Propagation Of Whistler Waves Research Articles

Low‐Frequency Whistler Waves Excited by Electron Butterfly Distributions in Turbulent Reconnection Outflow

AbstractWhistler waves, leading to electron scattering and energy transport, are frequently observed in magnetic reconnection. High‐energy electrons produced by magnetic reconnection are expected to excite low‐frequency whistler waves. However, the study on low‐frequency whistler waves in magnetic reconnection is still quite scarce. Utilizing high‐resolution data from the Magnetospheric Multiscale (MMS) mission, we provide observations of low‐frequency whistler waves in a turbulent reconnection outflow. The quasi‐antiparallel propagating whistler waves have power peaked at ∼0.1 and wave number of ∼0.43 in the plasma rest frame. It can be excited through the cyclotron resonance by the electron butterfly distributions, which can be interpreted by a model comprising the addition of electron beams hosting perpendicular anisotropy to electron isotropy distributions. The energy of resonant electrons is calculated as 1.06∼4.16 keV, the parts corresponding to lower frequency (<∼0.1) falling into suprathermal energy range. Our study can promote the understanding of generation of whistler waves in magnetic reconnection.

Particle Simulation Study of Obliquely Propagating Whistler Waves in Low‐Beta Plasmas

AbstractWhistler mode waves, which are electromagnetic emissions commonly observed in various space plasma environments, play critical roles in electron dynamics. While most whistler waves are driven by temperature anisotropy and propagate parallel to the background magnetic field, these waves can also be excited in the oblique direction when electron plasma beta is very low (<0.025). Although linear theory accounts for the excitation processes of obliquely propagating whistler waves, the subsequent evolution and saturation processes remain inadequately understood. This study utilizes two‐dimensional self‐consistent simulations to investigate the complete wave‐particle interaction process. By scanning a broad parameter range, we derive scaling laws for the wave intensity, linking the wave properties to initial and final plasma conditions. The saturated temperature anisotropy from simulations can explain the upper bound anisotropy constraint observed by spacecraft well. Additional phase space analysis shows that both Landau and cyclotron resonance play critical roles in the evolution of electron velocity distribution, albeit in different energy ranges. Oblique whistler waves can effectively heat electrons through Landau resonance, creating a plateau distribution in the parallel direction. This research advances our understanding of the mechanisms behind obliquely propagating whistler waves in low‐beta plasmas and their impact on electron dynamics.

Whistler Waves in the Young Solar Wind: Statistics of Amplitude and Propagation Direction from Parker Solar Probe Encounters 1–11

In the interplanetary space solar wind plasma, whistler waves are observed in a wide range of heliocentric distances (from ∼20 solar radii (RS) to Jupiter’s orbit). They are known to interact with solar wind suprathermal electrons (strahl and halo) and to regulate the solar wind heat flux through scattering the strahl electrons. We present the results of applying the technique to determine the whistler wave propagation directions to the spectral data continuously collected by the FIELDS instruments on board Parker Solar Probe (PSP). The technique was validated based on the results obtained from burst mode magnetic and electric field waveform data collected during Encounter 1. We estimated the effective length of the PSP electric field antennas for a variety of solar wind conditions in the whistler wave frequency range and utilized these estimates for determining the whistler wave properties during PSP Encounters 1–11. Our findings show that (1) the enhancement of the whistler wave occurrence rate and wave amplitudes observed between 25 and 35 RS is predominantly due to the sunward-propagating whistler wave population associated with the switchback-related magnetic dips; (2) the antisunward or counterpropagating cases are observed at 30–40 RS; (3) between 40 and 50 RS, sunward and antisunward whistlers are observed with comparable occurrence rates; and (4) almost no sunward or counterpropagating whistlers were observed at heliocentric distances above 50 RS.

Weibel- and non-resonant Whistler wave growth in an expanding plasma in a 1D simulation geometry

Ablating a target with an ultraintense laser pulse can create a cloud of collisionless plasma. A density ramp forms, in which the plasma density decreases and the ion’s mean speed increases with distance from the plasma source. Its width increases with time. Electrons lose energy in the ion’s expansion direction, which gives them a temperature anisotropy. We study with one-dimensional particle-in-cell simulations the expansion of a dense plasma into a dilute one, yielding a density ramp similar to that in laser-plasma experiments and a thermal-anisotropy-driven instability. Non-propagating Weibel-type wave modes grow in the simulation with no initial magnetic field. Their magnetic field diffuses across the shock and expands upstream. Circularly polarized propagating Whistler waves grow in a second simulation, in which a magnetic field is aligned with the ion expansion direction. Both wave modes are driven by non-resonant instabilities, they have similar exponential growth rates, and they can leave the density ramp and expand into the dilute plasma. Their large magnetic amplitude should make them detectable in experimental settings.

