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. Our simulations find that the dispersive whistler modes evolve entirely differently in the two regimes. While the dispersive whistler wave effects are stronger in the large scale regime, they do not influence the spectral cascades which are describable by a Kolmogorov-like $k^{-7/3}$ spectrum. By contrast, the small scale turbulent fluctuations exhibit a Navier-Stokes like evolution where characteristic turbulent eddies exhibit a typical $k^{-5/3}$ hydrodynamic turbulent spectrum. By virtue of equipartition between the wave velocity and magnetic fields, we quantify the role of whistler waves in the solar wind plasma fluctuations.
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…
The observed sub-proton scale turbulence spectrum in the solar wind raises the question of how that turbulence originates. Observations of keV energetic electrons during solar quite-time suggest them as possible source of free energy to drive the turbulence. Using particle-in-cell simulations, we explore how free energy in energetic electrons, released by an electron two-stream instability drives Weibel-like electromagnetic waves that excite wave-wave interactions. Consequently, both kinetic Alfvénic and whistler waves are excited that evolve through inverse and forward magnetic energy cascade…
Whistler waves are intermittently present in the solar wind, while their origin and effects are not entirely understood. We present a statistical analysis of magnetic field fluctuations in the whistler frequency range (above 16 Hz) based on about 801,500 magnetic field spectra measured over three years aboard ARTEMIS spacecraft in the pristine solar wind. About 13,700 spectra (30 hours in total) with intense magnetic field fluctuations satisfy the interpretation in terms of quasi-parallel whistler waves. We provide estimates of the whistler wave occurrence probability, amplitudes, frequencies …
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…
The origins and properties of large amplitude whistler wave packets in the solar wind are still unclear. In this Letter we utilise single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wave packets over multiple intervals. This allows direct comparison of experimental measurements with theoretical dispersion relations to identify the observed waves as whistler waves. The whistlers are right-hand circularly polarised, travel anti-sunward and are aligned with the background magnetic field.…
Electron velocity distributions in the solar wind are known to have field-aligned skewness, which has been characterized by the presence of secondary populations such as the halo and strahl. Skewness may provide energy for the excitation of electromagnetic instabilities, such as the whistler heat-flux instability (WHFI), that may play an important role in regulating the electron heat-flux in the solar wind. Here we use kinetic theory to analyze the stability of the WHFI in a solar-wind-like plasma where solar wind core, halo and strahl electrons are described as a superposition of two distribu…
We use the one-dimensional TRISTAN-MP particle-in-cell code to model the nonlinear evolution of the whistler heat flux instability that was proposed by Gary et al. (1999, 2000) to regulate the electron heat flux in the solar wind and astrophysical plasmas. The simulations are initialized with electron velocity distribution functions typical for the solar wind. We perform a set of simulations at various initial values of the electron heat flux and $β_{e}$. The simulations show that parallel whistler waves produced by the whistler heat flux instability saturate at amplitudes consistent with the …
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 present an analysis of simultaneous particle and field measurements from the ARTEMIS spacecraft which demonstrate that quasi-parallel whistler waves in the solar wind can be generated locally by a bulk flow of halo electrons (whistler heat flux instability). ARTEMIS observes quasi-parallel whistler waves in the frequency range $\sim 0.05 - 0.2 f_{ce}$ simultaneously with electron velocity distribution functions that are a combination of counter-streaming core and halo populations. A linear stability analysis shows that the plasma is stable when there are no whistler waves, and unstable in t…
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…
In collision-poor plasmas from space, e.g., solar wind or stellar outflows, the heat-flux carried by the strahl or beaming electrons is expected to be regulated by the self-generated instabilities. Recently, simultaneous field and particle observations have indeed revealed enhanced whistler-like fluctuations in the presence of counter-beaming populations of electrons, connecting these fluctuations to the whistler heat-flux instability (WHFI). This instability is predicted only for limited conditions of electron beam-plasmas, and was not captured in numerical simulations yet. In this letter we …
