# First Observation of Kinetic Alfvén Waves behind Reconnection Front in Terrestrial Magnetotail

Z. Wang, X. Liu, H. Fu, J. Cao, L. Dai, S. Toledo-Redondo, W. Zhang, W.

Fu, J. Zhao, Y. Yu, et al.

► To cite this version:

Z. Wang, X. Liu, H. Fu, J. Cao, L. Dai, et al. First Observation of Kinetic Alfvén Waves behind Reconnection Front in Terrestrial Magnetotail. The Astrophysical Journal, 2023, 960 (1), pp.45. 10.3847/1538-4357/ad0cb5. hal-04919723

HAL Id: hal-04919723

https://hal.science/hal-04919723v1

Submitted on 20 Mar 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# First Observation of Kinetic Alfvén Waves behind Reconnection Front in Terrestrial Magnetotail

Z. Wang<sup>1,2</sup>, X. Y. Liu<sup>1,2</sup>, H. S. Fu<sup>1,2</sup>, J. B. Cao<sup>1,2</sup>, L. Dai<sup>3</sup>, S. Toledo-Redondo<sup>4,5</sup>, W. Z. Zhang<sup>1,2</sup>, W. D. Fu<sup>1,2</sup>, J. S. Zhao<sup>6</sup>, Y. Yu<sup>1,2</sup>, and Z. Z. Guo<sup>1,2</sup>

<sup>1</sup> School of Space and Environment, Beihang University, Beijing, People's Republic of China; huishanf@gmail.com

<sup>2</sup> Key Laboratory of Space Environment Monitoring and Information Processing, Ministry of Industry and Information Technology, Beijing, People's Republic of China

<sup>3</sup> State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, People's Republic of China

<sup>4</sup> Department of Electromagnetism and Electronics, University of Murcia, Murcia, Spain

<sup>5</sup> Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, CNRS, UPS, CNES, Toulouse, France

<sup>6</sup> Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, People's Republic of China
Received 2023 September 27; revised 2023 October 31; accepted 2023 November 13; published 2023 December 21

## Abstract

Reconnection fronts, also known as dipolarization fronts (DFs), and kinetic Alfvén waves (KAWs) are two of the widely observed structures and waves in the terrestrial magnetotail, but their correlation remains elusive in previous spacecraft measurements. Using high-resolution Magnetospheric Multiscale data, here we provide the first observational identification of KAWs behind the DF. These low-frequency dispersive KAWs propagate quasi-perpendicular to the magnetic field at phase speeds slower than local Alfvén speed, and are highly correlated with high-frequency whistlers propagating obliquely to the magnetic field. Specifically, whistlers appear at local magnetic field minima (wave troughs of KAWs) and disappear at local magnetic field maxima (wave crests of KAWs), highly consistent with the source region of whistler waves previously reported near equator and dayside magnetopause. Our study also suggests that the KAWs behind DFs could originate from the diffusion region of magnetic reconnection. These findings improve our understanding of the relationship between DFs, KAWs, and whistler waves in terrestrial magnetotail.

Unified Astronomy Thesaurus concepts: Alfvén waves (23); Space plasmas (1544); Plasma physics (2089)

## 1. Introduction

Reconnection fronts, also known as dipolarization fronts (DFs), are sharp magnetic boundaries separating hot-tenuous plasmas (possibly from the reconnection site) from cold-dense plasmas in the terrestrial magnetotail. They have been frequently observed in the terrestrial magnetotail associated with bursty bulk flows (Runov et al. 2009). Such structures, characterized by a sharp increase of magnetic field $B_z$ (Runov et al. 2009), preceded by a small $B_z$ dip structure (Pan et al. 2015; Yao et al. 2015; Schmid et al. 2019), and followed by a strong $B_z$ region that is termed flux pileup region (FPR; Fu et al. 2011, 2012a; Khotyaintsev et al. 2011) or dipolarizing flux bundle (DFB; Liu et al. 2013), play an important role in the transport of mass and magnetic flux (Nakamura et al. 2002, 2009; Ge et al. 2011; Hamrin et al. 2013), energy conversion (Angelopoulos et al. 2013; Huang et al. 2012, 2015; Khotyaintsev et al. 2017), particle acceleration (Cao et al. 2006; Zhou et al. 2010; Ashour-Abdalla et al. 2011; Fu et al. 2011, 2012b, 2013b; Birn et al. 2013; Wu et al. 2013; Grigorenko et al. 2017; Fu et al. 2019), and excitation of wave emissions (Zhou et al. 2009, 2014; Fu et al. 2020a, 2020c; Guo et al. 2021), and has been suggested as a consequence of transient reconnection (Fu et al. 2017) in both simulations (Sitnov et al. 2009) and observations (Fu et al. 2012c, 2013a; Xu et al. 2018).