Coherent structures of beam-driven whistler mode in the presence of magnetic islands in the magnetopause

The Magnetospheric Multiscale Mission (MMS) has perceived whistler wave generation, coherent structures, and related turbulence close to the magnetopause reconnection zones. The current research examines coherent structure of whistler wave driven by an intense electron beam at the magnetopause’s magnetic reconnection sites as well as by the dynamic growth of magnetic islands. A nonlinear model of high-frequency whistler wave and low-frequency magnetosonic wave has been developed by using the two-fluid approximation. Nonlinear dynamics of 3D whistler wave and magnetosonic wave have been solved by the pseudo spectral method along with the predictor-corrector method and finite difference method. The simulation’s outcomes demonstrate the temporal and spatial development of the whistler localized structures and current sheets as a witness to the turbulence’s existence. Moreover, the turbulent power spectra have been investigated. The formation of the thermal tail of energetic electrons has been studied using the power-law scaling of turbulence development. We determined the scale sizes of current sheets and localized structures using a semi-analytic model and showed that these scale sizes rely on the power of whistler wave. We predict that the acceleration of the energetic electrons and heating in the Magnetopause may be caused by whistler wave.

Localization of beam generated whistler wave and turbulence generation in reconnection region of magnetopause

Whistler waves have been studied for many years in relation to turbulence and particle heating, and observations show that they are crucial to magnetic reconnection. Recent research has revealed a close relationship between magnetic reconnection and turbulence. The current work investigates the whistler turbulence caused by the energetic electron beam in the magnetic reconnection sites of magnetopause and also due to dynamic evolution of magnetic islands. For this, we develop a model based upon the two-fluid approximation to study whistler dynamics, propagating in the medium with the pre-existing chain of magnetic islands and under the influence of background density perturbation originating from ponderomotive nonlinearity of wave. Dynamics of nonlinear whistler have been solved with pseudo-spectral approach and a finite difference method with a modified predictor–corrector method and a Runge Kutta method for the semianalytical model. In the current research, we study how the nonlinear whistler wave contributes to the significant space phenomenon, i.e., turbulence, localization, and magnetic reconnection. We have also investigated the formation of a current sheet in a magnetopause region of the order of few-electron inertial length. We analyzed the power spectrum at the magnetopause when the system reached a quasi-steady condition. Our new approach to study whistler turbulence by an energetic electron beam at the magnetic reconnection sites has extensive applications to space plasmas, shedding a new light on the study of magnetic reconnection in nature.

Velocity-space Signatures of Resonant Energy Transfer between Whistler Waves and Electrons in the Earth’s Magnetosheath

Wave–particle interactions play a crucial role in transferring energy between electromagnetic fields and charged particles in space and astrophysical plasmas. Despite the prevalence of different electromagnetic waves in space, there is still a lack of understanding of fundamental aspects of wave–particle interactions, particularly in terms of energy flow and velocity-space characteristics. In this study, we combine a novel quasilinear model with observations from the Magnetospheric Multiscale mission to reveal the signatures of resonant interactions between electrons and whistler waves in magnetic holes, which are coherent structures often found in the Earth’s magnetosheath. We investigate the energy transfer rates and velocity-space characteristics associated with Landau and cyclotron resonances between electrons and slightly oblique propagating whistler waves. In the case of our observed magnetic hole, the loss of electron kinetic energy primarily contributes to the growth of whistler waves through the n = −1 cyclotron resonance, where n is the order of the resonance expansion in linear Vlasov–Maxwell theory. The excitation of whistler waves leads to a reduction of the temperature anisotropy and parallel heating of the electrons. Our study offers a new and self-consistent understanding of resonant energy transfer in turbulent plasmas.

2D kinetic simulations of whistler wave generation by nonlinear scattering of lower-hybrid waves in turbulent plasmas

