 4a and 4b illustrate the distribution of chirping ECH elements in the L-MLAT frame.The chirping ECH elements can be observed in the broad region of −20° < MLAT < 20°.87 of 113 for the rising tones and 1,298 of 1,721 for the falling tones are found in the region of −10° < MLAT < 10°.It suggests that the ECH elements may propagate to higher MLAT, despite that ECH waves are generally excited in the equatorial region.At higher latitudes (MLAT > 10°), the chirping ECH elements are mainly observed during the disturbed period.It is probably because the occurrence of ECH wave increases and the wave becomes more intense when the geomagnetic activity intensifies (Ni et al., 2017).More chirping ECH elements can propagate to higher latitudes.As same as in the L-MLT frame, the occurrence of chirping ECH elements increases with the spatial region extending to lower L-shells during active geomagnetic periods (Figures 4c-4h).An interesting thing here is that the falling tones show a boomerang-like pattern in the L-MLAT frame.) by using the dipole field model.We mark the locations at which magnetic field respectively equals to   4.3 (red solid line) and   6 (red dashed line) in the (L, MLAT) space (Figure 4) and the dwell time distribution of the spacecraft (Figure S1).The contour of   6 roughly agrees with both the outer profiles of the distribution pattern and the outer edge of the spacecraft orbit, indicating that the outer boundary of the boomerang is caused by the orbit.However, the dwell time of the spacecraft does not exhibit any specific tendency alone the contour of   4.3 .According to the dispersion relation of ECH, the wave frequency can not cross the multiples of local gyro-frequency, which is approximately proportional to the magnetic field strength.Since the lowest location of the ECH elements is around L ∼ 4.3 at the equator as shown in Figure 4a, the wave frequency can not be lower than the local f ce when it is propagating to higher MLAT.Thus, the contour for   4.3 might be an impenetrable barrier to the chirping ECH elements, forming the inner boundary of the boomerang-like pattern.

Summary
In this study, we report the presence of ECH frequency chirping structures with the duration and frequency-chirping rate both comparable with those of chorus elements in the radiation belts.We provide a statistical result (1,834 samples) of ECH frequency chirping structures based on a 51-month database of Van Allen Probes observations from 1 October 2012 to 31 December 2016.The main results are summarized below.
1.All of the chirping ECH elements occur in the first harmonic band, and more than 93 percent of them exhibit a falling tone pattern, which is quite different from chorus.Few of the ECH elements occur accompanied by chorus elements, suggesting that the generation of such frequency chirping structures is independent on chorus waves.2. The chirping ECH elements cover a broad range of L = 4 − 7 from 18 MLT through dawn to 14 MLT, with a higher occurrence on the midnight to dawn sector (00-07 MLT) within the region L = 5 − 6.  3.More chirping ECH elements are observed as the AE index increases.The ECH elements can occur at lower L-shells during strong geomagnetic activities, which may be due to the compression of plasmapause.4. The chirping ECH elements can propagate to higher latitudes of |MLAT| ∼ 20°, but be confined by the contour of corresponding equatorial magnetic field strength.It is probably because the ECH waves are not allowed to be below the local gyro-frequency.
The current results could be important for investigating the mechanism of generating such ECH elements.Considering that the diffusion coefficients are very sensitive to the frequency of ECH (Ni et al., 2011a), this study may also be helpful for quantifying the ECH-electron resonance process in the radiation belts.

Figure 2
Figure 2 plots the example of ECH falling tone elements by Van Allen Probe B on 15 September 2016.As shown in Figures2a and 2b, distinct ECH waves were detected in the region of magnetic latitude (MLAT) = 13.3°-14.8°at nightside with MLT = 0.9-1.6 and L = 6.3 − 6.8.The signals with a constant frequency below f ce may be noises from the instrument.It's worthwhile to note that there is no detectable chorus waves during the ECH event, suggesting that the ECH falling tones are independent on the chorus elements here.The electric frequency spectrum (Figure2d) of burst mode data measured at 03:46:28 to 03:46:34 UT presents that successive ECH falling tone elements occurred with duration ∼400 milliseconds.The instantaneous frequency analysis of the waveform (Figures2f and 2g) shows that the wave frequency gradually decreases from 5.33 to 5.10 kHz in 30 milliseconds, corresponding to a chirping rate of −7.7 kHz/s.

Figure 1 .
Figure 1.Electron cyclotron harmonic (ECH) Rising tone observed on 8 January 2015.(a) Magnetic field spectrum from WFR during 06:00 to 09:00 UT.(b) Electric field spectrum from WFR and High Frequency Receiver.The red solid lines denote the multiples of the electron gyrofrequency f ce as labeled.(c, d) Magnetic (c) and electric (d) field spectrums obtained from the continuous waveform samples around 07:23:53 to 07:23:59 UT, which corresponds to the arrow in (a) and (b).(f) The electric waveform of the ECH emissions (E U,V,W in the spacecraft science coordinate system) within 30 milliseconds, corresponding to the time interval highlighted by the red vertical lines in (c) and (d).(g) The instantaneous frequency analysis result of the waveform in (f).(h) The waveform of the synchronously observed whistler mode waves.

Figure 2 .
Figure 2. Electron cyclotron harmonic (ECH) falling tone observed on 15 September 2016.(a) Magnetic field spectrum from WFR during 02:30 to 04:30 UT.(b) Electric field spectrum from WFR and High Frequency Receiver.The red solid lines denote the multiples of the electron gyrofrequency f ce as labeled.(c, d) Magnetic (c) and electric (d) field spectrums obtained from the continuous waveform samples around 03:46:28 to 03:46:34 UT, which corresponds to the arrow in Figures 2a and 2b.(f) The electric waveforms of the ECH emissions (E U,V,W ) within 30 milliseconds corresponding to the time interval highlighted by the red vertical lines in Figure 2d.(g) The instantaneous frequency analysis result of the waveform in Figure 2f.

Figure 4 .
Figure 4.The same as Figure 3 but in the L-MLAT frame.