Locally Generated Whistler-Mode Waves Before Dipolarization Fronts

Abstract

Whistler-mode waves, electromagnetic emissions with frequencies between the lower hybrid and electron cyclotron frequencies, are ubiquitous in planetary magnetotails. They are known to play a vital role in electron scattering and acceleration, originating primarily within strong magnetic field regions behind dipolarization fronts (DFs). In contrast to this established knowledge, we present a comprehensive analysis of whistler-mode waves generated locally within weak magnetic field regions ahead of DFs, utilizing high-cadence measurements from the MMS mission. By resolving the wave dispersion relations, we demonstrate that these emissions arise from cyclotron resonance with local electrons exhibiting weak perpendicular temperature anisotropy (A_e < 1.2). We further propose that this anisotropy may develop due to magnetic mirror structures forming upstream of DFs. Our findings challenge the conventional view that whistler-mode generation requires strong magnetic fields near DFs, providing new insights into understanding wave excitation mechanisms in planetary magnetotails.

1. Introduction

Dipolarization fronts (DFs), coherent magnetic structures featuring a dramatic increase in the northward magnetic field in the terrestrial magnetotail, have been extensively studied in recent years due to their important role in magnetospheric activity, such as the aurora substorms [1,2,3,4,5]. They are usually associated with bursty bulk flows (BBFs) [6,7,8], preceded by a small B_z dip [9,10,11], and followed by a strong B_z region termed as flux pileup region (FPR) [12,13,14]. The DFs have been traditionally termed as dipolarization fronts due to the enhanced B_z carried by the DFs. The DFs typically serve as leading boundaries of the flows, separating hot dilute plasmas inside the flow from the cold dense plasmas inside the ambient plasma sheet.

As kinetic-scale flow boundaries hosting strong currents and electric fields, DFs have been suggested to play a key role in magnetospheric particle dynamics through both adiabatic and nonadiabatic processes. The adiabatic dynamics, including Fermi and betatron acceleration, can uniformly elevate the energy of particles up to suprathermal levels [15,16,17,18,19]. Alternatively, the nonadiabatic dynamics, primarily leading to energy-dependent acceleration of particles, are typically associated with wave generation. To date, a variety of wave activities have been observed in the vicinity of the DFs, including whistler-mode waves [13,20,21], lower hybrid drift waves [22,23], electrostatic solitary waves [24,25], electron cyclotron harmonic waves [26,27], and magnetosonic waves [28].

Among all these waves, whistler-mode waves—right-hand circularly polarized electromagnetic waves with frequencies ranging from the lower hybrid frequency (f_lh) to the electron cyclotron frequency (f_ce)—have attracted intense interest, since they can lead to efficient electron diffusion, acceleration, and precipitation [29,30,31,32,33,34,35,36,37,38]. Statistically, it has been documented that over 30% of DF events are associated with the whistlers, with a notable tendency occurring in the FPRs near the magnetic equator [36]. In conjunction with these waves, the electron distribution exhibits a pronounced perpendicular anisotropy at energy higher than 5 keV [37]. Previous observations have also disclosed that the electron temperature anisotropy, denoted by $A_e=T_{\perp }/T_{\parallel }$, usually exceeds one in the FPRs. This anisotropy provides compelling evidence for ongoing betatron acceleration attributed to the accumulation of magnetic flux [14]. Although some studies have revealed the presence of whistler-mode waves ahead of the DFs [39,40,41], they have not performed detailed analyses or explored the underlying physical processes, thus leaving the phenomena poorly understood.

In this paper, we present MMS observations of whistler-mode waves preceding the DFs in the magnetotail. Taking advantage of the high-cadence measurements provided by MMS missions [42], we have analyzed the wave properties in detail and resolved their dispersion relation, revealing that they can be excited locally inside weak magnetic field regions ahead of the DFs. The potential mechanisms accounting for wave generation are also discussed in this paper.

