A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic field topological structures consistent with the observations and our simulations in linear regime. In agreement with experiment, we find that the parallel group velocity of the wave is large compared to its perpendicular counterpart. Numerical simulations of collisional interactions demonstrate that the wave magnetic field either coalesces or repels depending upon the polarity of the associated current. In the nonlinear regime, our simulations demonstrate that the evolution of wave magnetic field is governed essentially by the nonlinear Hall force.
It is shown that the dispersion relation for whistler waves is identical for a high or low beta plasma. Furthermore in the high-beta solar wind plasma whistler waves meet the Landau resonance with electrons for velocities less than the thermal speed, and consequently the electric force is small compared to the mirror force. As whistlers propagate through the inhomogeneous solar wind, the perpendicular wave number increases through refraction, increasing the Landau damping rate. However, the whistlers can survive because the background kinetic Alfven wave turbulence creates a plateau by quasili…
Whistler waves are present in solar wind plasma. These waves possess characteristic turbulent fluctuations that are characterized typically by the frequency and length scales that are respectively bigger than ion gyro frequency and smaller than ion gyro radius. The electron inertial length is an intrinsic length scale in whistler wave turbulence that distinguishably divides the high frequency solar wind turbulent spectra into scales smaller and bigger than the electron inertial length. We present nonlinear three dimensional, time dependent, fluid simulations of whistler wave turbulence to inve…
We consider the weak turbulence of whistler waves in the in low-β inner magnetosphere of the Earth. Whistler waves with frequencies, originating in the ionosphere, propagate radially outward and can trigger nonlinear induced scattering by thermal electrons provided the wave energy density is large enough. Nonlinear scattering can substantially change the direction of the wave vector of whistler waves and hence the direction of energy flux with only a small change in the frequency. A portion of whistler waves return to the ionosphere with a smaller perpendicular wave vector resulting in diminis…
Nonlinear three dimensional, time dependent, fluid simulations of whistler wave turbulence are performed to investigate role of whistler waves in solar wind plasma turbulence in which characteristic turbulent fluctuations are characterized typically by the frequency and length scales that are respectively bigger than ion gyro frequency and smaller than ion gyro radius. The electron inertial length is an intrinsic length scale in whistler wave turbulence that distinguishably divides the high frequency solar wind turbulent spectra into scales smaller and bigger than the electron inertial length.…
Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. This mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth…
AIM: Large amplitude narrowband obliquely propagating whistler-mode waves at frequencies of ~0.2 fce (electron cyclotron frequency) are commonly observed at 1 AU, and are most consistent with the whistler heat flux fan instability. We want to determine whether similar whistler-mode waves occur inside 0.2 AU, and how their properties compare to those at 1 AU. METHODS: We utilize the waveform capture data from the Parker Solar Probe Fields instrument to develop a data base of narrowband whistler waves. The SWEAP instrument, in conjunction with the quasi-thermal noise measurement form Fields, pro…
Whistler Wave Observations by \textit{Parker Solar Probe} During Encounter $1$: Counter-Propagating Whistlers Collocated with Magnetic Field Inhomogeneities and their Application to Electric Field Measurement Calibration
We report observations of electromagnetic electron holes (EHs). We use multi-spacecraft analysis to quantify the magnetic field contributions of three mechanisms: the Lorentz transform, electron drift within the EH, and Cherenkov emission of whistler waves. The first two mechanisms account for the observed magnetic fields for slower EHs, while for EHs with speeds approaching half the electron Alfvén speed, whistler waves excited via the Cherenkov mechanism dominate the perpendicular magnetic field. The excited whistlers are kinetically damped and typically confined within the EHs.
A range of nonlinear wave structures, including Langmuir waves, unipolar electric fields and bipolar electric fields, are often observed in association with whistler-mode chorus waves in the near-Earth space. We demonstrate that the three seemingly different nonlinear wave structures originate from the same nonlinear electron trapping process by whistler-mode chorus waves. The ratio of the Landau resonant velocity to the electron thermal velocity controls the type of nonlinear wave structures that will be generated.
