Unusual Loss of Van Allen Belt Relativistic Electrons by Extremely Low-Frequency Chorus

Abstract

Chorus waves with the frequency usually between 0.1 and 0.8 equatorial electron gyrofrequency f_ce can accelerate energetic electrons to relativistic energies (several mega-electron volts, MeV). Here, we report a unique event that both regular chorus and unusual chorus with extremely low frequency (ELF) below 0.1 f_ce occurred during the 22 December 2014 geomagnetic storm. Relativistic electron fluxes decreased with decreasing wave frequency and had minima exactly corresponding to the presence of ELF chorus. Performing a two-dimensional simulation, we find that ELF chorus can result in unusual loss of relativistic electrons while regular chorus contributes to the acceleration, leading to the frequency-modulated fluxes of such high-energy electrons. The current results provide a new scenario that ELF chorus waves can potentially mitigate space weather by inhibiting relativistic electron flux enhancements.

Key Points

• Chorus waves in both regular and ELF frequency band are observed to modulate the relativistic electron fluxes
• Simulations show that ELF chorus can yield unusual losses of relativistic electrons
• The competing effects that induced by regular chorus-electron and ELF chorus-electron interactions lead to the modulated electron fluxes

1 Introduction

Chorus wave is one of the most intense electromagnetic emissions in the magnetosphere of Earth and other magnetized planets. Chorus waves are considered to be generated by anisotropic energetic electrons (∼10–100 keV) injected from the plasma sheet with the wave frequency usually between 0.1 and 0.8 equatorial electron gyrofrequency f_ce (Li et al., 2008; Omura et al., 2008; Tao et al., 2020; Xiao et al., 2010). Numerous studies have demonstrated that those regular chorus waves can accelerate electrons to the relativistic energies, leading to enhancements of ∼MeV electron fluxes during geomagnetic storms or substorms (Horne et al., 2005; Li et al., 2014; S. Liu et al., 2015; Reeves et al., 2013; Turner et al., 2013; Xiao et al., 2014; Zhu et al., 2019).

Recently, chorus waves with extremely low frequency (ELF) below 0.1 f_ce are observed in Van Allen belts (Cattell et al., 2015; Gao et al., 2016; Meredith et al., 2014). Observational and theoretical studies suggest that chorus waves can be locally generated at frequencies lower than 0.1 f_ce due to the resonance with more energetic electrons (∼300 keV) (Cattell et al., 2015; Xiao et al., 2017). However, the effect of ELF chorus on relativistic electron dynamics is still an open question.

Here, we report a unique event recorded by the Van Allen Probes (Mauk et al., 2012) that both regular chorus and unusual ELF chorus occurred during the 22 December 2014 geomagnetic storm. The synchronous measurements of waves and particles show that relativistic electron (1.8–2.6 MeV) flux exhibits an evidently modulated profile by the chorus frequency. We examine the effect of ELF chorus waves on the relativistic electrons and explain the modulation of relativistic electron fluxes by chorus frequency.

2 Correlated Observation

A nearly continuous distribution of chorus was observed during a geomagnetic storm on 22 December 2014. Data in Figure 1 show that the moderate storm was triggered by a strong interplanetary shock hitting the Earth's magnetosphere. The wave intensification (highlighted by the gray-shaded area in Figure 1) was measured by the Electric and Magnetic Field Instrument Suite and Integrated Science (EMIFSIS) instrument (Kletzing et al., 2013) on the Van Allen Probe A (Figure 1d) during the interval of large negative (or southward) interplanetary magnetic field (Figure 1a), which is associated with enhanced convective injections of energetic electrons during geomagnetic disturbance (the dip in SYM-H index in Figure 1b) and thus chorus generations (Jordanova et al., 2010; Li, Thorne, Angelopoulos, Bonnell, et al., 2009). Figure 1c shows the electric field spectra from the high-frequency data of EMFISIS. The sudden decrease of the upper hybrid frequency denotes the location of plasmapause. Obviously, intense electromagnetic waves occurred outside the plasmasphere over a range of L = 4.5–6.5 (the radial distance in Earth radius R_E). Most waves stayed between the frequency range 0.1–0.5 f_ce. The wave fell down far below 0.1 f_ce in the region L = 6.3–5.8 during the inbound pass of the spacecraft. A very interesting thing here is that the fluxes of Van Allen belt relativistic electrons (1.8–2.6 MeV) measured by the Relativistic Electron-Proton Telescope (REPT) instrument (Baker et al., 2013) (Figures 1f–1h) show a very similar profile to the wave frequency, viz., the flux decreased with the decreasing wave frequency and vice versa.

