Low-frequency Whistler Waves Research Articles

Low-frequency whistler waves driven by energetic electrons in plasmas of solely electron cyclotron wave heating

Whistler waves are a type of low-frequency electromagnetic wave common in nature, which is usually associated with energetic electron phenomena. This study presents experimental observations of low-frequency whistler wave instabilities driven by energetic electrons through wave–particle interactions on EXL-50. The energetic electrons are generated by electron cyclotron waves (ECWs) through stochastic heating [Wang et al., J. Plasma Phys. 89, 905890603 (2023)] and do not match the characteristics of the runaway electrons [Shi et al., Nucl. Fusion 62, 086047 (2022)]. In the steady-state plasma of the Energy iNNovation XuanLong-50 (EXL-50), whistler waves within the 30–120 MHz frequency range were observed during electron cyclotron resonance heating. These waves displayed multiple frequency bands, and the frequencies of waves were directly proportional to the Alfvén velocity. Furthermore, it was interesting to find that superposition of lower hybrid wave into ECW resulted in the suppression of these whistler waves. The experimental results may indicate that the whistler waves are driven by energetic electrons (excluding runaway electrons). These discoveries carry significant implications for several areas of research, including the investigation of wave–particle interactions, the development of radio frequency wave current drivers, their potential impact on the electron dynamics in future fusion devices, and even the presence of unusually low-frequency whistler waves in Earth's radiation belts.

Dispersion Characteristics of Low-Frequency Electron Waves in a Magnetoactive Plasma of Arbitrary Density

The article studies waves in a collisionless magnetoactive plasma with frequencies much lower than the electron cyclotron frequency at an arbitrary ratio between the electron plasma and cyclotron frequencies. A general dispersion relation is obtained for the wave frequency as a function of the wave vector and the ratio of the plasma frequency to the cyclotron frequency. This relation is a bicubic equation with respect to frequency. Based on this equation, the existence domains of various wave modes depending on the specified parameter, their group velocity, polarization, and energy density are studied. Special attention is paid to low-frequency whistler waves in a low-density plasma, since, among the propagating wave modes existing in the specified range of parameters, whistler waves have the highest refractive index and play an important role in theresonant interaction of waves and particles.

Properties of Whistler Waves’ Ducting in Plasmas With Systems of Small‐Scale Density Depletions

AbstractThe ducting of whistler waves by systems of small‐scale field‐aligned plasma density depletions is studied. Similarly to our previous paper (Zudin et al., 2019, https://doi.org/10.1029/2019ja026637), we carry out analytical calculations and numerical simulations for the parameters of an active experiment in which very low frequency whistler waves emitted by a ground‐based transmitter at a frequency of 18 kHz were received onboard the DEMETER satellite at 700 km above the SURA heating facility. Random‐sized density depletions with a level around 10%–20% and perpendicular sizes ranging from 10 m up to about 300 m are considered. The properties of ducted waves are determined by the perpendicular size of individual depletions. Particularly, depletions with a width of more then d0 ∼ 100 m form separate ducting structures, that is, coupled waveguides capable of exchanging energy by means of mode overlap. Depletions with a width of less than d0 ∼ 100 m form a common waveguide structure, whose properties are equivalent to those of a wider irregularity with a smoothed density profile. Two important differences are revealed in ducting properties of density depletions compared to density enhancements considered in Zudin et al. (2019, https://doi.org/10.1029/2019ja026637). First, depletions support highly oblique Gendrin mode waves, rather than quasi‐longitudinal whistlers as in the case of density enhancements. Second, the characteristic perpendicular size d0 ∼ 100 m of density depletions separating the regimes of “coupled waveguides” and of “equivalent ducting structure” with smoothed density profile is by an order of magnitude smaller than for density enhancements of the same 10–20% relative level.

