Interplanetary shock induced intensification of electron cyclotron harmonic waves in the Earth’s inner magnetosphere

1 Introduction

Electron cyclotron harmonic (ECH) waves are electrostatic emissions [1] that typically appear in thermal plasmas in the Earth’s magnetosphere [2–6]. They are usually observed as harmonic wave bands at frequencies between multiples of electron gyrofrequency (f_ce) [7–9]. Through cyclotron resonance, ECH waves are able to efficiently precipitate keV electrons from the magnetosphere to the ionosphere, contributing to the formation of diffuse aurora [10–16]. Therefore, a comprehensive understanding of the spatiotemporal distribution of ECH waves is required to forecast space weather [17–22].

The generation of ECH waves is proposed to be associated with Bernstein-mode instability driven by hot electron loss cone distributions [23,24]. These emissions with quasi-perpendicular wave vectors are confined near their source regions [24]. While extensive event and statistical studies have focused on the strong dependence of ECH waves on geomagnetic activities [3,25–27], none have directly established a link between ECH waves and solar wind disturbances. Interplanetary shocks, a subset of solar wind discontinuities frequently observed during active days [28–31], are highly geoeffective [32–35]. Numerous works have reported the immediate impacts of interplanetary shocks on magnetospheric plasma waves, including ultra low frequency waves, whistler-mode waves, magnetosonic waves, and EMIC waves [36–44]. Thus, the questions that naturally arise are whether and how an interplanetary shock can abruptly influence magnetospheric ECH waves.

In this study, using observations from the WIND [45] and Van Allen Probes missions [46], we present a representative ECH wave event during an interplanetary shock. The observations and analyses show that a shock compression can increase $>$0.1 keV hot electron fluxes in the Earth’s dayside inner magnetosphere, thus leading to the prompt intensification of ECH waves by promoting the wave instability.

2 Observation

Here we utilize the combined observations of WIND and Van Allen Probes to monitor the prompt response of ECH wave to an interplanetary shock. The Wind satellite operated in a halo orbit near the L1 Lagrange point. The Solar Wind Experiment (SWE) [47], the Magnetic Fields Investigation (MFI) [48], and the Three-Dimensional Plasma and Energetic Particle Investigation (3DP) [49] onboard WIND measured the solar wind parameters. The Van Allen Probes mission, comprising two identical probes (termed as RBSP-A and RBSP-B), orbited near the equator with perigees of approximately 0.1 R_E and apogees of approximately 6 R_E [46]. In this work, we mainly used the High Frequency Receiver (HFR) of the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument [50] to observe ECH waves. The HFR provided electric spectral intensities in the frequency range of 10–400 kHz in survey mode. Note the Waveform Frequency Receiver (WFR) of EMFISIS can provide electric spectral intensities at frequencies ranging from 10 Hz to 12 kHz. However, the WFR electric spectral data had been contaminated seriously above 5 kHz during the event in this work, and did not allow the clear observation of ECH waves. Following the method in Kurth et al. [51], we can derive the background plasma density N_e from the upper hybrid resonance frequency. The fluxgate magnetometer (MAG) of EMFISIS and the Electric Field and Waves (EFW) [52] instrument captured the background electromagnetic field. The Helium Oxygen Proton Electron (HOPE) Mass Spectrometer [53] of the Energetic particle, Composition and the Thermal (ECT) plasma suite [54] provided the electron flux data from several eV to $\sim 50$ keV. The geomagnetic indices were obtained from the OMNI database.