Kinetic Alfvén waves (KAWs)—dispersive shear Alfvén fluctuations modified by short wavelength effects—have also been widely detected in the terrestrial magnetotail accompanied with parallel electric field (Wu & Chao 2004; Duan et al. 2022). Such waves, characterized by a comparable perpendicular wavelength to the ion thermal gyroradius (Louarn et al. 1994; Wygant et al. 2002; Salem et al. 2012; Zhao et al. 2014), have long been proposed to be responsible for forming turbulence (Sahraoui et al. 2010; Zhang et al. 2023) and triggering magnetic reconnection (Rogers et al. 2001; Dai 2009; Dai et al. 2017), and provide a potential approach for energy exchange between electromagnetic fields and plasma particles (Johnson & Cheng 1997; Liu et al. 2023). Therefore, DFs and KAWs are both significant for understanding the nature of magnetotail, and are both worthy of being investigated.

Although DFs and KAWs have been widely studied respectively (Hollweg 1999; Wu & Chao 2004; Fu et al. 2020b, 2022), the relation between them in spacecraft observation is still unclear. In other words, despite the wide presence of both DFs and KAWs in the magnetotail (Fu et al. 2012a; Duan et al. 2022), whether KAWs can exist and propagate behind DFs is still in mystery. To answer this question, identifying the wave mode (dispersion relation) by spacecraft measurements is necessary. With advanced multi-spacecraft missions and innovative methods, it is now possible to resolve propagation properties of a wave controlled by the dispersion relation (such as phase velocity, group velocity, and wave normal angle) via independently measurements of frequencies and wavevectors. Being aware of these issues, we aim to report the first observation of KAWs behind the DF

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
in this Letter. We use high-resolution data from the Magnetospheric Multiscale (MMS) mission (Burch et al. 2016). Specifically, the instruments used are the Fast Plasma Investigation (Pollock et al. 2016), the Flux Gate Magnetometer (Russell et al. 2016), the Search Coil Magnetometer (Le Contel et al. 2016), the Electric Double Probe (Lindqvist et al. 2016), and the Axial Double Probe (Ergun et al. 2016).

## 2. Observation

The event of interest is observed on 2018 July 6, from 12:37:30 to 12:39:30 UT, when MMS was located at [−14.0, 2.5, 3.8] $R_E$ in Geocentric Solar Magnetospheric (GSM) coordinates in the terrestrial magnetotail, with average separations of ~57 km (Figures 1(a) and (b)). Figures 1(c)–(i) present an overview of this event, with the magnetic field shown in panel (c), particle number density shown in panel (d), ion velocity shown in panel (e), electron temperature shown in panel (f), electron flux in panel (g), and ion flux in panel (h). Before 12:37:49 UT, MMS observed a similar $B_z$ and $|B|$ and a relatively small $B_x$ and $B_y$ (Figure 1(c)), a high plasma density ($N_e > 0.7 \text{ cm}^{-3}$; Figure 1(d)), and a larger plasma $\beta$ (not shown), meaning that it was located in the plasma sheet. At 12:37:49 UT, MMS detected a sharp increase of $B_z$ from 5 to 20 nT (Figure 1(c)). Such an increase of $B_z$, associated with a flow burst ($V_i > 200 \text{ km s}^{-1}$; Figure 1(e); Cao et al. 2006, 2013), a drop of plasma density (from 0.8 to 0.4 $\text{cm}^{-3}$; Figure 1(d)), and a rising of electron temperature (from 1000 to 2500 eV; Figure 1(f)), is the typical signature of a DF (Fu et al. 2020a) and thus can be identified as a DF structure. Behind the DF, from 12:37:39 to 12:39:15 UT, is a traveling strong $B_z$ region that is traditionally referred to as the DFB (Fu et al. 2011; Liu et al. 2013; Yu et al. 2022), inside which we can see that both ions (Figure 1(h)) and electrons (Figure 1(i)) are heated. The DFB and DF have both been suggested to be parts of the reconnection outflow. Specifically, the DF is the sharp boundary leading the DFB, and the DFB is the associated structure of the DF.