Low-frequency Whistler Waves Modulate Electrons and Generate Higher-frequency Whistler Waves in the Solar Wind

Abstract The role of whistler-mode waves in the solar wind and the relationship between their electromagnetic fields and charged particles is a fundamental question in space physics. Using high-temporal-resolution electromagnetic field and plasma data from the Magnetospheric MultiScale spacecraft, we report observations of low-frequency whistler waves and associated electromagnetic fields and particle behavior in the Earth’s foreshock. The frequency of these whistler waves is close to half the lower-hybrid frequency (∼2 Hz), with their wavelength close to the ion gyroradius. The electron bulk flows are strongly modulated by these waves, with a modulation amplitude comparable to the solar wind velocity. At such a spatial scale, the electron flows are forcibly separated from the ion flows by the waves, resulting in strong electric currents and anisotropic ion distributions. Furthermore, we find that the low-frequency whistler wave propagates obliquely to the background magnetic field ( B 0), and results in spatially periodic magnetic gradients in the direction parallel to B 0. Under such conditions, large pitch-angle electrons are trapped in wave magnetic valleys by the magnetic mirror force, and may provide free perpendicular electron energy to excite higher-frequency whistler waves. This study offers important clues and new insights into wave–particle interactions, wave generation, and microscale energy conversion processes in the solar wind.

Characteristics of Resonant Electrons Interacting With Whistler Waves in the Nearest Dipolarizing Magnetotail

AbstractThe Magnetospheric Multiscale spacecraft observations in the burst mode allow the determination of the characteristics of resonant electrons interacting with quasi‐parallel whistler waves during prolonged dipolarizations in the near Earth magnetotail at −22 RE < X ≤ −8 RE. We have detected 163 whistler bursts observed during 48 dipolarization events. The bursts were registered within ∼13 min following the dipolarization onset when the burst mode observations were available. In the majority of events, electrons with energies Wres ≥ 10 keV and pitch angles αres ∼ 100°–130° and αres ∼ 50°–80°made the maximum positive contribution to the growth rate of whistler waves propagating quasi‐parallel and antiparallel to the ambient magnetic field, respectively. Our analysis shows that electrons with Wres ∼ 10–20 keV could potentially be scattered into the loss cone by the low frequency whistler waves with fw ∼ (0.05–0.2)fce (fw is the wave frequency and fce is the electron gyrofrequency). The electrons that are scattered into the loss cone can contribute to electron precipitation within ∼13 min following the dipolarization onset. We suggest that whistler waves that are excited due to cyclotron instability driven by the temperature anisotropy of suprathermal electrons (≥2 keV) may, in turn, affect electron distribution in this energy range. Specifically, lower energy resonant electrons transfer a part of their kinetic energy to waves, while more energetic electrons absorb wave energy increasing their kinetic energy. This may lead to the transformation of higher‐energy part of electron distribution from Maxwellian to the power law shape.

Low-frequency whistler waves excited by relativistic laser pulses.

It is shown by multidimensional particle-in-cell simulations that intense secondary whistler waves with special vortexlike field topology can be excited by a relativistic laser pulse in the highly magnetized, near-critical density plasma. Such whistler waves with lower frequencies obliquely propagate on both sides of the laser propagation axis. The energy conversion rate from laser to whistler waves can exceed 15%. Their dispersion relations and field polarization properties can be well explained by the linear cold-plasma model. The present work presents a new excitation mechanism of whistler modes extending to the relativistic regime and could also be applied in magnetically assisted fast ignition.

Electron Scattering by Low-frequency Whistler Waves at Earth’s Bow Shock

Abstract Electrons are accelerated to nonthermal energies at shocks in space and astrophysical environments. While shock drift acceleration (SDA) has been considered a key process of electron acceleration at Earth’s bow shock, it has also been recognized that SDA needs to be combined with an additional stochastic process to explain the observed power-law energy spectra. Here, we show mildly energetic (∼0.5 keV) electrons are locally scattered (and accelerated while being confined) by magnetosonic-whistler waves within the shock transition layer, especially when the shock angle is large ( ). When measured by the Magnetospheric Multiscale mission at a high cadence, ∼0.5 keV electron flux increased exponentially in the shock transition layer. However, the flux profile was not entirely smooth and the fluctuation showed temporal/spectral association with large-amplitude ( ), low-frequency ( where is the cyclotron frequency), obliquely propagating ( , where is the angle between the wave vector and background magnetic field) whistler waves, indicating that the particles were interacting with the waves. Particle simulations demonstrate that, although linear cyclotron resonances with ∼0.5 keV electrons are unlikely due to the obliquity and low frequencies of the waves, the electrons are still scattered beyond 90° pitch angle by (1) resonant mirroring (transit-time damping), (2) non-resonant mirroring, and (3) subharmonic cyclotron resonances. Such coupled nonlinear scattering processes are likely to provide the stochasticity needed to explain the power-law formation.