Figures 1A–G plot the solar wind parameters observed by WIND from 07 June 2014 to 11 June 2014. At 16:12 UT on 07 June 2014, a fast forward interplanetary shock was monitored, marked by abrupt increases in magnetic field strength, velocity, density, temperature, and dynamic pressure. According to the list by Chi et al. [55], there was an interplanetary coronal mass ejection (ICME) between approximately 19:00 UT on 08 June 2014 and 10:00 UT on 10 June 2014. This ICME exhibited typical features, including a declining velocity profile, low proton temperature, and bidirectional streaming of suprathermal electrons [56,57]. In a statistical sense, ICMEs ^c1might be the major driver of shocks ^c2during solar maximum, but shocks exist during solar minimum even if few ICMEs are present [58]. The large time lapse between the shock and the ICME front makes it uncertain to determine their relations. Whether this shock was driven by the ICME or a fast solar wind stream requires detailed studies in future and beyond the scope of this work. Approximately 41 min after its arrival in WIND data, the interplanetary shock with a drastic increase in solar wind dynamic pressure from 1 nPa to 6 nPa, compressed the Earth’s magnetosphere. This compression caused an increase of SYM-H index from −5 nT to 23 nT. Figure 1H shows the response of inner magnetospheric ECH waves to the interplanetary shock as observed by RBSP-A on 07 June 2014. Around the shock arrival, RBSP-A operated in the northern hemisphere (MLAT$\sim 15°$) of dayside magnetosphere (L$\sim 6$, MLT$\sim 9$ hr) under relatively quiet conditions (SYM-H$>$-10 nT and AE$<$350 nT). Before the shock arrival, RBSP-A received faint and intermittent ECH wave signals (P_E < 1 × 10⁻¹⁰ mV²m⁻²Hz⁻¹) appearing as harmonic bands below the upper hybrid resonance frequency f_UHR. Note the WFR observations were too noisy to identify ECH waves below 10 kHz. As marked by the vertical dashed lines (16:53 UT), the shock compression caused a sudden and significant intensification of ECH wave power, increasing by approximately one order of magnitude to P_E ∼ 1 × 10⁻⁹ mV²m⁻²Hz⁻¹. Compared with the ECH waves typically confined in the near equatorial region, this ECH wave event was observed at relatively higher latitudes (MLAT$\sim 15°$) with a weak intensity. This is consistent with the statistical characteristics of ECH waves showed in previous studies [25,59,60]. It should also be mentioned that this ECH wave intensification was not a manifestation of the spatial variation of waves but a temporal behavior. During the inbound pass before the shock arrival, RBSP-A only observed weak or no ECH waves in larger L-shells with comparable MLT (as shown in Figure 1H). The inward movement of these weak ECH waves triggered by shock compression could not explain the wave intensification. Thus, the ECH wave intensification should be related to variations in plasma environment triggered by the shock compression, which will be further investigated in the following section.

FIGURE 1

FIGURE 1. Overview of the ECH wave event on 07 June 2014: (A) Magnetic field magnitude B_t and components (B_X, B_Y, B_Z) in the geocentric solar magnetospheric (GSM) coordinate. (B) Bulk velocity V_sw. (C) Proton density N_p. (D) Proton temperature T_p. (E) suprathermal electron flux j. (F) Solar wind dynamic pressure P_sw. (G) Geomagnetic SYM-H index. (H) Zoom-in figure of Wave electric power spectra P_E with overplotted electron gyrofrequency (f_ce) harmonics and upper hybrid resonance frequency (f_UHR). The solar wind measurements by Wind satellite at $\sim 1.26\times 10^6$ km from Earth have been shifted 41 min according to the SYM-H measurements. The shadowed areas mark an ICME. The vertical dashed lines in each panel mark the arrival of interplanetary shock.

3 Physical explanations

Figure 2 presents the temporal evolutions of background electromagnetic fields and plasmas measured by RBSP-A during the event. Corresponding to the shock compression at 16:53 UT (marked by the vertical dashed line in Figure 2), the background magnetic field intensity increased from 200 nT to 223 nT. In contrast, the background plasma density N_e in the low-density plasma trough remained consistently below 10 cm⁻³ (which is dominant by the cold plasma) with no systematic variations after the shock. The interplanetary shock also induced ultralow-frequency waves with impulsive electric field amplitudes of 5 mV/m, subsequently resulting in a significant acceleration of hot electron fluxes above 0.1 keV. It is noteworthy that the similar responses of magnetospheric electron fluxes ranging from low energy to relativistic energy to interplanetary shocks have been reported by numerous studies [37,61–65]. However, the modulation of hot electron fluxes by the ULF wave can not be clearly observed in Figures 2D–F. Possible explanations for this could be the following: 1) rapid relaxation by magnetospheric plasma waves (ECH waves and chorus); 2) the comparable cadence (∼21 s) of HOPE instrument to ULF wave period (∼1–2 min). As reported by previous theoretical studies [23,24], the enhancement of hot electron fluxes could promote the wave instability by providing more free energy, and then lead to the wave intensification.