Inside the DFB behind the DF, interestingly, there is a wiggly feature of magnetic fields from 12:38:25 to 12:39:15 UT (the shaded region in Figure 1). The period of these waves is between 5 and 25 s, corresponding to wave frequency around 0.04–0.2 Hz; thus, these waves are ultralow-frequency (ULF) waves. We perform wavelet transforms to $B_x$, $B_y$, and $B_z$ components (Figure 2(a)) and obtain the wave power in Figures 2(b)–(d), from which one can see that the dominant frequency of these waves corresponding to the maximum wave power is $f_{cs} \sim 0.086 \text{ Hz}$ (marked by the dashed line in Figure 2(d)). We perform a band-pass filter to the $B_z$ component at 0.086–0.087 Hz (Figure 2(e)), and then use the timing (Russell et al. 1983) method to estimate the wave phase velocity of these waves in the satellite-rest frame as $v_p = 200^\circ(-0.69, -0.69, 0.23) \text{ km s}^{-1}$ (Figure 2(f)), about half of the local Alfvén velocity ($v_A = B_0/\sqrt{\mu_0 m_i n_i} \approx 400 \text{ km s}^{-1}$). Such propagation direction is very close to the normal direction calculated from minimum variation analysis (MVA) that is as $N = (-0.64, -0.69, 0.34)$ (Figures 2(g) and (h)), validating the reliability of the obtained results. As a result, the wave normal angles derived from the timing and MVA methods are highly consistent and are both slightly larger than 90° (Figure 2(i)), indicating these waves propagate quasi-perpendicularly to the background magnetic field. We project these waves to the directions parallel to propagation ($\delta B_\|)$ and perpendicular to

propagation ($\delta B_\perp$1 and $\delta B_\perp$2) (Figure 2(l)) and then investigate the hodograph of the two perpendicular components (Figure 2(m)), where one can see these waves are left-handed and circularly polarized (Gershman et al. 2017; Toledo-Redondo et al. 2021). We consider the Doppler shift and then obtain the wave frequency in the plasma rest frame as $f_{pls} = f_{sc}(1 - \frac{v_i - v_p}{v_p^2}) = 0.048 \text{ Hz}$, which is below the local ion cyclotron frequency ($f_{ci} \approx 0.23 \text{ Hz}$). We then estimate the wave phase velocity and wavenumber in the plasma rest frame as $v_{pls} = v_p - vi = 180^\circ(0.06, 0.76, 0.64) \text{ km s}^{-1}$ and $k = 2\pi f_{pls}/|v_{pls}| = 0.017 \text{ km}^{-1}$. We can further calculate the ratio of the perpendicular wavenumber to the parallel wavenumber $k_\perp/k_\| = 13$, and the $k_\perp d = 3.4$ ($d \sim 200 \text{ km}$ is the ion thermal gyroradius here), indicating that the waves are at ion scale. All these features, including wave-frequency range, wave phase speed, quasi-perpendicular propagation, $k_\perp/k_\| \gg 1$, $k_\perp d > 1$, and polarization manifest that the waves in this event are KAWs (Wu & Chao 2004; Duan et al. 2022). These analysis results suggest that KAWs can exist and propagate behind DFs.

To investigate the dispersion relation ($\omega-k$ relation) of these KAWs behind the DF, here we perform a dispersion relation from timing (DRAFT) analysis (Zhang et al. 2022) from 12:38:15 to 12:39:15 UT, where the phase speed and wavevector were calculated at each time for each single-frequency wave in the range from zero to Nyquist frequency. The analysis results indicate that (not shown here) there are strong wave emissions roughly around $f_{sc} = 0.08 \text{ Hz}$ (consistent with the results in Figures 2(b)–(d)), and these waves have a phase-velocity magnitude of around $200 \text{ km s}^{-1}$, a wave normal angle roughly between 60° and 90°, and a wavenumber near $0.002 \text{ km}^{-1}$. The determined frequencies and wavenumbers are shown in Figures 2(j) and (k), where the colored data points respectively donate the wave power (Figure 2(j)) and sampling counts (Figure 2(k)). Such experimental data, converted into the plasma rest frame, constitute the dispersion relation of these waves for wave normal angle between 60° and 90°. As it can be seen, the wave power and wave sampling counts are clearly larger at frequencies around 0.04–0.06 Hz. These waves have wave phase speeds ($2\pi f/k$) much slower than Alfvén speed and are dispersive: wave phase speed changes with frequency.