Low-frequency whistler waves in quiescent runaway electron plasmas

In quiescent runaway electron plasmas in the DIII-D tokamak, whistler waves with frequencies between 90 and 200 MHz are driven unstable in plasmas with appreciable hard x-ray and non-thermal electron cyclotron emission (ECE). Narrow (δf < 50 kHz) discrete modes with erratically spaced frequencies are observed. Unstable modes often extend over a range Δf ≃ 50 MHz but lower frequency unstable modes are usually most intense. The dependency of the frequency on field and density implies a wavenumber k ≃ 150 m−1 with parallel wavenumber k∥ ≪ k. Reducing the gap between the plasma and the wall increases the number of detected modes. Lowering the magnetic field promotes instability. Nonlinear limit-cycle-like oscillations in the whistler amplitude occur on a 10 ms timescale. The ECE signals often jump at whistler bursts, suggesting that the modes pitch-angle scatter the runaways. Sawteeth cause transient stabilization of the whistlers.

Whistler interaction with field‐aligned density irregularities in the ionosphere: Refraction, diffraction, and interference

AbstractField‐aligned density irregularities (FAI) with kilometer‐scale sizes transverse to the background magnetic field are a common feature in the ionosphere at all latitudes and local times. In this paper, we investigate the effect of these irregularities on the transionospheric propagation of very low frequency whistler waves and develop a quantitative description of FAI‐related effects on whistler propagation through the lower ionosphere. Using an electron magnetohydrodynamics simulation, we provide two applications of our model. First, we show that the presence of kilometer‐scale FAI in the ionosphere can reduce the power observed in the equatorial magnetosphere by more than 10 dB in some cases. Second, we demonstrate that multiple FAIs can act as a discrete lens for whistlers, providing a possible means for increasing wave power in artificial whistler ducting experiments.

Resonant scattering of energetic electrons in the plasmasphere by monotonic whistler-mode waves artificially generated by ionospheric modification

Abstract. Modulated high-frequency (HF) heating of the ionosphere provides a feasible means of artificially generating extremely low-frequency (ELF)/very low-frequency (VLF) whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high-energy electrons in the plasmasphere. By ray tracing the magnetospheric propagation of ELF/VLF emissions artificially generated at low-invariant latitudes, we evaluate the relativistic electron resonant energies along the ray paths and show that propagating artificial ELF/VLF waves can resonate with electrons from ~ 100 keV to ~ 10 MeV. We further implement test particle simulations to investigate the effects of resonant scattering of energetic electrons due to triggered monotonic/single-frequency ELF/VLF waves. The results indicate that within the period of a resonance timescale, changes in electron pitch angle and kinetic energy are stochastic, and the overall effect is cumulative, that is, the changes averaged over all test electrons increase monotonically with time. The localized rates of wave-induced pitch-angle scattering and momentum diffusion in the plasmasphere are analyzed in detail for artificially generated ELF/VLF whistlers with an observable in situ amplitude of ~ 10 pT. While the local momentum diffusion of relativistic electrons is small, with a rate of &lt; 10−7 s−1, the local pitch-angle scattering can be intense near the loss cone with a rate of ~ 10−4 s−1. Our investigation further supports the feasibility of artificial triggering of ELF/VLF whistler waves for removal of high-energy electrons at lower L shells within the plasmasphere. Moreover, our test particle simulation results show quantitatively good agreement with quasi-linear diffusion coefficients, confirming the applicability of both methods to evaluate the resonant diffusion effect of artificial generated ELF/VLF whistlers.

