Lower-band Waves Research Articles

Coexistence of Antisunward and Sunward Ion Cyclotron Waves in the Near-Sun Solar Wind: Excitation by the Proton Cyclotron Instability

Based on observations from the Parker Solar Probe in the near-Sun solar wind, this study identifies an ion-scale wave event characterized by two distinct frequency bands. The lower-band waves exhibit right-hand polarization, while the upper-band waves have left-hand polarization. Alongside these waves, there are clear indications of the existence of both proton core and beam components, with the perpendicular temperature being higher than the parallel temperature in the measured proton velocity distribution functions (VDFs). Utilizing the plasma parameters derived from typical proton VDFs, instability analyses are conducted to investigate the mode nature of the observed waves and their excitation mechanism. The lower-band waves are identified as sunward ion cyclotron waves (ICWs), generated through the proton beam cyclotron instability; the upper-band waves are recognized as antisunward ICWs, induced by the proton core cyclotron instability. This study provides the first direct observational evidence confirming the presence of counterpropagating ICWs and proton cyclotron instability in the solar wind.

Gap formation around <em>Ω</em><sub>e</sub>/2 and generation of low-band whistler waves by Landau-resonant electrons in the magnetosphere: Predictions from dispersion theory

In this paper we show that two significant phenomena of magnetospheric chorus emission can be explained by the participation of beam-like electron structures, created by Landau-resonant interaction with growing oblique whistler waves. The first concerns the widely observed spectral gap near half the electron cyclotron frequency Ωe; the second is related to the observation of very obliquely propagating lower-band waves that cannot be directly generated by temperature anisotropy. Concerning the gap, kinetic dispersion theory reveals that interference of the beam-related cyclotron mode ω~Ωe-kVb with the conventional whistler mode leads to mode splitting and the appearance of a ‘forbidden’ area in the ω-k space. Thereby the beam velocity Vb appears as an essential parameter. It is directly related to the phase velocity of the most unstable whistler wave mode, which is close to VAe/2 for sufficiently hot electrons (VAe is the electron Alfven velocity). To clarify the second point, we show that Landau-resonant beams with Vb < VAe/2, which arise in cold plasmas from unstable upper-band waves, are able to generate lower-band whistler mode waves at very oblique propagation (θ ≥ 60°). Our studies demonstrate the important role of Landau-resonant electrons in nonlinear whistler wave generation in the magnetosphere.

Non-adiabatic extension of the Zak phase and charge pumping in the Rice–Mele model

In this study, the Landau–Zener (LZ) transition method is applied to investigate a weak non-adiabatic effect on the Zak phase and the topological charge pumping in the Rice–Mele model. The non-adiabatic effect is formulated using the LZ transfer matrix. The effective lower band wave function picks up the Stokes phase as well as the usual dynamical phase through two avoided crossings appearing in the two band instantaneous energy spectrum. The interference effect from the upper band has a decisive influence on the decay behavior of the lower band population. A non-adiabatic extension of the Zak phase can then be formulated, corresponding to the center of mass of the lower band Wannier function. Furthermore, we estimate the validity of the LZ formalism and verify the breakdown of the quantization of the topological charge pumping by changing the sweeping speed.

Theoretical analysis on lower band cascade as a mechanism for multiband chorus in the Earth’s magnetosphere

Whistler-mode waves play a crucial role in controlling electron dynamics in the Earth’s Van Allen radiation belt, which is increasingly important for spacecraft safety. Using THEMIS waveform data, Gao et al. [X. L. Gao, Q. Lu, J. Bortnik, W. Li, L. Chen, and S. Wang, Geophys. Res. Lett., 43, 2343-2350, 2016] have reported two multiband chorus events, wherein upper-band chorus appears at harmonics of lower-band chorus. They proposed that upper-band harmonic waves are excited through the nonlinear coupling between the electromagnetic and electrostatic components of lower-band chorus, a second-order effect called “lower band cascade”. However, the theoretical explanation of lower band cascade was not thoroughly explained in the earlier work. In this paper, based on a cold plasma assumption, we have obtained the explicit nonlinear driven force of lower band cascade through a full nonlinear theoretical analysis, which includes both the ponderomotive force and coupling between electrostatic and electromagnetic components of the pump whistler wave. Moreover, we discover the existence of an efficient energy-transfer (E-t) channel from lower-band to upper-band whistler-mode waves during lower band cascade for the first time, which is also confirmed by PIC simulations. For lower-band whistler-mode waves with a small wave normal angle (WNA), the E-t channel is detected when the driven upper-band wave nearly satisfies the linear dispersion relation of whistler mode. While, for lower-band waves with a large WNA, the E-t channel is found when the lower-band wave is close to its resonant frequency, and the driven upper-band wave becomes quasi-electrostatic. Through this efficient channel, the harmonic upper band of whistler waves is generated through energy cascade from the lower band, and the two-band spectral structure of whistler waves is then formed. Both two types of banded whistler-mode spectrum have also been successfully reproduced by PIC simulations.