Based on the two-fluid description of the plasma, the dispersion relation for KAW can be theoretically expressed as follows (Lysak & Lotko 1996): $\omega^2 = k_\| v_A^2 (1 + k_\perp^2 \omega_i^2)$, where $\rho_i = \sqrt{Q} v_{Te}/\omega_{ci}$ is the ion acoustic gyroradius, $Q = m_e/m_i$ is the mass ratio of electron to ion, $\omega_{ci}$ is the ion gyrofrequency, and $v_{Te}$ is the thermal speed of electrons, respectively. Such theoretical prediction is represented in Figures 2(j) and (k), where the red, blue and green curves respectively donating to KAWs with wave normal angles 75°, 80°, and 85°. The local plasma environment used for the prediction is $\rho_i \approx 1000 \text{ km}$ and $v_A \approx 400 \text{ km s}^{-1}$. The measured dispersion relations agree best with the blue solid curves (wave normal angle 80°) and are generally clustered between the theoretical curves of KAW dispersion relations with wave normal angles between 75° and 85°, implying the multiple wave branches of KAWs.

The high-resolution MMS data show that, in addition to the low-frequency KAWs, there are some high-frequency (10–300 Hz) electromagnetic fluctuations inside the DFB (Figures 3(c) and (d)). Figure 3 represents the correlation between these waves in detail: specifically, the waveform data of the low-frequency KAWs are shown in Figures 3(a) and (b), in which a
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Overview for the plasma and magnetic field measurements from MMS1. (a) and (b) Spacecraft location in XZ and XY coordinates. (c) The magnetic field. (d) The plasma number density. (e) The magnitude of ion flow velocity. (f) The electron temperature. (g) The differential energy flux of electrons (h) The differential energy flux of ions. The gray shaded area corresponds to the ULF wave region.</figcaption></figure>

band-pass filter between 0.086 and 0.087 Hz is applied to $|B|$, $B_x$, $B_y$, and $B_z$ measured by MMS1, and the local magnetic field is shown in Figure 3(a); the wave propagation analysis of the high-frequency waves resolved by the singular value decomposition (SVD) method (Santolík et al. 2003) are shown in

Figures 3(c)–(g). The cyan and black lines in Figures 3(c)–(h) separately represent $f_{\text{lh}}$ and $0.5f_{\text{ce}}$, where $f_{\text{lh}}$ and $f_{\text{ce}}$ denoting the electron gyrofrequency and the lower hybrid frequency. The power spectral densities of electric and magnetic field (Figure 4(c) and (d)) show that, there are strong wave emissions roughly
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Wave-property analyses of the low-frequency KAWs behind the dipolarization front. (a) Three components of the magnetic field. (b)–(d) Power spectral density of $B_x$, $B_y$, and $B_z$. The white lines in panels (b)–(d) correspond to the ion cyclotron frequency $f_{ci}$. (e) Band-pass filtering of $B_Z$ measured by MMS1 (black), MMS2 (red), MMS3 (green), and MMS4 (blue) between 0.086 and 0.087 Hz. (f) Time-shift analysis of the wave propagation direction. (g) and (h) Minimum variation analysis of the wave propagation direction. (i) Wave normal angle solved by timing and MVA methods. (j) and (k) Dispersion relation of the KAWs determined by the DRAFT method. Panels (j) and (k) show the wave power and the sampling counts in the ion rest frame between different wave normal angles 60°–90°, respectively. The red, blue, and green solid curves in (j) and (k) indicate theoretical dispersion relations of KAWs with wave normal angles 75°, 80°, and 85°. (l) Projection of wave magnetic fields to the directions parallel to propagation ($\delta B_\|$) and perpendicular to propagation ($\delta B_\perp$). (m) Hodograph of the two components perpendicular to propagation, for analyzing wave polarization.</figcaption></figure>