Turbulent plasmas in space, laboratory experiments, and astrophysical domains can often be described by weak turbulence theory, which can be characterized as a broad spectrum of incoherent interacting waves. We investigate a fundamental nonlinear kinetic mechanism of weak turbulence that can explain the generation of whistler waves in homogeneous plasmas by nonlinear scattering of short wavelength electrostatic lower-hybrid (LH) waves. Two particle-in-cell (PIC) simulations with different mass ratios in two dimensions (2D) were performed using a ring ion velocity distribution to excite broadband LH waves. The wave modes evolve in frequency, and wavenumber space such that the LH waves are converted to whistler waves. The simulations show the formation of quasi-modes, which are low-frequency density perturbations driven by the ponderomotive force due to the beating of LH and whistler waves. These low-frequency oscillations are damped due to resonant phase matching with thermal plasma particles. By comparing the phase and thermal speeds, we confirm the nonlinear scattering mechanism and its role in the 2D evolution of the ring ion instability. Although the nonlinear scattering is theoretically slower in 2D than in 3D due to the absence of the vector nonlinearity, these simulations show that quasi-modes are an important diagnostic for nonlinear landau damping in PIC simulations that has not been utilized in the past. The nonlinear scattering mechanism described here plays an important role in the generation of whistler waves in active experiments, which will be experimentally studied in the upcoming Space Measurement of a Rocket Release Turbulence experiment.

Whistler modes guided by a nonuniform cylindrical duct in a magnetoplasma below the lower hybrid frequency

Guided propagation of whistler waves and their excitation by a loop antenna in the presence of a field-aligned cylindrical duct with enhanced density in a magnetoplasma are studied below the lower hybrid resonance frequency. The emphasis is placed on the case where the duct is transversely nonuniform such that the plasma density in it decreases monotonically from a constant value in the near-axis inner region to the lower background value in the outer medium. Conditions are determined under which the dispersion characteristics and field structures of the modes guided by such a duct allow an approximate description within the framework of perturbation theory. The approximate results are shown to be in good agreement with the numerical results obtained using a full-wave approach. It is also found that the radiation resistance of a loop antenna located in the smooth-walled enhanced density duct can be notably greater than that of the same antenna immersed in the background magnetoplasma due to the excitation of the modes guided by the duct. The reported results extend previous analyses performed for sharp-walled uniform ducts to the case of a more realistic plasma density profile in the duct and can be useful in understanding the basic features of whistler wave guidance and excitation as well as in planning the related experiments.

Whistler waves generated inside magnetic dips in the young solar wind: Observations of the search-coil magnetometer on board Parker Solar Probe

Context. Whistler waves are electromagnetic waves produced by electron-driven instabilities, which in turn can reshape the electron distributions via wave–particle interactions. In the solar wind they are one of the main candidates for explaining the scattering of the strahl electron population into the halo at increasing radial distances from the Sun and for subsequently regulating the solar wind heat flux. However, it is unclear what type of instability dominates to drive whistler waves in the solar wind. Aims. Our goal is to study whistler wave parameters in the young solar wind sampled by Parker Solar Probe (PSP). The wave normal angle (WNA) in particular is a key parameter to discriminate between the generation mechanisms of these waves. Methods. We analyzed the cross-spectral matrices of magnetic field fluctuations measured by the search-coil magnetometer (SCM) and processed by the Digital Fields Board (DFB) from the FIELDS suite during PSP’s first perihelion. Results. Among the 2701 wave packets detected in the cross-spectra, namely individual bins in time and frequency, most were quasi-parallel to the background magnetic field; however, a significant part (3%) of the observed waves had oblique (> 45°) WNA. The validation analysis conducted with the time series waveforms reveal that this percentage is a lower limit. Moreover, we find that about 64% of the whistler waves detected in the spectra are associated with at least one magnetic dip. Conclusions. We conclude that magnetic dips provide favorable conditions for the generation of whistler waves. We hypothesize that the whistlers detected in magnetic dips are locally generated by the thermal anisotropy as quasi-parallel and can gain obliqueness during their propagation. We finally discuss the implications of our results for the scattering of the strahl in the solar wind.

Quasi-parallel Whistler Waves and Their Interaction with Resonant Electrons during High-velocity Bulk Flows in the Earth’s Magnetotail

In collisionless space, plasma waves are important channels of energy conversion, affecting the local particle velocity distribution functions through wave–particle interactions. In this paper we present a comparative statistical analysis of the characteristics of quasi-parallel narrowband whistler waves and the properties of resonant electrons interacting with these waves during the intervals of earthward and tailward high-velocity bulk flows produced by the near-Earth X-line and observed by Magnetospheric Multiscale Mission spacecraft. We found that on both sides of the X-line, the suprathermal electrons (≥1 keV) having large pitch angles make the major contribution to the maximal growth rate (γ) of these waves. The whistler waves were observed almost simultaneously with strong enhancements of perpendicular magnetic gradients localized at electron scales near dipolarization fronts associated with the earthward bulk flows, and near flux ropes/magnetic islands embedded into the tailward bulk flows. Betatron energization of electrons due to the appearance of such gradients increases the perpendicular anisotropy of electron distribution, which could be responsible for the whistler wave generation. We found that in the course of electron interactions with the whistler waves the lower-energy resonant electrons can transfer a part of their kinetic energy to the higher-energy electrons, especially in the Central Plasma Sheet. This results in formation/enhancement of energy-dependent perpendicular anisotropy and power-law tails in the high-energy range of electron velocity distribution. We conclude that despite the differences in the magnetic structure of the earthward and tailward bulk flows, the mechanisms of the quasi-parallel whistler wave generation and the properties of resonant electrons are quite similar.