When a wave packet composed of short wavelength lower hybrid modes traveling in an homogeneous plasma region encounters an inhomogeneity, it can resonantly excite long wavelength whistler waves via a linear mechanism known as mode conversion. An enhancement of lower hybrid/whistler activity has been often observed by sounding rockets and satellites in the presence of density depletions (striations) in the upper ionosphere. We address here the process of linear mode conversion of lower hybrid to whistler waves, mediated by a density striation, using a scalar-field formalism (in the limit of col…
Chorus-like whistler-mode waves that are known to play a fundamental role in driving radiation-belt dynamics are excited on the Large Plasma Device by the injection of a helical electron beam into a cold plasma. The mode structure of the excited whistler wave is identified using a phase-correlation technique showing that the waves are excited through a combination of Landau resonance, cyclotron resonance and anomalous cyclotron resonance. The dominant wave mode excited through cyclotron resonance is quasi-parallel propagating, whereas wave modes excited through Landau resonance and anomalous c…
We present waveform observations of electromagnetic lower hybrid and whistler waves with f_ci << f < f_ce downstream of four supercritical interplanetary (IP) shocks using the Wind search coil magnetometer. The whistler waves were observed to have a weak positive correlation between \partialB and normalized heat flux magnitude and an inverse correlation with T_eh/T_ec. All were observed simultaneous with electron distributions satisfying the whistler heat flux instability threshold and most with T_{perp,h}/T_{para,h} > 1.01. Thus, the whistler mode waves appear to be driven by a heat flux inst…
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earths radiation belt. By tracking PIC particles, and comparing with test-particle simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi- linear theory routinely used in radiation belt studies. In particular we show that pitch angle diffusion is enhanced during the linear …
The interplay between electron-scale and ion-scale phenomena is of general interest for both laboratory and space plasma physics. In this paper we investigate the linear coupling between whistler waves and slow magnetosonic solitons through two-fluid numerical simulations. Whistler waves can be trapped in the presence of inhomogeneous external fields such as a density hump or hole where they can propagate for times much longer than their characteristic time scale, as shown by laboratory experiments and space measurements. Space measurements have detected whistler waves also in correspondence t…
Electron beam-generated whistler waves are widely found in the Earth's space plasma environment and are intricately involved in a number of phenomena. Here we study the linear growth of whistler eigenmodes excited by a finite gyrating electron beam, to facilitate the interpretation of relevant experiments on beam-generated whistler waves in the Large Plasma Device at UCLA. A linear instability analysis for an infinite gyrating beam is first performed. It is shown that whistler waves are excited through a combination of cyclotron resonance, Landau resonance and anomalous cyclotron resonance, co…
It is shown by multi-dimensional particle-in-cell simulations that intense secondary whistler waves with special vortex-like 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 whistle…
The discovery of large-amplitude narrowband whistler-mode waves at frequencies of tenths of the electron cyclotron frequency in large numbers both inside ~.3 AU and at ~1 AU provides an answer to longstanding questions about scattering and energization of solar wind electrons. The waves can have rapid nonlinear interactions with electrons over a broad energy range. Counter-propagation between electrons and waves is not required for resonance with the obliquely propagating waves in contrast to the case for parallel propagation. Using a full 3d particle tracing code, we have examined interaction…
Efficient energy transfer from electromagnetic waves to ions has been demanded to control laboratory plasmas for various applications and could be useful to understand the nature of space and astrophysical plasmas. However, there exists a severe unsolved problem that most of the wave energy is converted quickly to electrons, but not to ions. Here, an energy conversion process to ions in overdense plasmas associated with whistler waves is investigated by numerical simulations and theoretical model. Whistler waves propagating along a magnetic field in space and laboratories often form the standi…