Lower Band Cascade of Whistler Waves Excited by Anisotropic Hot Electrons: One‐Dimensional PIC Simulations

AbstractBased on Time History of Events and Macroscale Interactions during Substorms waveform data, Gao, Lu, et al. (2016) have reported two special multiband chorus events, where upper band waves are located at harmonics of lower band waves. And they proposed a new generation mechanism to explain this multiband chorus wave, named as lower band cascade. With a 1‐D particle‐in‐cell (PIC) simulation model, we have investigated the lower band cascade of whistler waves excited by anisotropic hot electrons. During each simulation, lower band whistler mode waves are firstly excited by the anisotropy of hot electrons. Later, upper band harmonic waves are generated through the nonlinear coupling between the electromagnetic and electrostatic components of lower band waves, which supports the scenario of lower band cascade. Moreover, the peak wave number (or frequency) of lower band waves will continuously drift to smaller values due to the decline of the anisotropy of hot electrons. While the peak wave number of upper band harmonic waves will be kept nearly unchanged, but their amplitude continues to decrease after their saturation. We further find that the magnetic amplitude of upper band harmonic waves tends to increase with the increase of the wave normal angle of lower band waves or the anisotropy of hot electrons. Besides, the amplitude ratio between upper band and lower band waves is positively correlated with the wave normal angle of lower band waves but is anticorrelated with the anisotropy of hot electrons. Our study has provided a more comprehensive understanding of the lower band cascade of whistler waves.

First report of resonant interactions between whistler mode waves in the Earth's magnetosphere

AbstractNonlinear physics related to whistler mode waves in the Earth's magnetosphere are now becoming a hot topic. In this letter, based on Time History of Events and Macroscale Interactions during Substorms waveform data, we report several interesting whistler mode wave events, where the upper band whistler mode waves are believed to be generated through the nonlinear wave‐wave coupling between two lower band waves. This is the first report on resonant interactions between whistler mode waves in the Earth's magnetosphere. In these events, the two lower band whistler mode waves are observed to have oppositely propagating directions, while the generated upper band wave has the same propagating direction as the lower band wave with the relatively higher frequency. Moreover, the wave normal angle of the excited upper band wave is usually larger than those of two lower band whistler mode waves. Our results reveal the large diversity of the evolution of whistler mode waves in the Earth's magnetosphere.

Bandwidths and amplitudes of chorus‐like banded emissions measured by the TC‐1 Double Star spacecraft

AbstractCharacteristics of banded whistler‐mode emissions are derived from a database of chorus‐like events obtained from the complete data set of the wave measurements provided by the Spatio‐Temporal Analysis of Field Fluctuation‐Digital Wave Processing (STAFF‐DWP) wave instrument on board the TC‐1 Double Star spacecraft. Our study covers the full operational period of this spacecraft (almost 4 years). Our entire data set has been collected within 30° of geomagnetic latitude at L shells between 2 and 12 and below 4 kHz. All events have been processed automatically to accurately determine their power spectral density (PSD), bandwidth, and amplitude. We found most cases of chorus‐like banded emissions at L≤10 on the dawnside and dayside. The upper band emissions (above one half of the equatorial electron cyclotron frequency) occur almost 20 times less often than the lower band, and their average amplitude is almost 3 times smaller than for the lower band. Intense upper band emissions cover smaller L shell, magnetic local time (MLT), and magnetic latitudes regions than intense lower band emissions. The intense nightside and dawnside chorus‐like banded emissions were observed at low magnetic latitudes, while the intense dayside and duskside emissions were mostly found at higher magnetic latitudes. The amplitudes of dayside lower band waves slightly increase as they propagate away from the geomagnetic equator and are smaller than chorus amplitudes on nightside and dawnside. The PSD, the amplitude of the lower band, its frequency bandwidth, and its occurrence rate significantly increase with increasing geomagnetic activity, while all these parameters for the upper band are not so strongly dependent on the geomagnetic activity.

Characteristics of the Poynting flux and wave normal vectors of whistler‐mode waves observed on THEMIS

The characteristics of the Poynting flux and wave normal vectors of whistler‐mode waves outside the plasmapause are investigated for the lower (0.1–0.5 fce) and upper bands (0.5–0.8 fce), where fce is the equatorial electron cyclotron frequency. To analyze the wave properties, we utilized high‐resolution waveform data from multiple THEMIS spacecraft in the near‐equatorial magnetosphere from June 2008 to November 2012. Full measurements of the wave electric and magnetic fields are used to calculate the Poynting fluxes and construct the wave normal vectors, which are then used to calculate the polar and azimuthal angles with respect to the background magnetic field. Statistical results show that the majority of whistler‐mode waves propagate away from the magnetic equator, suggesting that the major source region is very close to the equator. The lower band wave normal angle distribution shows a major peak close to the field line direction and a secondary peak near the resonance cone. In contrast, the wave normal distribution of upper band waves exhibits a broad distribution between 0° and 60° with the largest probability at ~0°. The azimuthal component of the wave normal vector predominantly points radially outward for both lower and upper band waves, but a tendency for azimuthal propagation is observed for lower band waves in the day and dusk sectors probably due to pronounced azimuthal density gradients in the afternoon sector. Our statistical results provide crucial information on the Poynting fluxes and wave normal vectors of whistler‐mode waves, which play a significant role in radiation belt electron dynamics.