We present surprising observations by the NASA Van Allen Probes spacecraft of whistler waves with substantial electric field power at harmonics of the whistler wave fundamental frequency. The wave power at harmonics is due to nonlinearly steepened whistler electrostatic field that becomes possible in the two-temperature electron plasma due to whistler wave coupling to the electron-acoustic mode. The simulation and analytical estimates show that the steepening takes a few tens of milliseconds. The hydrodynamic energy cascade to higher frequencies facilitates efficient energy transfer from cyclo…
The nature of the magnetic field fluctuations in the solar wind between the ion and electron scales is still under debate. Using the Cluster/STAFF instrument, we make a survey of the power spectral density and of the polarization of these fluctuations at frequencies $f\in[1,400]$ Hz, during five years (2001-2005), when Cluster was in the free solar wind. In $\sim 10\%$ of the selected data, we observe narrow-band, right-handed, circularly polarized fluctuations, with wave vectors quasi-parallel to the mean magnetic field, superimposed on the spectrum of the permanent background turbulence. We …
We present the analysis of narrowband whistler wave signatures observed in the inner heliosphere (0.3-1 au). These signatures are bumps in the spectral density in the 10-200 Hz frequency range of the AC magnetic field as measured by the search coil magnetometer on board the Helios1 spacecraft. We show that the majority of whistler signatures are observed in the slow solar wind (<500 km/s) and their occurrence increases with the radial distance (R), from ~3% at 0.3 au to ~10% at 0.9 au. In the fast solar wind (>600 km/s), whistler activity is significantly lower; whistler signatures start to ap…
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…
Context. Solar outflows are a considerable source of free energy which accumulates in multiple forms like beaming (or drifting) components and/or temperature anisotropies. However, kinetic anisotropies of plasma particles do not grow indefinitely and particle-particle collisions are not efficient enough to explain the observed limits of these anisotropies. Instead, the self-generated wave instabilities can efficiently act to constrain kinetic anisotropies, but the existing approaches are simplified and do not provide satisfactory explanations. Thus, small deviations from isotropy shown by the …
We present a statistical study of the characteristics of very large amplitude whistler waves inside the terrestrial magnetosphere using waveform capture data from the Wind spacecraft as an addition of the study by Kellogg et al., [2010b]. We observed 244(65) whistler waves using electric(magnetic) field data from the Wind spacecraft finding ~40%(~62%) of the waves have peak-to-peak amplitudes of >/- 50 mV/m(>/- 0.5 nT). We present an example waveform capture of the largest magnetic field amplitude (>/- 8 nT peak-to-peak) whistler wave ever reported in the radiation belts. The estimated Poyntin…
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…
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…
A nonlinear two dimensional fluid model of whistler turbulence is developed that nonlinearly couples wave magnetic field with electron density perturbations. This coupling leads essentially to finite compressibility effects in whistler turbulence model. Interestingly it is found from our simulations that despite strong compressibility effects, the density fluctuations couple only weakly to the wave magnetic field fluctuations. In a characteristic regime where large scale whistlers are predominant, the weakly coupled density fluctuations do not modify inertial range energy cascade processes. Co…
The nature of subproton scale fluctuations in the solar wind is an open question, partly because two similar types of electromagnetic turbulence can occur: kinetic Alfven turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfven turbulence, has negligible power in density fluctuations. In this Letter, we present new observational data, as well as analytical and numerical results, to investigate this difference. The results show, for the first time, that the fluctuations well below the proton scale are p…
Large amplitude whistler waves at frequencies of 0.2 to 0.4 times electron cyclotron frequency are frequently observed in the solar wind. The waves are obliquely propagating close to the resonance cone, with significant electric fields parallel to the background magnetic field, enabling strong interactions with electrons. Propagation angles are distinctly different from whistlers usually observed in the solar wind, and amplitudes are significantly larger. Waves occur most often in association with stream interaction regions (SIRs), and are often close-packed. 68 percent of the 54 SIRs had narr…
We present multi-satellite observations indicating a strong correlation between large amplitude radiation belt whistler-mode waves and relativistic electron precipitation. On separate occasions during the Wind petal orbits and STEREO phasing orbits, Wind and STEREO recorded intense whistler-mode waves in the outer nightside equatorial radiation belt with peak-to-peak amplitudes exceeding 300 mV/m. During these intervals of intense wave activity, SAMPEX recorded relativistic electron microbursts in near magnetic conjunction with Wind and STEREO. The microburst precipitation exhibits a bursty te…