2. Observations

High-resolution electromagnetic field data from the Fluxgate Magnetometer [40], the Search-Coil Magnetometer [41], and the Electric Double Probe [43,44], as well as particle data from the Fast Plasma Investigation [45], are utilized in this study. All the data are presented in geocentric solar magnetospheric (GSM) coordinates unless specified otherwise. Three events are selected in this study to illustrate the generation of whistler-mode waves ahead of the DFs. Since these events are similar in terms of the wave properties, we focus on one event here to show the local plasma environment near the DFs, which was observed by MMS on 25 June 2018 from 11:45:37.5 to 11:45:38.5 UT, when MMS was located at [−14.68 10.34 2.07] R_E (Earth radius).

Figure 1 provides an overview of this event. During the whole interval, MMS remained within the central plasma sheet (Figure 1i,j, plasma beta β ~ 20) and observed a steady earthward BBF with ion speed V_x close to 300 km/s (Figure 1d). At ~11:45:38.5 UT, a DF, manifested by a dramatic increase in B_z (from ~3 to ~10 nT, Figure 1a) and a decrease in plasma density (from ~0.4 to ~0.3 cm⁻³, Figure 1b), was detected. The magnetic field exhibits a dip in B_z from ~4 to ~3 nT, occurring from 11:45:37.5 to 11:45:38.5 UT, prior to the DF (Figure 1a). The DF propagation velocity, estimated by timing analysis, is calculated as 145 × [0.73 0.48 −0.48] km/s. Considering the DF’s duration (~2s), its thickness is ~290 km or equivalent to ~0.8 d_i (ion inertial length, estimated based on the ambient plasma density of ~0.4 cm⁻³). The electric field is significantly enhanced at the front, with x component exhibiting a dipolar variation from ~5.0 to ~−1.9 mV/m (Figure 1g), indicating the potential development of electrostatic waves. These characteristics are consistent with the canonical DFs documented by previous studies [1,4,46].

During the DF interval (from ~11:45:38.5 to 11:45:40.5 UT), electron speed is dramatically increased, approaching 1000 km/s (Figure 1c), suggesting the presence of electron jets. Electron temperature exhibits a slow augmentation (from ~800 to ~l000 eV) during the front except for a slight trough (<800 eV) in the dip region, where electron perpendicular temperature anisotropy exceeds 1.1 (Figure 1h). Inside the magnetic dip, the electron pitch angle distributions with 1–4 keV and 4–8 keV concentrated in 90° degrees, forming the so-called pancake distribution. Different from previous studies [36,37], electron betatron acceleration inside the FPR does not dominate. The ratio of electron plasma frequency (f_pe) to electron gyrofrequency (f_ce) peaks at ~70 within the dip region, substantially reducing the required free energy for wave generation compared to the FPR (f_pe/f_ce ~ 10). Combined with the electron perpendicular temperature anisotropy—the free energy source for the generation of whistlers [13,47,48]—is present before but absent inside and behind the DF. Whistlers are expected to occur in the dip region preceding the DF rather than in the conventional sites: inside the DFs or FPRs. This expectation is corroborated by the observation of fluctuations in both the magnetic and electric fields preceding the DF, indicating the presence of electromagnetic emissions.

As shown in Figure 2, clear enhancement of magnetic and electric field power spectral density near 0.1 f_ce is observed ahead of the DF (Figure 2c,d). We use the singular value decomposition (SVD) method to resolve the wave property [49] based on the wave electric and magnetic data measured by MMS. The electromagnetic waves exhibit positive ellipticity (~1, Figure 2e), small wave angle (<20°, Figure 2f), and planarity approaching 1 (Figure 2g). Therefore, these waves are in line with right-handed-polarized and parallel-propagating whistler-mode waves [21,50,51]. Note that the observed wave frequency is well below local ion plasma frequency (>100 Hz) and above local lower hybrid frequency (~2.4 Hz).