between $f_{\text{th}}$ and $0.5f_{\text{ce}}$. Clearly, these high-frequency emissions are strong at local magnetic field minima (wave trough) and weak at local magnetic field maxima (wave crest); see blue vertical lines in Figures 4(a)–(c). Such modulation exhibits that the low-frequency KAWs are highly correlated with the existence of these high-frequency waves. We will discuss the source region of these high-frequency waves in the next section. These waves have ellipticity close to 1 (right-hand polarization; Figures 3(e)), wave normal angle around 40°~90° (oblique propagation; Figure 3(f)), and planarity close to 1 (Figure 3(g)). These features indicate presence of whistler-mode waves. Figure 3(h) shows the electron flux anisotropy ($F_\perp/F_\| - 1$) associated with these whistler waves in detail, where $F_\perp$ is the perpendicular electron flux and $F_\|$ is the parallel electron flux. The white solid line shows the electron temperature, which describes the hot population. The population above the electron temperature can be considered as energetic electrons (2–30 keV). As it can be seen, during propagation of these whistlers, the electron flux anisotropy in 0.8–30 keV significantly enhances ($F_\perp/F_\| \sim 0$), meaning that the parallel electron temperature is much higher than the perpendicular one, the electron pitch angle is mainly distributed at 0° and 180° (not shown here), and energetic electrons (2–30 keV) are the main contributors to the electron anisotropies. Such electron parallel flux anisotropy may relate to the generation of the whistler-mode waves.

### 3. Discussion

KAW physics can predict the ratio ($E_n/B_m$) of Hall fields in reconnection. For KAW (in the case of $T_i \gg T_e$), the ratio

$E_n/B_m$ is $V_A * \sqrt{1 + k_\perp^2 \rho_i^2}$, which is usually examined in previous studies to identify KAWs (Dai et al. 2017). However, in this event, the MMS spacecraft were located in the magnetotail plasma sheet, which often includes cold plasma (few eV), and the measurement of low-frequency electric field may be not reliable due to the local electrostatic potential structure (wake) that is formed around the spacecraft (e.g., Toledo-Redondo et al. 2019; André et al. 2021). Therefore, we do not investigate such relationship between the magnetic and electric fields in this paper, especially considering that the four-point measurements from the MMS together with the DRAFT method can reliably resolve the wave propagation properties.

Recent studies have also suggested that generation of KAWs may be attributed to the ion perpendicular temperature anisotropy or ion beam (Wu & Chen 2020). Nevertheless, in our event, neither ion perpendicular temperature anisotropy or ion beam is present (not shown). Since the KAWs were detected behind the DF, we posit that they may be generated inside the diffusion region of magnetic reconnection (see Figure 4; Shay et al. 2011; Duan et al. 2016). In this situation, both the KAWs and the DF are products of magnetic reconnection, and they both propagate together with the reconnection jet (see Figure 4), while the DF is the leading edge of the reconnection jet. Poynting flux can be utilized to determine the wave generation: the KAWs may either originate from magnetic reconnection region if the Poynting flux is mainly toward the Terra or be generated by local tailward currents if the Poynting flux is mainly toward the magnetotail (Wygant et al. 2002; Keiling et al. 2003). However, again in
<figure><img src="image_6.png" /><figcaption>**Figure 3.** The correlation between low-frequency KAWs and high-frequency whistler waves. (a) and (b) Band-pass filtering of $B_x$, $B_y$, and $B_z$ measured by MMS1 between 0.086 and 0.087 Hz. (c) and (d) Power spectral density of the magnetic field and electric field between 10 and 300 Hz. (e)–(g) Ellipticity, wave normal angle, and planarity of the high-frequency waves. (h) Parallel flux anisotropy ($F_{\perp}/F_{\parallel} - 1$) at each energy bin. The solid white line shows the total electron temperature. The cyan and black lines in panels (c)–(h) correspond to $f_{\text{th}}$ and $0.5 f_{\text{cc}}$.</figcaption></figure>

our event, the measured low-frequency electric field has
significant uncertainties, leading to the unreliable calculation
of the Poynting flux. As shown in Figure 4, sufficient evidences
from spacecraft observations (Sitnov et al. 2009; Fu et al.
2012a, 2013a) have been provided that the DFs can form in
magnetic reconnection diffusion region. Meanwhile, the KAWs
have been suggested as eigenmodes of magnetic reconnection
(Dai 2009), and can intrinsically develop inside the diffusion
region. In such a sense, it may be reasonable to infer that both

the KAWs and the DF originate from the diffusion region and
propagate toward the Terra together.