Low frequency Whistler waves excited in fast magnetic reconnection processes

Whistler waves generated in fast magnetic reconnection processes of collisionless high beta plasmas are reviewed in experiments and satellite observations, as well as in theory and simulation, and further studied in the two-fluid theory. It is found that low frequency whistler waves can be excited in the ion inertial range of the reconnection region. The wave is found right-handed polarized with a quadrupolar out-of-plane magnetic perturbation, in accord with satellite observations in the geomagnetosphere.

Quasistationary magnetic field generated in a plasma by a whistler-mode radio pulse

It has been shown experimentally that a quasistationary magnetic field is generated in a weakly collisional magnetized plasma by a spatially nonuniform high-frequency whistler-mode field. The sources of the quasistationary magnetic field are nonlinear currents generated due to the longitudinal and transverse components of the ponderomotive force, acting on charged particles in the spatially localized high-frequency pump field. The dynamics of the excited magnetic fields has been analyzed. It was found that the settling time of the quasistationary magnetic field is determined by the switching-on time of the high-frequency field and the propagation of pulsed current and magnetic fields from the region of their generation occurs with the velocity of low-frequency whistler waves.

Parametric generation of low-frequency waves by plasma electrons accelerated under electron cyclotron resonance conditions

It has been shown experimentally that the diamagnetic effect appearing when electrons of a magnetized plasma in the antenna near field are accelerated under electron cyclotron resonance conditions can be used to generate low-frequency waves. The amplitude modulation of a signal supplied to the antenna is accompanied by the modulation of the diamagnetic effect and leads to the emission of waves at the modulation frequency to the surrounding plasma. In this process, the extended plasma region containing accelerated electrons serves as a parametric bodiless antenna. The results of the model laboratory experiments make it possible to propose a method for the parametric generation of low-frequency whistler waves in the Earth’s ionosphere by a powerful amplitude-modulated signal supplied to the satellite-borne antenna.

Self-focusing of a whistler propagating at an angle to the magnetic field in a plasma

The self-focusing of a low-frequency whistler wave, propagating at an angle to the ambient magnetic field in a plasma, is studied. The nonlinearity arises due to the pondermotive force on electrons and subsequent redistribution of plasma along the magnetic field. The direction of self-focusing differs from that of phase propagation due to plasma anisotropy. In the three-dimensional (3D) case, the self-focusing is sharper and increases as θ increases. In the 2D slab model, self-focusing occurs with spatial periodicity.

On the dispersion law of low-frequency electron whistler waves in a multi-ion plasma

Abstract. A new and simple dispersion law for extra-low-frequency electron whistler waves in a multi-ion plasma is derived. It is valid in a plasma with finite ratio ωc/ωpe of electron gyro-to-plasma frequency and is suitable for wave frequencies much less than ωpe but well above the gyrofrequencies of most heavy ions. The resultant contribution of the ions to the dispersion law is expressed by means of the lower hybrid resonance frequency, the highest ion cutoff frequency and the relative content of the lightest ion. In a frequency domain well above the ions' gyrofrequencies, this new dispersion law merges with the "modified electron whistler dispersion law" determined in previous works by the authors. It is shown that it fits well to the total cold plasma electron whistler dispersion law, for different orientations of the wave vectors and different ion constituents, including negative ions or negatively charged dust grains.

Parametric generation of whistler waves due to the interaction of high-frequency wave beams with a magnetoplasma

The parametric generation of low-frequency whistler waves by a pump wave beam formed by high-frequency whistler waves with close frequencies is studied experimentally. The electromagnetic fields excited by the beats of two co- or counterpropagating high-frequency waves, or by an amplitude-modulated pump are studied. It is shown that the nonlinear currents at the beat (modulation) frequency are generated by a transverse ponderomotive force arising due to the finite width of the high-frequency beam. In this case, the nonlinear azimuthal drift currents enclose the pump beam and can radiate low-frequency whistler waves to the surrounding plasma.