FIGURE 2

FIGURE 2. Temporal evolution of background fields and plasmas of 07 June 2014 event: (A) background magnetic field strength B. (B) Background plasma density N_e. (C) Electric field components in the modified geocentric solar ecliptic (mGSE) coordinate system. (D) electron spin-averaged differential flux j. (E,F) differential electron fluxes j at specific energies. The vertical dashed line mark the arrival of interplanetary shock, and the vertical dash-dotted lines mark the pre-shock and post-shock moments for the growth rate calculation.

To further determine the influence of shock compression on the generation of ECH waves, we use the BO code [66] to calculate the linear dispersion relations and wave growth rates. The inputs of the code include the background magnetic field intensity and electron phase space density F. The observed electron PSD is fitted by a total of N bi-Maxwellian components.

$F\left(v_{\perp },v_{\Vert }\right)={\displaystyle \sum _{i=1}^N}{F}_i,(1)$

$\begin{array}{ccc}\hfill & \hfill & F_i=\frac{n_i}{{\pi }^{3/2}{V}_{\Vert t{h}_i}{V}_{\perp t{h}_i}^2}\exp \left[-\frac{{\left(v_{\Vert }-V_{d{z}_i}\right)}^2}{V_{\Vert t{h}_i}^2}\right]\hfill \\ \hfill & \hfill & \times \left\{\frac{r_{a_i}}{A_{a_i}}\exp \left[-\frac{{\left(v_{\perp }-V_{d{r}_i}\right)}^2}{V_{\perp t{h}_i}^2}\right]+\frac{r_{b_i}}{{\alpha }_i{A}_{b_i}}\exp \left[-\frac{{\left(v_{\perp }-V_{d{r}_i}\right)}^2}{{\alpha }_i{V}_{\perp t{h}_i}^2}\right]\right\},\hfill \end{array}(2)$

where $r_{a_i}=\frac{1-{\alpha }_i{\mathrm{\Delta }}_i}{1-{\alpha }_i},r_{b_i}=\frac{-{\alpha }_i+{\alpha }_i{\mathrm{\Delta }}_i}{1-{\alpha }_i}$. For the ith plasma component, n_i is the density; $V_{\Vert t{h}_i}$, $V_{\perp t{h}_i}$, $V_{d{z}_i}$, and $V_{d{r}_i}$ are the parallel thermal velocity, perpendicular thermal velocity, parallel drift velocity, and perpendicular ring beam velocity; expressions $A_{a_i}=A_{b_i}=1$ when $V_{d{r}_i}=0$; α_i and Δ_i characterize the size and the depth of the loss cone. According to previous numerical studies [24,67,68], we set the background cold electrons as the 1 eV component for calculation. Note the sum of each component density n_i is equal to the background plasma density N_e.

As the ECH wave powers (Figure 1H) and background plasma conditions (Figure 2) exhibited systematic variations following the interplanetary shock, we selected two specific times for analyses (marked by the vertical dash-dotted lines in Figure 2): 1) pre-shock moment at 16:50 UT; 2) post-shock moment at 17:00 UT. The satellite data provide direct measurements of background magnetic field intensity and plasma density for the growth rate calculation. However, because of the instrumentation constraints and data quality, electron flux data from HOPE are unavailable in small pitch angles $(<18°)$ during this event. Theoretically, the local loss cone angle α_loss of bounced electrons can be determined by the following expression [69]:

$\sin {{\alpha }_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}}^2=\frac{B_0}{B_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}}(3)$