Figure 1

(a) The interplanetary magnetic field (red) and solar wind dynamic pressure (black). (b) SYM-H index (red) and Kp index (black). (c) Electric field spectrum of high-frequency range. (d) Magnetic spectral intensity of chorus waves. Superimposed white lines demarcate the equatorial electron gyrofrequency f_ce, 0.5 f_ce and 0.1 f_ce. (e–g) Spin-averaged differential fluxes of relativistic electrons (1.8–2.6 MeV).

The details of the relativistic electron flux modulation by wave frequencies are shown in Figure 2. The intense waves occurred in the equatorial regions (magnetic latitude MLAT < 4°) at nightside (magnetic local time MLT = 23–4), exhibiting right-handed circular polarization (ellipticity ≈ 1 in Figure 2c) and propagating approximately parallel or antiparallel to the ambient magnetic field direction (wave normal angle θ ≈ 0 in Figure 2d), which are the typical characteristics of chorus waves (Li, Thorne, Angelopoulos, Bortnik, et al., 2009; Santolík et al., 2014). We also check the 6-s burst waveform data for the ELF waves (detected at 0517 and 0523 UT, respectively). A 2,048-point fast Fourier transform (FFT) is conducted to obtain the wave spectrum. As shown in Figure S1, the discrete elements exhibited in the spectra further identify the ELF chorus waves (Li et al., 2012). The relativistic electron (2.6 MeV) fluxes remained a high level (>10² cm⁻² s⁻¹ sr⁻¹ MeV⁻¹) at the L-shells where regular chorus occurred. Around L = 6, those fluxes were significantly reduced to ∼10¹ cm⁻² s⁻¹ sr⁻¹ MeV⁻¹, exactly corresponding to the appearance of ELF chorus (Cattell et al., 2015; Xiao et al., 2017).

Figure 2

Modulation of relativistic electron fluxes by the chorus waves. (a) Magnetic spectral intensity and (b) Electric spectral intensity of chorus waves. Red lines denote the equatorial electron gyrofrequency f_ce, 0.5 f_ce and 0.1 f_ce, respectively. (c) Degree of elliptical polarization, with 1 and −1 representing right-handed and left-handed polarization, respectively. (d) Wave normal angle θ. (e) Spin-averaged differential fluxes of relativistic electrons (2.6 MeV) as a function of L.

It is well known that the variations of relativistic electron fluxes in Van Allen belts ultimately rely on the competition between the acceleration and loss mechanisms (Y.  Shprits et al., 2012, 2016). Regular chorus at the frequency range between 0.1 and 0.8 f_ce can produce local flux enhancements via efficiently accelerating electrons to relativistic energies (Horne et al., 2005; Li et al., 2014; Reeves et al., 2013; Thorne et al., 2013; Xiao et al., 2014) (e.g., the correlated data during 0800–1100 UT on 21 December). However, the fluxes of relativistic electrons form an obvious localized dip at lower L-shells (L ∼ 6) exactly corresponding to the ELF chorus occurrence, which is different from the electron acceleration by regular chorus. The similar profiles of electron fluxes and chorus frequencies lead to a reasonable speculation that the ELF chorus-electron interaction is likely to inhibit the flux enhancements as a loss mechanism.