We perform the first statistical study of the effects of the interaction of suprathermal electrons with narrow-band whistler mode waves in the solar wind. We show that this interaction does occur and that it is associated with enhanced widths of the so called strahl component. The latter is directed along the inter- planetary magnetic field away from the Sun. We do the study by comparing the strahl pitch angle widths in the solar wind at 1AU in the absence of large scale discontinuities and transient structures, such as interplanetary shocks, interplanetary coronal mass ejections, stream inter…
Solar wind electrons play an important role in the energy balance of the solar wind acceleration by carrying energy into interplanetary space in the form of electron heat flux. The heat flux is stored in the complex electron velocity distribution functions (VDFs) shaped by expansion, Coulomb collisions, and field-particle interactions. We investigate how the suprathermal electron deficit in the anti-strahl direction, which was recently discovered in the near-Sun solar wind, drives a kinetic instability and creates whistler waves with wave vectors that are quasi-parallel to the direction of the…
In the absence of efficient collisions, deviations from thermal equilibrium of plasma particle distributions are controlled by the self-generated instabilities. The whistler instability is a notorious example, usually responsible for the regulation of electron temperature anisotropy $A = T_{\perp}/T_\parallel>$ (with $\perp, \parallel$ respective to the magnetic field direction) observed in space plasmas, e.g., solar wind and planetary magnetospheres. Suprathermal electrons present in these environments change the plasma dispersion and stability properties, with expected consequences on the ki…
There is wide observational evidence that electron velocity distribution functions (eVDF) observed in the solar wind generally present enhanced tails and field-aligned skewness. These properties may induce the excitation of electromagnetic perturbations through the whistler heat-flux instability (WHFI), that may contribute to a non-collisional regulation of the electron heat-flux values observed in the solar wind via wave-particle interactions. Recently, a new way to model the solar wind eVDF has been proposed: the core-strahlo model. This representation consist in a bi-Maxwellian core plus a …
Motivated by the upcoming Solar Orbiter and Solar Probe Plus missions, qualitative and quantitative predictions are made for the effects of the violation of the Taylor hypothesis on the magnetic energy frequency spectrum measured in the near-Sun environment. The synthetic spacecraft data method is used to predict observational signatures of the violation for critically balanced Alfvénic turbulence or parallel fast/whistler turbulence. The violation of the Taylor hypothesis can occur in the slow flow regime, leading to a shift of the entire spectrum to higher frequencies, or in the dispersive r…
We studied the properties and occurrence of narrow band whistler waves and their interaction with strahl electrons observed between 0.17 and 0.26 au during the first encounter of Parker Solar Probe. We observe that occurrence of whistler waves is low, nearly 1.5% and less than 0.5% in the analyzed peak and average BPF data respectively. Whistlers occur highly intermittently and 80% of the whistlers appear continuously for less than 3 s. Occurrence rate of whistler waves was found to be anti-correlated with the solar wind bulk velocity. The study of the duration of the whistler intervals reveal…
We develop a kinetic theory for {the electron strahl, a beam of energetic electrons which propagate} from the sun along the Parker-spiral-shaped magnetic field lines. By assuming a Maxwellian electron distribution function in the near-sun region where the plasma is collisional, we derive the strahl distribution function at larger heliospheric distances. We consider the two most important mechanisms that broaden the strahl: Coulomb collisions and interactions with oblique ambient whistler turbulence (anomalous diffusion). We propose that the energy regimes where these mechanisms are important a…
The electrons are an essential particle species in the solar wind. They often exhibit non-equilibrium features in their velocity distribution function. These include temperature anisotropies, tails (kurtosis), and reflectional asymmetries (skewness), which contribute a significant heat flux to the solar wind. If these non-equilibrium features are sufficiently strong, they drive kinetic micro-instabilities. We develop a semi-graphical framework based on the equations of quasi-linear theory to describe electron-driven instabilities in the solar wind. We apply our framework to resonant instabilit…
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…
A long-lasting debate in space plasma physics concerns the nature of subproton-scale fluctuations in solar wind (SW) turbulence. Over the past decade, a series of theoretical and observational studies were presented in favor of either kinetic Alfvén wave (KAW) or whistler turbulence. Here, we investigate numerically the nature of the subproton-scale turbulent cascade for typical SW parameters by means of unprecedented high-resolution simulations of forced hybrid-kinetic turbulence in two real-space and three velocity-space dimensions. Our analysis suggests that small-scale turbulence in this m…