We have studied the nonlinear dynamics of whistler waves in magnetized plasmas. Since plasmas and beam-plasma systems considered here are assumed to be weakly collisional, the point of reference for the analysis performed in the present paper is the system of hydrodynamic and field equations. We have applied the renormalization group method to obtain dynamical equations for the slowly varying amplitudes of whistler waves. Further, it has been shown that the amplitudes of eigenmodes satisfy an infinite system of coupled nonlinear Schrödinger equations. In this sense, the whistler eigenmodes for…
Observations of plasma waves by the Fields Suite and of electrons by the Solar Wind Electrons Alphas and Protons Investigation (SWEAP) on Parker Solar Probe provide strong evidence for pitch angle scattering of strahl-energy electrons by narrowband whistler-mode waves at radial distances less than ~0.3 AU. We present two example intervals of a few hours that include 8 waveform captures with whistler-mode waves and 26 representative electron distributions that are examined in detail. Two were narrow; 17 were clearly broadened, and 8 were very broad. The two with narrow strahl occurred when ther…
Whistler mode wave is a fundamental perturbation of electromagnetic fields and plasmas in various environments including planetary space, laboratory and astrophysics. The origin and evolution of the waves are a long-standing question due to the limited instrumental capability in resolving highly variable plasma and electromagnetic fields. Here, we analyse data with the high time resolution from the multi-scale magnetospheric spacecraft in the weak magnetic environment (i.e., foreshock) enabling a relatively long gyro-period of whistler mode wave. Moreover, we develop a novel approach to separa…
Relativistic electron beam transport through a high-density, magnetized plasma is studied numerically and theoretically. An electron beam injected into a cold plasma excites Weibel and two-stream instabilities that heat the beam and saturate. In the absence of an applied magnetic field, the heated beam continues to propagate. However, when a magnetic field of particular strength is applied along the direction of beam propagation, a secondary instability of off-angle whistler modes is excited. These modes then couple nonlinearly creating a large amplitude parallel propagating whistler that stop…
The role of solar wind expansion in generating whistler waves is investigated using the EB-iPic3D code, which models solar wind expansion self-consistently within a fully kinetic semi-implicit approach. The simulation is initialized with an electron velocity distribution function modeled after Parker Solar Probe observations during its first perihelion at 0.166 au, consisting of a dense core and an anti-sunward strahl. This distribution function is initially stable with respect to kinetic instabilities. Expansion drives the solar wind into successive regimes where whistler heat flux instabilit…
Thermalization and heating of plasma flows at shocks result in unstable charged-particle distributions which generate a wide range of electromagnetic waves. These waves, in turn, can further accelerate and scatter energetic particles. Thus, the properties of the waves and their implication for wave-particle interactions are critically important for modeling energetic particle dynamics in shock environments. Whistler-mode waves, excited by the electron heat flux or a temperature anisotropy, arise naturally near shocks and foreshock transients. As a result, they can often interact with supra-the…
The electron beam-plasma system is ubiquitous in the space plasma environment. Here, using a Darwin particle-in-cell method, the excitation of electrostatic and whistler instabilities by a gyrating electron beam is studied in support of recent laboratory experiments. It is assumed that the total plasma frequency $ω_{pe}$ is larger than the electron cyclotron frequency $Ω_e$. The fast-growing electrostatic beam-mode waves saturate in a few plasma oscillations by slowing down and relaxing the electron beam parallel to the background magnetic field. Upon their saturation, the finite amplitude ele…
Zebra-like patterns have been observed in the electron cyclotron emission spectra from strongly nonequilibrium plasma confined in a table-top mirror magnetic trap. The analysis of the experimental data suggests that the formation of zebra-like patterns could eventually be related to modulation of the whistler waves by the ion-acoustic waves excited during the abrupt ejection of electrons into a loss cone caused by the development of the whistler instability under the electron cyclotron resonance condition.