3 Simulation and Analysis

To investigate whether ELF chorus, together with regular chorus, can account for such morphologies of relativistic electron fluxes, we choose four representative intervals A–D (parameters used in the simulation are listed in Table 1) and solve the two-dimensional Fokker-Planck diffusion equation (Albert, 2004; Kozyra et al., 1994).

(1)

where f_t is electron phase space density (PSD), p is the electron momentum, α_e is the equatorial pitch angle, ⟨D_αα⟩, ⟨D_pp⟩, and represent bounce-averaged pitch angle, momentum, and cross pitch angle-momentum diffusion coefficients, respectively. The explicit expressions of those bounce-averaged diffusion coefficients for chorus waves can be found in the previous works (Glauert & Horne, 2005). The simulation of momentum, pitch angle, and mixed momentum-pitch angle diffusions allows us to treat the competition between the local acceleration and scattering loss (Y. Y.  Shprits et al., 2009; Su et al., 2009; Thorne et al., 2013).

Table 1. Adopted Model Parameters

Interval	Bt (pT)	fm/fce	δf/fce	λm		fpe/fce	χ1	χ2	δχ	χm
A	173	0.208	0.055	15	5.6	8.5	0	1	0.577	0
B	44	0.024	0.006	15	15.4	12.5	0	1	0.577	0
C	24	0.022	0.006	15	16.9	12.4	0	1	0.577	0
D	248	0.192	0.044	15	12.2	8.5	0	1	0.577	0

In our simulation, the background plasma density N_e estimated from the sc potential is from the data of Electric Field and Waves (EFW) instrument for intervals B and C. For intervals A and D, N_e is calculated by using an empirical model (Sheeley et al., 2001) due to the lack of observations. The ambient magnetic field is obtained from the fluxgate magnetometer of EMFISIS instrument. The equatorial electron gyrofrequency is calculated by substituting the local magnetic field into the dipole field model. The initial conditions of the energetic electrons PSD are described by a normalized kappa-type distribution function with the parameters , , and , considering that the hot plasma is rare and collsionless in the space (Pierrard & Lazar, 2010; Summers & Thorne, 1992; Xiao et al., 2008). We adopt a Gaussian distribution fitting to the measured wave spectrum (Figure S2), and the wave normal angle ( ) is also chosen to follow a Gaussian distribution (Glauert & Horne, 2005), with the lower angle , the upper angle , the half-width , and the peak angle . We solve the Fokker-Planck diffusion equation by following the previous technique (Albert & Young, 2005; Su et al., 2010; Xiao et al., 2009).

To directly compare the simulation with observation, we plot the electron PSD evolution for the three selected energies (1.8, 2.1, and 2.6 MeV) in Figure 3. As expected, regular chorus waves (intervals A and D) can efficiently accelerate the energetic electrons, yielding distinct increases of relativistic electron fluxes on the timescale ∼10 hr mainly at higher pitch angles (>45°) where the momentum diffusion rates maximize (Figure S3). In contrast, ELF chorus waves (intervals B and C) scatter the relativistic electrons into smaller pitch angles, as the pitch angle diffusion dominates over the energy diffusion (Figure S3). As shown in Figures 3d–3i, the ELF chorus-induced scattering can slightly flatten the PSD at higher pitch angles for electrons in the indicated energies, yielding the losses of multi-MeV electrons. The spectral plots of relativistic electron (1–3 MeV) PSD evolution as a function of energy and pitch angle are shown in Figure S4, and the plots of PSD against energy for pitch angle are displayed in Figure S5. It should be mentioned that the scattering effect is not very significant. However, the regular chorus can accelerate electrons to relativistic energies and cause the rapid enhancements of the electron fluxes as shown in the simulation. As the wave frequency gradually decreases, the effect of acceleration is decreasing, and the pitch angle scattering is increasing, which allow the visible flux dip corresponding to the ELF chorus.