Duct Effect of Magnetic Structures on Whistler Waves

AbstractPrevious studies have demonstrated that the propagation of whistler waves can be ducted by plasma density structures, within which the trapped waves can interact with electrons for a rather long time. In this paper, we develop a theoretical model to investigate the effects of magnetic structures on the propagation of whistler waves. Our results show that whistler waves can be ducted both in magnetic dips and peaks under specific conditions, providing another trapping mechanism for whistler waves. These theoretical predictions have been verified through two typical wave events observed by the Van Allen Probe mission based on the magnetic dip ahead of and magnetic peak inside a dipolarizing flux bundle. The theoretical analysis and satellite observations reveal the important role of magnetic structures in the propagation of whistler waves.

First Results of the Wave Measurements by the WHU VLF Wave Detection System at the Chinese Great Wall Station in Antarctica

AbstractA Very Low Frequency (VLF) wave detection system has been designed at Wuhan University (WHU) and recently deployed by the Polar Research Institute of China at the Chinese Great Wall station (GWS, 62.22°S, 58.96°W) in Antarctica. With a dynamic range of ∼110 dB and timing accuracy of ∼100 ns, this detection system can provide observational data with a resolution that can facilitate space physics and space weather studies. This paper presents the first results of the wave measurements by the WHU VLF wave detection system at GWS to verify the performance of the system. With the routine operation for 3 months, the system can acquire the dynamic changes of the wave amplitudes and phases of various ground‐based VLF transmitter signals emitted in both North America and Europe. A preliminary analysis indicates that the properties of the VLF transmitter signals observed at GWS during the X‐class solar flare events are consistent with previous studies. As the HWU‐GWS path crosses the South Atlantic Anomaly region, the observations also imply a good connection in space and time between the VLF wave disturbances and the lower ionosphere variation potentially caused by magnetospheric electron precipitation during the geomagnetic storm period. It is therefore well expected that the acquisition of VLF wave data at GWS, in combination with datasets from other instruments, can be beneficial for space weather studies related to the radiation belt dynamics, terrestrial lightning discharge, whistler wave propagation, and the lower ionosphere disturbance, etc., in the polar region.

Kinetic Generation of Whistler Waves in the Turbulent Magnetosheath.

The Earth's magnetosheath (MSH) is governed by numerous physical processes which shape the particle velocity distributions and contribute to the heating of the plasma. Among them are whistler waves which can interact with electrons. We investigate whistler waves detected in the quasi‐parallel MSH by NASA's Magnetospheric Multiscale mission. We find that the whistler waves occur even in regions that are predicted stable to wave growth by electron temperature anisotropy. Whistlers are observed in ion‐scale magnetic minima and are associated with electrons having butterfly‐shaped pitch‐angle distributions. We investigate in detail one example and, with the support of modeling by the linear numerical dispersion solver Waves in Homogeneous, Anisotropic, Multicomponent Plasmas, we demonstrate that the butterfly distribution is unstable to the observed whistler waves. We conclude that the observed waves are generated locally. The result emphasizes the importance of considering complete 3D particle distribution functions, and not only the temperature anisotropy, when studying plasma wave instabilities.

Scaling of Electron Heating by Magnetization During Reconnection and Applications to Dipolarization Fronts and Super‐Hot Solar Flares

AbstractElectron ring velocity space distributions have previously been seen in numerical simulations of magnetic reconnection exhausts and have been suggested to be caused by the magnetization of the electron outflow jet by the compressed reconnected magnetic fields (Shuster et al., 2014, https://doi.org/10.1002/2014GL060608). We present a theory of the dependence of the major and minor radii of the ring distributions solely in terms of upstream (lobe) plasma conditions, thereby allowing a prediction of the associated temperature and temperature anisotropy of the rings in terms of upstream parameters. We test the validity of the prediction using 2.5‐dimensional particle‐in‐cell (PIC) simulations with varying upstream plasma density and temperature, finding excellent agreement between the predicted and simulated values. We confirm the Shuster et al. suggestion for the cause of the ring distributions, and also find that the ring distributions are located in a region marked by a plateau, or shoulder, in the reconnected magnetic field profile. The predictions of the temperature are consistent with observed electron temperatures in dipolarization fronts, and may provide an explanation for the generation of plasma with temperatures in the 10s of MK in super‐hot solar flares. A possible extension of the model to dayside reconnection is discussed. Since ring distributions are known to excite whistler waves, the present results should be useful for quantifying the generation of whistler waves in reconnection exhausts.