The recent simulations showed that the whistler heat flux instability, which presumably produces the most of quasi-parallel coherent whistler waves in the solar wind, is not efficient in regulating the electron heat conduction. In addition, recent spacecraft measurements indicated that some fraction of coherent whistler waves in the solar wind may propagate anti-parallel to the electron heat flux, being produced due to a perpendicular temperature anisotropy of suprathermal electrons. We present analysis of properties of parallel and anti-parallel whistler waves unstable at electron heat fluxes…
We investigate parametric processes in magnetised plasmas, driven by a large-amplitude pump light wave. Our focus is on laser-plasma interactions relevant to high-energy-density (HED) systems, such as the National Ignition Facility and the Sandia MagLIF concept. We derive dispersion relations for three-wave interactions in a multi-species plasma using Maxwell's equations, the warm-fluid momentum equation and the continuity equation. The application of an external B field causes right and left polarised light waves to propagate with differing phase velocities. This leads to Faraday rotation of …
Simultaneous observation of characteristic 3-dimensional (3D) signatures in the electron velocity distribution function (VDF) and intense quasi-monochromatic waves by the Magnetospheric Multiscale (MMS) spacecraft in the terrestrial magnetosheath are investigated. The intense wave packets are characterised and modeled analytically as quasi-parallel circularly-polarized whistler waves and applied to a test-particle simulation in view of gaining insight into the signature of the wave-particle resonances in velocity space. Both the Landau and the cyclotron resonances were evidenced in the test-pa…
The solar wind in the inner heliosphere has been observed by Parker Solar Probe (PSP) to exhibit abundant wave activities. The cyclotron wave modes in the sense of ions or electrons are among the most crucial wave components. However, their origin and evolution in the inner heliosphere close to the Sun remain mysteries. Specifically, it remains unknown whether it is an emitted signal from the solar atmosphere or an eigenmode growing locally in the heliosphere due to plasma instability. To address and resolve this controversy, we must investigate the key quantity of the energy change rate of th…
The problem of standing wave formation by superposing two counter-propagating whistler waves in an overdense plasma, studied recently by Sano et al. (Phys. Rev. E 100, 053205 (2019) and Phys. Rev. E 101, 013206 (2020)), has been revisited in the relativistic limit. A detailed theory along with simulation has been performed to study the standing wave formation in the interaction of two counter propagating relativistically intense whistler waves. The relativistic theory explains such interaction process more precisely and predicts correct field amplitudes of the standing wave for a much wider ra…
Effects of increasing whistler amplitude and propagation angle are studied through a variational test particle simulation and calculations of the resonance width. While high amplitude and oblique whistlers in typical 1 AU solar wind parameters are capable of forming an isotropic population without any additional processes, anomalous interactions with quasi-parallel whistlers may be essential to the process of halo formation near the Sun. High amplitude and quasi-parallel whistlers can scatter strahl electrons to low velocities (less than the wave phase velocity) to form a halo population, as l…
A non-relativistic Fokker-Planck equation for the electron distribution function is formulated incorporating the effects of stochastic acceleration by whistler-mode waves and Coulomb collisions. The stationary solution $f$ to the equation, subject to a zero-flux boundary condition, is found to be a generalized Lorentzian (or kappa) distribution, which satisfies $f\propto v^{-2(κ+1)}$ for large velocity $v$, where $κ$ is the spectral index. The parameter $κ$ depends strongly on the relative wave intensity $R$. Taking into account the critical energy required for resonance of electrons with whis…
Magnetic holes are plasma structures that trap a large number of particles in a magnetic field that is weaker than the field in its surroundings. The unprecedented high time-resolution observations by NASA's Magnetospheric Multi-Scale (MMS) mission enable us to study the particle dynamics in magnetic holes in the Earth's magnetosheath in great detail. We reveal the local generation mechanism of whistler waves by a combination of Landau-resonant and cyclotron-resonant wave-particle interactions of electrons in response to the large-scale evolution of a magnetic hole. As the magnetic hole conver…