Observations of whistler emissions are common in the
magnetosphere, such as near the equator in the form of chorus
(Santolík et al. 2004), in the magnetosheath as so-called lion
roars (Baumjohann et al. 1999). Whistler waves are also widely
observed associated with dipolarization fronts in the magneto-
tail (Eastwood et al. 2009; Fu et al. 2014; Hwang et al. 2014;
Viberg et al. 2014; Cao et al. 2017). Although whistler
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Schematic of the generation and propagation of KAWs behind the dipolarization front. In this inference, both the KAWs and DF are formed inside the diffusion region of magnetic reconnection and the waves and structure propagate along with each other toward the Terra.</figcaption></figure>

emissions have been known for several decades, their source regions are still a subject of active experimental and theoretical research. In previous spacecraft observations, magnetic field minima that are present at the low-latitude equator (Santolík et al. 2004) and high-latitude magnetopause (Vaivads et al. 2007) have been suggested as the source regions of whistler waves. Here we find that due to the presence of KAWs, a similar source region can also be located in the magnetotail: whistler emissions are modulated by KAWs and occur at localized magnetic field minima behind DF (see Figure 3). This result suggests the local generation of whistler waves and provides observational evidence for the source region of whistler waves in the terrestrial magnetotail. Whistler waves are known to be generated by electron temperature anisotropy, but can also be generated by heat flux instabilities and electron beams. The parallel electric fields carried with KAWs may lead to formation of electron beam, which can be indicated by electron parallel flux anisotropy and the pitch angle distribution of cigar type, and can further generate oblique whistler waves (Tokar et al. 1984; Gurnett et al. 1986).

## 4. Conclusion

In this paper, we present the first observation of KAWs behind a DF in the terrestrial plasma sheet. Taking advantage of the MMS high-cadence data together with the DRAFT method, the property and dynamics of KAWs are resolved in great detail. The KAWs behind the DF may originate from the diffusion region of magnetic reconnection at middle magnetotail and propagate outward along with the reconnection jet. We find that the low-frequency KAWs are coupled with high-frequency whistler-mode waves and modulate the occurrence of these whistler waves, revealing a wave-wave coupling process behind the DF. This study can help us better

understand the relationship between DFs, KAWs, and whistler waves.

## Acknowledgments

We thank the MMS Data Center (https://lasp.colorado.edu/mms/sdc/public/) for providing the data. This work was supported by NSFC grants 42125403, 41821003, and “the Fundamental Research Funds for the Central Universities.” S.T.-R. acknowledges support of MCIN/AEI/PRTR 10.13039/501100011033 (grants PID2020-112805GA-I00 and TED2021-129357A-I00) and Seneca Agency from Region of Murcia (grant 21910/PI/22).

## ORCID iDs

Z. Wang https://orcid.org/0000-0002-1720-964X

H. S. Fu https://orcid.org/0000-0002-4701-7219

J. B. Cao https://orcid.org/0000-0002-5637-2976

L. Dai https://orcid.org/0000-0002-5122-3066

S. Toledo-Redondo https://orcid.org/0000-0002-4459-8783

W. Z. Zhang https://orcid.org/0000-0003-4364-3252

J. S. Zhao https://orcid.org/0000-0002-3859-6394

Y. Yu https://orcid.org/0000-0001-8078-8624

Z. Z. Guo https://orcid.org/0000-0002-4479-7045

## References

Angelopoulos, V., Runov, A., Zhou, X.-Z., et al. 2013, *Sci*, **341**, 1478

André, M., Eriksson, A. I., Khotyaintsev, Y. V., et al. 2021, *JGRA*, **126**, e29493

Ashour-Abdalla, M., El-Alaoui, M., Goldstein, M., et al. 2011, *NatPh*, **7**, 360

Baumjohann, W., Treumann, R. A., Georgescu, E., et al. 1999, *AnGeo*, **17**, 1528

Birn, J., Hesse, M., Nakamura, R., & Zaharia, S. 2013, *JGRA*, **118**, 1960

Burch, J. L., Moore, T. E., Torbert, R. B., & Giles, B. L. 2016, *SSRv*, **199**, 5