First Results From the SCM Search‐Coil Magnetometer on Parker Solar Probe

AbstractParker Solar Probe is the first mission to probe in situ the innermost heliosphere, revealing an exceptionally dynamic and structured outer solar corona. Its payload includes a search‐coil magnetometer (SCM) that measures up to three components of the fluctuating magnetic field between 3 Hz and 1 MHz. After more than 3 years of operation, the SCM has revealed a multitude of different wave phenomena in the solar wind. Here we present an overview of some of the discoveries made so far. These include oblique and sunward propagating whistler waves that are important for their interaction with energetic electrons, the first observation of the magnetic signature associated with escaping electrons during dust impacts, the first observation of the magnetic field component for slow extraordinary wave modes during type III radio burst events, and more. This study focuses on the major observations to date, including a description of the instrument and lessons learned.

Ray-tracing simulations of whistler-mode wave propagation in different rescaled dipole magnetic fields

Kinetic simulation is a powerful tool to study the excitation and propagation of whistler-mode waves in the Earth’s inner magnetosphere. This method typically applies a scaled-down dipole magnetic field to save computational time. However, it remains unknown whether whistler wave propagation in the scaled-down dipole field is consistent with that in the realistic dipole field. In this work, we develop a ray-tracing code with a scalable dipole magnetic field to address this concern. The simulation results show that parallel whistler waves at different frequencies gradually become oblique after leaving the equator and propagate in different raypaths in a dipole magnetic field. During their propagation, the higher frequency waves tend to have larger wave normal angles at the same latitude. Compared with the wave propagation in a realistic dipole field, the wave raypath and wave normal remain the same, whereas the wave amplification or attenuation is smaller because of the shorter propagation time in a scaled-down dipole field. Our study provides significant guidance for kinetic simulations of whistler-mode waves.

Short Periodic VLF Emissions Observed Simultaneously by Van Allen Probes and on the Ground

AbstractWe present simultaneous observations of very low‐frequency emissions with periodic bursts by Van Allen Probe near geomagnetic equator and Kannuslehto and Lovozero ground‐based sites. The repetition period and ground–spacecraft delay are consistent with guided whistler wave propagation between conjugate ionospheres. In contrast to lightning whistlers, the group velocity dispersion is not accumulated from one burst to another, thus implying a nonlinear mechanism of its compensation. Two regimes are observed. In one regime, Poynting flux direction alternates in the magnetosphere, and the burst period (2 s) is half of that detected on the ground (4 s), corresponding to single‐wave packet bouncing along the field line. This regime is switched to the other one, with burst period unchanged in the magnetosphere but halved on the ground. In this second regime, no alternating Poynting flux direction is observed. The second regime corresponds to two symmetrically propagating wave packets synchronously meeting at the equator.

Generation of High-frequency Whistler Waves in the Earth’s Quasi-perpendicular Bow Shock

Abstract We use observations from the Magnetospheric Multiscale spacecraft to identify a free energy source for high-frequency whistler waves in the Earth’s quasi-perpendicular bow shock. In the considered measurements, whistlers propagate both parallel and antiparallel to the background magnetic field B 0 with frequencies around 100 Hz (0.15 f ce, where f ce is the electron cyclotron frequency) and amplitudes between 0.1 and 1 nT. Their growth can be attributed to localized pitch angle anisotropy in the electron velocity distribution function that cannot be precisely described by macroscopic parameters like heat flux or temperature anisotropy. However, the presence of heat flux along − B 0 does create preferential conditions for the high-frequency whistler waves that propagate in this direction. These waves are directed partially toward the shock, meaning they can scatter electrons that are streaming from the shock. This prolongs the time the electrons spend in the shock transition region and thereby promotes electron energization.

Pulse duration constraint of whistler waves in magnetized dense plasma.

Interactions between large-amplitude laser light and strongly magnetized dense plasma have been investigated by one- and two-dimensional electromagnetic particle-in-cell simulations. Since whistler waves have no critical density, they can propagate through plasmas beyond the critical density in principle. However, we have found the propagation of whistler waves is restricted significantly by the stimulated Brillouin scattering. It is confirmed that the period during which the whistler wave can propagate in overcritical plasmas is proportional to the growth time of the ion-acoustic wave via the Brillouin instability. The allowable pulse duration of the whistler wave has a power-law dependence on the amplitude of the whistler wave and the external magnetic field.