Using the MMS high-cadence data, we calculated the wave vector by using the Ampere’s law [52] given as follows:

$${\mu }_0\mathbf{J}=i\mathbf{k}\times \mathbf{B}$$

where B, J, k, and μ₀ represent, respectively, magnetic field, current density, wave vector, and magnetic permeability in empty space. As shown in Figure 3a, the wave power spectrum density is consistent with the whistler-mode wave theoretical dispersion relation (DR) for cold plasma approximation (the dashed line). We performed an instability analysis to examine whether local electron perpendicular temperature anisotropy could drive the whistlers in the dip region. Local plasma parameters, B ~ 5 nT, N_e ~ 0.45 cm⁻³, T_e ~ 860 eV, and A_e ~ 1.1, are taken as inputs in to the kinetic plasma DR solver, BO [53]. The predicted DR is displayed in Figure 3b, showing that whistler-mode waves could be locally excited. Wave growth corresponds to the frequency range of ~6–13 Hz, consistent with the observational outcome. Corresponding to the maximum value of power density in Figure 3a, we find that it is close to the wave growth region in the predicted DR of the whistler wave (marked by red dot in Figure 3b). Combining the theoretical and observational analysis results, we conclude that these whistlers were locally generated by the electron temperature anisotropy developed ahead of the DF.

3. Discussion and Conclusions

Previous studies have revealed a close relationship between the whistler-mode waves and the DFs, proposing that their generation is associated with electron-perpendicular temperature anisotropy, which is attributed to betatron acceleration driven by an enhanced magnetic field within the FPRs [36,37]. The detection of whistlers preceding the DFs is beyond conventional expectations since the magnetic field strength is typically weak therein [46]. Given that whistlers primarily propagate along magnetic field lines, it is unlikely that they could be excited behind the DFs and propagate across the DFs. Here, we present two more events to further illustrate the whistler waves ahead of DFs. As depicted in Figure 4, they exhibit similar characteristics of right-handed parallel-propagating electromagnetic waves. On the other hand, they host similar local plasma environments that are conducive to triggering whistler anisotropy instability, with magnetic field B < 5 nT and temperature anisotropy A_e ~ 1.1–1.2. Whistler generation depends not only on electron temperature anisotropy, but also on magnetic field strength and electron density. To quantify this, we calculated the ratio of electron plasma frequency to electron gyrofrequency f_pe/f_ce, which increases locally during the wave interval in all three events. This explains why A_e exceeds one in the DFs or FPRs, yet the whistlers are absent in these regions.

The generation of the observed whistlers should be related to local plasma dynamics ahead of the DFs. The local electron perpendicular temperature anisotropy was indeed observed and could account for wave generation, as verified by instability analysis. It is noted that, although the observed electron perpendicular temperature anisotropy is not very strong (A_e < 1.2), the weak magnetic field (B < 5 nT) ahead of the DFs provides a more favorable condition for wave generation compared to the strong magnetic field behind the DFs (B > 15 nT). Consequently, even a modest electron perpendicular temperature anisotropy can effectively drive whistler-mode waves ahead of DFs. The generation mechanism of this electron anisotropy remains puzzling, particularly given the characteristically weak B_z component in these regions. The decreased B_z preceding DFs suggest that conventional betatron acceleration cannot fully account for the observed anisotropy. Instead, we propose that magnetic mirror structures—enabled by closed field line configurations—may provide the dominant anisotropy generation mechanism. The loss cone angle θ for a magnetic mirror, given by ${\mathit{sin}}^2\theta =B/B_m$, where B_m is the maximum magnetic field strength during the magnetic dip (~4.2 nT), is plotted (black lines) in Figure 1k,l. As can be seen, the electrons with a 90° pitch angle were trapped inside the magnetic mirror structure. Previous simulations [54] have also demonstrated that closed field lines (magnetic islands) form ahead of DFs, effectively trapping particles. These magnetic islands (manifested as dips in B_z) are likely generated upstream of the DF through ion tearing instabilities [55,56]. The weak magnetic field in the dip region corresponds to the central portion of the magnetic mirror configuration, while the mirror points reside in adjacent lobe regions characterized by stronger magnetic fields. Within this magnetic mirror structure, electrons with pitch angles approaching 90° become trapped, resulting in the development of electron perpendicular temperature anisotropy.

In summary, our observations provide evidence that whistler-mode waves can be generated in the weak magnetic field region preceding the DFs. The generation of the whistlers may differ from those within the FPRs, where electron perpendicular temperature anisotropy is driven by betatron acceleration. Instead, the whistlers are associated with the magnetic mirror structure developed preceding the DFs. These findings are pivotal for advancing our understanding of the whistler-mode waves in the magnetotail. To elucidate the whistlers in more detail, a more comprehensive and statistical analysis is necessary in the future.