Figure 3

Fokker-Planck simulation results. Modeled evolution of the relativistic electron (1.8, 2.1 and 2.6 MeV as labeled) PSD for the four selected intervals A–D as a function of pitch angles. Relativsitic electron PSD evolution for (a–c) interval A, (d–f) interval B, (g–i) interval C and (j–l) interval D.

The physical picture is schematically illustrated in Figure 4. Both regular and ELF chorus are observed by the spacecraft along the orbit, which can be in resonance with the trapped energetic electrons in the radiation belt. Regular chorus accelerates energetic electrons to relativistic energies, yielding the relativistic electron flux enhancement. ELF chorus produces scattering loss of relativistic electrons, leading to the localized dip of the fluxes. Finally, the competition between acceleration and scattering can modulate the population of relativistic electrons, forming the frequency dependency of fluxes.

Figure 4

Schematic illustration of modulation of relativistic electrons by chorus. (1) The energetic electrons are trapped in the Earth's magnetic field. (2) Van Allen Probe A finds both regular (2a) and ELF (2b) chorus along the orbit. (3) Regular chorus accelerates energetic electrons to relativistic energies, yielding the relativistic electron flux enhancement (3a), and ELF chorus produces unexpected scattering loss of relativistic electrons, leading to the localized dip of the fluxes (3b). (4) The competition between the acceleration and scattering loss forms the modulated profiles of relativistic electron fluxes.

The simulation presented here does not include the process of radial diffusion due to the relatively minor transport effect associated with radial diffusion mechanism in the inner magnetosphere (L < 7) during the storm (Kp ∼ 5) (W. Liu et al., 2016; Ozeke et al., 2014). The localized dip of relativistic electron fluxes and the presence of ELF chorus are confined to a narrow range of L-shells (ΔL < 0.5), where the contribution from radial diffusion is nonessential. Because our simulation provides remarkable agreement with the observed relativistic electron population, it is clear that the flux modulation is mainly attributed to the competing effects that induced by regular chorus-electron and ELF chorus-electron interactions.

4 Discussion and Summary

We report a unique event that continuous distribution chorus waves stay in both regular and ELF bands, modulating the profile of Van Allen belt relativistic electron fluxes. Simulations demonstrate that ELF chorus waves can scatter the relativistic electrons into smaller pitch angle while regular chorus waves contribute to the energization of electrons. This is probably due to the high minimum threshold energy for the gyro-resonance between electrons and ELF chorus. Namely, the energetic electrons (a few of kilo-electron volts) may not be capable of resonantly interacting with ELF chorus waves. Consequently, no efficient acceleration occurs. On the other hand, the pitch angle diffusion is more important when the wave frequency gradually decreases, leading to the effective scattering of relativistic electrons by ELF chorus. Our study provides a new picture that ELF chorus can yield potential losses of such high-energy electrons, mitigating against space weather caused by relativistic electron flux enhancements, which is in contrast to the conventional picture that regular chorus waves usually accelerate the radiation belt electrons. The scattering loss of relativistic electrons by ELF chorus can also be effective in Jupiter, Saturn, and other magnetized planets.

Acknowledgments

This work is supported by the National Natural Science Foundation of China grants 41974212, 41531072, 41674166, and 41774194; the Hunan Provincial Natural Science Foundation of China grant 2018JJ2425; the Specialized Research Fund for State Key Laboratories; and the Construct Program of the Key Discipline in Hunan Province. The authors are thankful to the Van Allen Probe scientific instrument teams for making their data available to the public.

Open Research

Data Availability Statement

The Van Allen Probe scientific instrument data are available to the public at the following website: https://spdf.gsfc.nasa.gov/pub/data/rbsp/. The geomagnetic indexes are downloaded from https://omniweb.gsfc.nasa.gov.