Modeling the wave normal distribution of chorus waves

The propagation and attenuation characteristics of lower band and upper band chorus waves are investigated by ray tracing, and the evaluation of Landau damping based on an empirical suprathermal electron model derived from Time History of Events and Macroscale Interactions during Substorms (THEMIS) data. The rate of Landau damping is found to increase at larger L‐shell, for more oblique wave normal angles, and for higher geomagnetic activity. Damping is also larger on the nightside than on the dayside and is more pronounced in the upper band than in the lower band. These features can account for the statistical pattern of chorus waves observed away from the equatorial source region. A physical model of the wave normal angle distribution along a field line is presented, which provides insight on how the wave normal angle distribution varies as chorus waves propagate away from the equatorial source region. Our modeling shows that wave emissions at low latitudes (λ ≲ 30°) come predominately from the equatorial source at the same L‐shell and that their wave normal angles increase with increasing latitude due to wave refraction caused by magnetic gradients and curvature. However, at high latitudes (λ ≳ 30°), the wave normal angle distribution along a particular field line is affected by chorus waves that arrive from an equatorial source at lower L because of significant cross‐L propagation. As a consequence, the lower band wave normal angle tends to decrease with increasing latitudes, while the upper band wave normal angle can either increase or decrease depending on the equatorial source at lower L. The effect of cross‐L propagation might also explain why observed wave normal angle distribution tends to become more field‐aligned at high latitudes. Interestingly, the upper band chorus at such high latitudes originates from lower band waves originating near the equator at lower L. A global model of wave normal variation along a field line constructed in this study is not currently available from observations but is nonetheless critically important for evaluating bounce‐averaged diffusion coefficients for future radiation belt modeling.

Excitation of banded whistler waves in the magnetosphere

Banded whistler waves can be generated by the whistler anisotropy instability driven by two bi-Maxwellian electron components with T{sub {perpendicular}}/T{sub {parallel}} > 1 at different T{sub {parallel}} For typical magnetospheric condition of 1 < {omega}{sub e}/{Omega}{sub e} < 5 in regions associated with strong chorus, upper-band waves can be excited by anisotropic electrons below {approx} 1 keV, while lower-band waves are excited by anisotropic electrons above {approx} 10 keV. Lower-band waves are generally field-aligned and substantially electromagnetic, while upper-band waves propagate obliquely and have quasi-electrostatic fluctuating electric fields. The quasi-electrostatic feature of upper-band waves suggests that they may be more easily identified in electric field observations than in magnetic field observations. Upper-band waves are liable to Landau damping and the saturation level of upperband waves is lower than lower-band waves, consistent with observations that lower-band waves are stronger than upper-band waves on average. The oblique propagation, the lower saturation level, and the more severe Landau damping together would make upper-band waves more tightly confined to the geomagnetic equator (|{lambda}{sub m}| < {approx}10{sup o}) than lower-band waves.

Statistics of multispacecraft observations of chorus dispersion and source location

We report emission characteristics of 52 chorus events on 23 August 2003 and 10 events on three other days, modeled with a ray tracing technique. Chorus waves have a characteristic frequency/time variation that is a combination of frequency separation by propagation dispersion and a time‐dependent source frequency emission drift. A cross‐correlation technique comparing data from multiple Cluster spacecraft quantifies the frequency variation owing to propagation dispersion. The comparison of the data cross correlations with the simulated cross correlations allows the identification of a correlation region which has at least one common point with the chorus source region. Any remaining frequency/time variation in the single‐spacecraft spectrograms not accounted for by the cross correlations is then used to determine the time‐dependent source frequency emission drift. The final modeled correlation region and source frequency emission drift for each chorus event is consistent with both the cross‐correlation and single‐spacecraft data. The modeled correlation regions are located near the magnetic equator and are, in general, more extended parallel to the Earth's magnetic field than perpendicular to it. It is found that waves with frequencies above and below 1/2 the equatorial electron cyclotron frequency on the magnetic field line of the spacecraft (lower and upper band, respectively) are emitted in a broad spectrum of wave normal angles. There is also some preference for lower band waves observed at the spacecraft to have been emitted near the Gendrin angle and at earthward‐pointing wave normal angles of between −20° and −30°. The latter result is close to the range of wave normal angles shown recently to be connected with chorus that propagates into the plasmasphere and evolves into the incoherent plasmaspheric hiss spectrum, known to be connected to pitch angle scattering and loss of electrons in the electron slot region. Finally, the time‐dependent source frequency emission drift for these events ranges from 1 to 20 kHz/s. For most events these rates account for at least 2/3 of the chorus frequency/time variation with the rest being due to propagation dispersion.