where B₀ and B_loss are the magnetic field intensities at the satellite position and low altitude mirror point where electrons get lost. Here we assume the mirror point locates at 100 km height. Because of the absence of measurements for B_loss, we rely on geomagnetic models to derive the ratio $\frac{B_0}{B_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}}$. Figure 3 shows comparisons between different Tsyganenko geomagnetic models [70–72] around the interplanetary shock. Since the satellite was located in the inner magnetosphere, the field line configurations of the Tsyganenko models closely resemble those of the dipole field. Different with the situation in larger L-shells, there was no off-equatorial magnetic field minimum on the field lines of this event, which has been suggested to explain the latitudinal extension of ECH waves. However, even in the inner magnetosphere (5 < L < 6.6) usually with the absence of off-equatorial magnetic field minimums, ECH waves can extend to MLAT$>15°$ with decreasing amplitudes according to MMS observations (as shown in Figure 3 of Lou et al. [59]). Further understanding of the high-latitude ECH waves requires detailed investigations in the future. Comparing with the T96 and T01 models, the magnetic field strengths derived from TS04 model align more closely with the observation values after the shock compression. Therefore, we use TS04 geomagnetic model [72] to estimate the loss cone size. Based on Eq. 3, the modeled loss cone angles α_loss are 3.49° and 3.68° at the pre-shock and post-shock moments. These approximations suggest that the interplanetary shock may not trigger significant changes in the electron loss cone through adiabatic processes during this event. Taking into account the estimated loss cone sizes, Figure 4 plots the modeled and observed electron phase space densities at the pre-shock and post-shock moments. To reduce the intense fluctuations of electron flux data (as shown in Figures 2E, F), we smoothed the data over 8 adjacent time points (∼168 s) and symmetrized the data with respect to the 90° pitch angle. The detailed fitting parameters of bi-Maxwellian components are given in Table 1. Generally speaking, the modeled electron phase space densities are in reasonable agreement with the observations.

FIGURE 3

FIGURE 3. Comparison between different geomagnetic models at the pre-shock and post-shock moments on 07 June 2014: (A,C) Modeled magnetic field configurations in the SM X-Z plane along the field lines traced from the RBSP-A location and (B,D) corresponding field intensities as a function of magnetic latitude for dipole (black dashed lines), T96 (red solid lines), T01 (blue solid lines), and TS04 (black solid lines) geomagnetic models. The orange asterisks represent the locations of RBSP-A and observed magnetic field intensities at specific moments.

FIGURE 4

FIGURE 4. Electron phase space densities in pitch angle-energy space at pre-shock (A) and post-shock (B) moments on 07 June 2014. The solid lines and circles represent modeled and observed electron phase space densities, and the black vertical dashed lines represent the modeled loss cone angles.

TABLE 1

TABLE 1. The fitting parameters of electron phase space densities for the 07 June 2014 event.

Figures 5A, D illustrate the ECH wave linear growth rates calculated by the BO code within 87° < θ < 90° at the pre-shock and post-shock moments. Based on the observations (Figure 1H), we focus on the first three harmonic bands below the upper hybrid resonance frequency. It is evident that the modeled growth rates roughly share the similar frequency distributions with the observed ECH wave intensities, indicating the electron phase space density fittings reasonably reflect the real conditions. In comparison to the pre-shock moment, the modeled growth rates at the post-shock moment increase by approximately threefold, qualitatively explaining the intensification of ECH waves after the interplanetary shock. Figures 5B, E show the wave frequency ω/Ω_e as a function of normalized wave vector kρ_e at θ = 89° (ω is the wave angular frequency, Ω_e is the electron angular gyrofrequency, and ρ_e is the gyroradius). These dispersion relations enable the calculation of the wave minimum resonant energy E_min, which can be determined as follows.

$E_{\text{min}}=\frac{1}{2}{m}_{\text{e}}{v}_{\Vert }^2,(4)$

$v_{\Vert }=\frac{\omega -n{\mathrm{\Omega }}_{\text{e}}}{k_{\Vert }},(5)$

here v‖ is the electron parallel velocity, k‖ = k cos θ is the wave parallel vector, n is the resonance order, and m_e is the electron rest mass. Based on Figures 5B, C, E, F show the minimum resonant energy E_min of different harmonic bands (each with a specific resonance order) as a function of wave frequency ω/Ω_e at θ = 89°. Combined with the wave growth rates shown in Figures 5A, D, the corresponding E_min for the frequencies with positive growth rates predominantly falls within the range of 0.1 keV–1 keV. These calculations indicate the ECH wave intensification is highly associated with the shock-induced enhancement of $>$0.1 keV hot electrons, which enlarges the free energy for ECH wave excitation.

FIGURE 5

FIGURE 5. ECH wave growth rates, dispersion relations, and minimum resonant energy of first three harmonic bands at pre-shock and post-shock moments. (A,D) linear wave growth rates γ/Ω_e as a function of frequency ω/Ω_e and wave normal angle θ with overplotted electric power intensity P_E of ECH waves from HFR data; (B,E) wave frequency ω/Ω_e as a function of normalized wave vector kρ_e (ρ_e is the gyroradius) at θ = 89°; (C,F) minimum resonant energy E_min of different harmonic bands (with specific resonance order) as a function of wave frequency ω/Ω_e at θ = 89°.