Oblique propagation of electromagnetic waves in a kappa-Maxwellian plasma

Space plasmas are often observed to contain more particles in the high-energy tail than the usual Maxwellian distributions, and are well modeled by kappa distributions. The hybrid kappa-Maxwellian distribution and associated generalized plasma dispersion function ZκM were recently introduced to model magnetized space plasmas. The susceptibility tensor for a kappa-Maxwellian plasma component is derived, making use of ZκM. This enables one to make general studies of obliquely propagating electromagnetic waves in a magnetoplasma. The susceptibility and dielectric tensors reduce to the Maxwellian expressions in the limit κ→∞. As an illustration, the formalism is applied to the lower branch of the R mode and its off-parallel variant. For low κ values, low-wavenumber, low-frequency parallel whistler waves are shown to be stable, unlike the Maxwellian case, which is unstable if the perpendicular temperature exceeds the parallel temperature. A numerical study is made of the effects of the value of kappa, the propagation angle, and the temperature anisotropy ratio on dispersion and damping. The kappa-Maxwellian distribution with very low κ is found to be unstable in an overdense plasma near the electron-cyclotron frequency even when the parallel and perpendicular temperatures are equal, because of the anisotropy of the contours in velocity space.

Upconversion of whistler waves by gyrating ion beams in a plasma

A gyrating ion beam, with a ring-shaped distribution in velocity, supports negative energy beam modes near the harmonics of beam gyro-frequency. An investigation of the non-linear interaction of high-frequency whistler waves with the negative energy beam cyclotron mode is made. A non-linear dispersion relation is derived for the coupled modes. It is shown that a gyrating ion-beam frequency upconverts the whistler waves separated by harmonics of beam gyro-frequency. The expression for the growth rate of whistler mode waves has been derived. In Case 1, a high-amplitude whistler wave decays into two lower frequency waves, called a low-frequency mode and a side band of frequency lower than that of pump wave. In Case 2 a high-amplitude whistler wave decays into two lower frequency daughter waves, called the low-frequency mode and whistler waves. Generation mechanism of these waves has application in space and laboratory plasmas.

Effect of loss-cone distribution on the generation of whistler waves in the magnetosphere

An anisotropic kappa velocity distribution with loss-cones is used to investigate whistler wave instability occurring in the magnetosphere. The elements of the dielectric tensor and dispersion relation using modified plasma dispersion function Z κ ∗(ξ) with loss-cone angle have been obtained for the linear waves propagating exactly parallel to a uniform local magnetic field in a homogeneous and hot plasma. The modified plasma dispersion function and integrals have been expressed in power-series form for argument of ξ≫1. Temporal/spatial growth rates for whistler wave in the magnetosphere have been evaluated by the method of numerical techniques. The results of such a kappa loss-cone distribution function on the generation of whistler waves are compared with those obtained by Maxwellian loss-cone distribution. Calculations show that either a loss-cone or a thermal anisotropy in the hot plasma component of the magnetosphere can lead to the generation of incoherent emission of low-frequency whistler waves. This methodology could be easily extended to the study of low frequency emissions from planetary magnetospheres under suitable choice of models of density and magnetic field and other plasma parameters.

Parametric transformation of the amplitude and frequency of a whistler wave in a magnetoactive plasma

The results of experiments studying the propagation of a high-frequency whistler wave in a magnetized plasma duct in the presence of an intense low-frequency wave also related to the whistler frequency range are reported. Amplitude-frequency modulation of the high-frequency whistler wave trapped in the duct was observed. A deep amplitude modulation of the signal that can lead to its splitting into separate wave packets is observed. It is shown that an increase in the wave propagation path leads to a broadening of the wave frequency spectrum and to a shift of the signal spectrum predominantly toward the red side. The transformation of the frequency of the high-frequency wave is related with the time-dependent perturbation of the external magnetic field by the field of the low-frequency whistler wave (the relative perturbation of the magnetic field δB/B≤5×10−2).