Cao, D., Fu, H. S., Cao, J. B., et al. 2017, *GeoRL*, **44*, 3954

Cao, J. B., Ma, Y. D., Parks, G., et al. 2006, *JGRA*, **111**, A04206
Cao, J. B., Ma, Y. D., Parks, G., et al. 2013, JGRA, 118, 313

Dai, L. 2009, PhRvL, 102, 245003

Dai, L., Wang, C., Zhang, Y., et al. 2017, GeoRL, 44, 634

Duan, S., Dai, L., Wang, C., et al. 2016, JGRA, 121, 4316

Duan, S., Dai, L., & Wang, C. 2022, RvMPP, 6, 40

Eastwood, J. P., Phan, T. D., Bale, S. D., & Tjulin, A. 2009, PhRvL, 102, 035001

Ergun, R. E., Tucker, S., Westfall, J., et al. 2016, SSRv, 199, 167

Fu, H. S., Cao, J. B., Cully, C. M., et al. 2014, JGRA, 119, 9089

Fu, H. S., Cao, J. B., Khotyaintsev, Y. V., et al. 2013a, GeoRL, 40, 6023

Fu, H. S., Chen, F., Chen, Z. Z., et al. 2020a, PhRvL, 124, 095101

Fu, H. S., Grigorenko, E. E., Gabrielse, C., et al. 2020b, ScChD, 63, 235

Fu, H. S., Khotyaintsev, Y. V., André, M., & Vaivads, A. 2011, GeoRL, 38, L16104

Fu, H. S., Khotyaintsev, Y. V., Vaivads, A., et al. 2012a, GeoRL, 39, L10101

Fu, H. S., Khotyaintsev, Y. V., Vaivads, A., et al. 2012b, JGRA, 117, A12221

Fu, H. S., Khotyaintsev, Y. V., Vaivads, A., André, M., & Huang, S. Y. 2012c, GeoRL, 39, L10101

Fu, H. S., Khotyaintsev, Y. V., Vaivads, A., Retinò, A., & André, M. 2013b, NatPh, 9, 426