4 Discussion and conclusion

In contrast to previous studies focusing on the dependence of ECH waves on geomagnetic activities [3,25,26,59], here we present the first report of the prompt response of ECH waves to an interplanetary shock based on the WIND and Van Allen Probes observations. A fast forward interplanetary shock with a drastic increase in solar wind dynamic pressure (from 1 nPa to 6 nPa) compressed the Earth’s magnetosphere, causing the prompt intensification of dayside inner magnetospheric ECH waves. The observations and analyses suggest that the shock-induced enhancement of $>$0.1 keV hot electron enlarges the free energy for the ECH wave excitation, consequently leading to the intensification of ECH waves by promoting the wave instability. Another intriguing phenomenon is the impact of a solar wind disturbance on ECH waves on 08 June 2014. As marked by the vertical dash-dotted line in Figures 1A–G, there were increases in solar wind magnetic field and dynamic pressure at ∼04:44 UT on 08 June 2014. Different with the event on 07 June 2014, this structure was not an interplanetary shock. Figure 6 shows ECH wave observations measured by the twin Van Allen Probes satellites on 08 June 2014. Corresponding to the arrival of the solar wind disturbance (marked by the vertical dash-dotted line in Figure 6), RBSP-A near the perigee was unable to receive ECH wave signals, while RBSP-B in the dayside magnetosphere (L ∼ 5.8) observed the prompt intensification of ECH waves. In addition to the prompt impacts, the solar wind compressions in magnetosheath on 07 and 08 June 2014 could increase the dayside reconnection rate and lead to the strong convection in the magnetosphere [73]. Probably because of the associated hot electron injections and plasmasphere erosions, both satellites observed the enhanced occurrences of ECH waves on 08 June 2014. A comprehensive understanding of the dependence of ECH waves on solar winds requires further investigation in the future.

FIGURE 6

FIGURE 6. Wave electric power spectra P_E observed by (A) RBSP-A and (B) RBSP-B on 08 June 2014. The vertical dash-dotted line in (A,B) marks the same moment as the dash-dotted line in Figures 1A–G.

In this work, we employ the BO code to compute the linear wave dispersion relation and growth rate of ECH waves. The calculations are based on the hot electron flux data measured by HOPE. However, as shown in Figure 4, the electron flux data exhibit irregular fluctuations over pitch angles and are notably absent within the loss cone, and the bi-Maxwellian fittings of electron fluxes are unable to capture all the subtle changes. Because of these data and technical limitations, the BO modeling here only provides a qualitative understanding of the observed wave evolutions following the interplanetary shock. In the future, detailed numerical studies are required to evaluate the results obtained in this work.

The prompt responses of magnetospheric waves to solar wind disturbances have attracted increasing interests. Recent works have reported the immediate effects of solar wind disturbances on chorus, hiss, magnetosonic waves, and electromagnetic ion cyclotron waves [36–44,74]. Owing to the important roles of these plasma waves in magnetosphere dynamics, solar wind disturbances could lead to non-negligible changes in space weather by affecting the spatiotemporal distribution of plasma waves. For instance, the ECH wave intensification event reported in this work might contribute to the formation of shock diffuse aurora, attributed to ECH waves’ capacity to scatter keV electrons [75]. Our present findings, in conjunction with previous research, have brought new insights into the solar wind-magnetosphere-ionosphere coupling and highlighted the dependence of magnetospheric waves on the solar wind disturbances.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding authors.

Author contributions

YX: Data curation, Formal Analysis, Visualization, Writing–review and editing. NL: Data curation, Formal Analysis, Investigation, Methodology, Project administration, Visualization, Writing–original draft. ZS: Funding acquisition, Project administration, Writing–review and editing. SY: Writing–review and editing. ZH: Writing–review and editing. JY: Writing–review and editing. KL: Writing–review and editing. ZC: Writing–review and editing. JC: Writing–review and editing.

Funding

The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This work was supported by the National Natural Science Foundation of China grants 42004140, 42130204, 42188101, and 42274198, the Strategic Priority Research Program of Chinese Academy of Sciences grant XDB 41000000, and the Key Research Program of the Chinese Academy of Sciences grant ZDRE-KT-2021-3.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

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