We study the wave-particle interactions between lower band chorus whistlers and an anisotropic tenuous population of relativistic electrons. We present the first direct comparison of first-principle Particle-in-Cell (PIC) simulations with a quasi-linear diffusion code, in this context. In the PIC approach, the waves are self-consistently generated by a temperature anisotropy instability that quickly saturates and relaxes the system towards marginal stability. We show that the quasi-linear diffusion and PIC results have significant quantitative mismatch in regions of energy/pitch angle where th…
Using the Parker Solar Probe FIELDS bandpass filter data and SWEAP electron data from Encounters 1 through 9, we show statistical properties of narrowband whistlers from ~16 Rs to ~130 Rs, and compare wave occurrence to electron properties including beta, temperature anisotropy and heat flux. Whistlers are very rarely observed inside ~28 Rs (~0.13 au). Outside 28 Rs, they occur within a narrow range of parallel electron beta from ~1 to 10, and with a beta-heat flux occurrence consistent with the whistler heat flux fan instability. Because electron distributions inside ~30 Rs display signatures…
The scattering of electrons by heat-flux-driven whistler waves is explored with a particle-in-cell (PIC) simulation relevant to the transport of energetic electrons in flares. The simulation is initiated with a large heat flux that is produced using a kappa distribution of electrons with positive velocity and a cold return current beam. This system represents energetic electrons escaping from a reconnection-driven energy release site. This heat flux system drives large amplitude oblique whistler waves propagating both along and against the heat flux, as well as electron acoustic waves. While t…
Rf plasma production in Whistler waves range of frequency f/fci >1 is applied on the compact helical system (CHS) in a steady state operation with low toroidal magnetic field strength, where f and fci are rf and ion cyclotron frequencies, respectively. Maximum rf power and pulse width are is170kW and 10 msec at 9MHz, respectively. The line averaged plasma density <ne> as high as 2x10^18 m-3 (He plasma) is produced in the region of toroidal magnetic field strength on magnetic axis B=100G~1.5kG and the electron temperature measured at plasma periphery is about 20eV. The wave magnetic field stren…
The nonlinear propagation of electromagnetic (EM) electron-cyclotron waves (whistlers) along an external magnetic field, and their modulation by electrostatic small but finite amplitude ion-acoustic density perturbations are investigated in a uniform quantum plasma with intrinsic spin of electrons. The effects of the quantum force associated with the Bohm potential and the combined effects of the classical as well as the spin-induced ponderomotive forces (CPF and SPF respectively) are taken into consideration. The latter modify the local plasma density in a self-consistent manner. The coupled …
The role of large amplitude whistler waves in the energization and scattering of solar wind electrons has long been an interesting problem in Space Physics. To study this wave-particle interaction, we developed a vectorized test particle simulation with a variational calculation of the Lyapunov exponents. From using secular perturbation theory on this Hamiltonian system of wave and particle, we confirmed that the pitch angle diffusion of the particle was along the constant Hamiltonian surface and that it was driven by the interaction with the resonance surfaces. We also showed that oblique whi…
Recently, observations from laboratory experiments have revealed amplitude modulation of whistlers by low-frequency perturbations. We here present theoretical and simulation studies of amplitude modulated whistler solitary waves (whistlerons) and their interaction with background low-frequency density perturbations created by the whistler ponderomotive force. We derive a nonlinear a nonlinear Schrodinger equation which governs the evolution of whistlers in the presence of finite-amplitude density perturbations, and a set of equations for arbitrary large amplitude density perturbations in the p…
The kinetic damping mechanism of low frequency transverse perturbations propagating parallel to the magnetic field in a magnetized warm electron plasma is simulated by means of electromagnetic (EM) Vlasov simulations. The short-time-scale damping of the electron magnetohydrodynamic whistler perturbations and underlying physics of finite electron temperature effect on its real frequency are recovered rather deterministically, and analyzed. The damping arises from an interplay between a global (prevailing over entire phase-space) and the more familiar resonant-electron-specific kinetic damping m…
Thermal fusion plasmas initiated by standing whistler waves are investigated numerically by two- and one-dimensional Particle-in-Cell simulations. When a standing whistler wave collapses due to the wave breaking of ion plasma waves, the energy of the electromagnetic waves transfers directly to the ion kinetic energy. Here we find that the ion heating by the standing whistler wave is operational even in multi-dimensional simulations of multi-ion species targets, such as deuterium-tritium (DT) ices and solid ammonia borane (H$_6$BN). The energy conversion efficiency to ions becomes as high as 15…