Fu, H. S., Vaivads, A., Khotyaintsev, Y. V., et al. 2017, GeoRL, 44, 37

Fu, H. S., Xu, Y., Vaivads, A., & Khotyaintsev, Y. V. 2019, ApJL, 870, L22

Fu, H. S., Zhao, M. J., Yu, Y., & Wang, Z. 2020c, GeoRL, 47, e86790

Fu, W. D., Fu, H. S., Cao, J. B., et al. 2022, JGRA, 127, e29642

Ge, Y. S., Raeder, J., Angelopoulos, V., et al. 2011, JGRA, 116, A00123

Gershman, D., F-Viñas, A., Dorelli, J., et al. 2017, NatCo, 8, 14719

Grigorenko, E. E., Kronberg, E. A., & Daly, P. W. 2017, CosRe, 55, 57

Guo, Z. Z., Fu, H. S., Cao, J. B., et al. 2021, JGRA, 126, e29900

Gurnett, D. A., Kurth, W. S., Steinberg, J. T., et al. 1986, GeoRL, 13, 225

Hamrin, M., Norqvist, P., Karlsson, T., et al. 2013, JGRA, 118, 6279

Hollweg, J. V. 1999, JGRA, 104, 14811

Huang, S. Y., Fu, H. S., Yuan, Z. G., et al. 2015, JGRA, 120, 4496

Huang, S. Y., Zhou, M., Deng, X. H., et al. 2012, AnGeo, 30, 97

Hwang, K.-J., Goldstein, M. L., F-Viñas, A., et al. 2014, JGRA, 119, 2484

Johnson, J. R., & Cheng, C. Z. 1997, GeoRL, 24, 1423

Keiling, A., Wygant, J. R., Cattell, C. A., et al. 2003, Sci, 299, 383

Khotyaintsev, Yu. V., Cully, C. M., Vaivads, A., et al. 2011, PhRvL, 106, 165001

Khotyaintsev, Yu. V., Divin, A., Vaivads, A., et al. 2017, GeoRL, 44, 1234

Le Contel, O., Leroy, P., Roux, A., et al. 2016, SSRv, 199, 257

Lindqvist, P.-A., Olsson, G., Torbert, R. B., et al. 2016, SSRv, 199, 137

Liu, J., Angelopoulos, V., Runov, A., & Zhou, X.-Z. 2013, JGRA, 118, 2000

Liu, Z.-Y., Zong, Q.-G., Rankin, R., et al. 2023, NatCo, 14, 2088

Louarn, P., Wahlund, J. E., Chust, T., et al. 1994, GeoRL, 21, 1847

Lysak, R. L., & Lotko, W. 1996, JGR, 101, 5085

Nakamura, R., Baumjohann, W., Klecker, B., et al. 2002, GeoRL, 29, 1942

Nakamura, R., Retinò, A., Baumjohann, W., et al. 2009, AnGeo, 27, 1743

Pan, D.-X., Zhou, X.-Z., Shi, Q.-Q., et al. 2015, GeoRL, 42, 4256

Pollock, C., Moore, T., Jacques, A., et al. 2016, SSRv, 199, 331

Rogers, B. N., Denton, R. E., Drake, J. F., & Shay, M. A. 2001, PhRvL, 87, 195004

Runov, A., Angelopoulos, V., Sitnov, M. I., et al. 2009, GeoRL, 36, L14106

Russell, C. T., Anderson, B. J., Baumjohann, W., et al. 2016, SSRv, 199, 189

Russell, C. T., Mellott, M. M., Smith, E. J., & King, J. H. 1983, JGR, 88, 4739

Sahraoui, F., Goldstein, M. L., Belmont, G., Canu, P., & Rezeau, L. 2010, PhRvL, 105, 131101

Salem, C. S., Howes, G. G., Sundkvist, D., et al. 2012, ApJL, 745, L9

Santolík, O., Gurnett, D., & Pickett, J. 2004, AnGeo, 22, 2555

Santolík, O., Parrot, M., & Lefeuvre, F. 2003, RaSc, 38, 10

Schmid, D., Volwerk, M., Plaschke, F., et al. 2019, JGRA, 124, 139

Shay, M. A., Drake, J. F., Eastwood, J. P., & Phan, T. D. 2011, PhRvL, 107, 065001

Sitnov, M. I., Swisdak, M., & Divin, A. V. 2009, JGRA, 114, A04202

Tokar, R. L., Gurnett, D. A., & Feldman, W. C. 1984, JGR, 89, 105

Toledo-Redondo, S., Lavraud, B., Fuselier, S. A., et al. 2019, JGRA, 124, 10048

Toledo-Redondo, S., Lee, J. H., Vines, S. K., et al. 2021, GeoRL, 48, e92376

Vaivads, A., Santolík, O., Stenberg, G., et al. 2007, GeoRL, 34, L09106

Viberg, H., Khotyaintsev, Yu. V., Vaivads, A., et al. 2014, JGRA, 119, 2605

Wu, D. J., & Chao, J. K. 2004, NPGeo, 11, 631

Wu, D. J., & Chen, L. 2020, Kinetic Alfvén Waves in Laboratory, Space and Astrophysical Plasmas (Singapore: Springer)

Wu, M., Lu, Q., Volwerk, M., et al. 2013, JGRA, 118, 4804

Wygant, J. R., Keiling, A., Cattell, C. A., et al. 2002, JGRA, 107, 24

Xu, Y., Fu, H. S., Liu, C. M., & Wang, T. Y. 2018, ApJ, 853, 11

Yao, Z. H., Liu, J., Owen, C. J., et al. 2015, AnGeo, 33, 1301

Yu, Y., Fu, H. S., Cao, J. B., Liu, C. M., & Wang, Z. 2022, ApJ, 926, 22

Zhang, W. Z., Fu, H. S., Cao, J. B., et al. 2022, ApJ, 936, 176

Zhang, W. Z., Fu, H. S., Cao, J. B., Wang, Z., & Liu, Y. Y. 2023, ApJ, 953, 23

Zhao, J. S., Voitenko, Y., Yu, M. Y., Lu, J. Y., & Wu, D. J. 2014, ApJ, 793, 107

Zhou, M., Ashour-Abdalla, M., Deng, X., et al. 2009, GeoRL, 36, L20107

Zhou, M., Ni, B., Huang, S., et al. 2014, JGRA, 119, 4335

Zhou, X. Z., Angelopoulos, V., Sergeev, V. A., & Runov, A. 2010, JGRA, 115, A00103