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…
Observations by the Parker Solar Probe mission of the solar wind at about 35.7 solar radii reveal the existence of whistler wave packets with frequencies below 0.1 f/fce (20-80 Hz in the spacecraft frame). These waves often coincide with local minima of the magnetic field magnitude or with sudden deflections of the magnetic field that are called switchbacks. Their sunward propagation leads to a significant Doppler frequency downshift from 200-300 Hz to 20-80 Hz (from 0.2 f/fce to 0.5 f/fce). The polarization of these waves varies from quasi-parallel to significantly oblique with wave normal an…
We analyze the micro-kinetic stability of the electron strahl in the solar wind depending on heliocentric distance. The oblique fast-magnetosonic/whistler (FM/W) instability has emerged in the literature as a key candidate mechanism for the effective scattering of the electron strahl into the electron halo population. Using data from Parker Solar Probe (PSP) and Helios, we compare the measured strahl properties with the analytical thresholds for the oblique FM/W instability in the low- and high-$β_{\parallel c}$ regimes, where $β_{\parallel c}$ is the ratio of the core parallel thermal pressur…
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…
We investigate the attenuation of whistler waves generated by hypotetical venusian lightning occurring at the altitude of the cloud layer under different ionospheric conditions. We use the Stanford Full Wave Method (FWM) for stratified media of \cite{Lehtinen2008/JGR} to model wave propagation through the ionosphere of Venus. This method calculates the electromagnetic field created by an arbitrary source in a plane-stratified medium (i.e. uniform in the horizontal direction). We see that the existence of holes in electronic densities and the magnetic field configuration caused by solar wind pl…
Reconstruction of Polarization Properties of Whistler Waves From Two Magnetic and Two Electric Field Components: Application to Parker Solar Probe Measurements
Whistler-mode waves are generated within and can propagate upstream of collisionless shocks. They are known to play a role in electron thermodynamics/acceleration and, under certain conditions, are markedly observed as wave trains preceding the shock ramp. In this paper, we take advantage of Cassini's presence at ~10 AU to explore the importance of whistler-mode waves in a parameter regime typically characterized by higher Mach number (median of ~14) shocks, as well as a significantly different IMF structure, compared to near Earth. We identify electromagnetic precursors preceding a small subs…
Recent statistical studies of observational data unveil relevant correlations between whistler fluctuations and the anisotropic electron populations present in space plasmas, e.g., solar wind and planetary magnetospheres. Locally, whistlers can be excited by two sources of free energy associated with anisotropic electrons, i.e., temperature anisotropies and beaming populations carrying the heat flux. However, these two sources of free energy and the resulting instabilities are usually studied independently preventing a realistic interpretation of their interplay. This paper presents the result…
Electron temperature anisotropies and electron beams are nonthermal features of the observed nonequilibrium electron velocity distributions in the solar wind. In collision-poor plasmas these nonequilibrium distributions are expected to be regulated by kinetic instabilities through wave-particle interactions. This study considers electron instabilities driven by the interplay of core electron temperature anisotropies and the electron beam, and firstly gives a comprehensive analysis of instabilities in arbitrary directions to the background magnetic field. It clarifies the dominant parameter reg…
The first observed connection between kinetic instabilities driven by proton temperature anisotropy and estimated energy cascade rates in the turbulent solar wind is reported using measurements from the Wind spacecraft at 1 AU. We find enhanced cascade rates are concentrated along the boundaries of the ($β_{\parallel}$, $T_{\perp}/T_{\parallel}$)-plane, which includes regions theoretically unstable to the mirror and firehose instabilities. A strong correlation is observed between the estimated cascade rate and kinetic effects such as temperature anisotropy and plasma heating, resulting in prot…
The goal of our study is to detect and characterize the electromagnetic waves that can modify the electron distribution functions, with a special attention to whistler waves. We analyse in details the electric and magnetic field fluctuations observed by the Solar Orbiter spacecraft during its first orbit around the Sun between 0.5 and 1 AU. Using data of the Search Coil Magnetometer and electric antenna, both parts of the Radio and Plasma Waves (RPW) instrumental suite, we detect the electromagnetic waves with frequencies above 3 Hz and determine the statistical distribution of their amplitude…
We investigate the kinetic properties of a typical fast-mode shock inside an interplanetary coronal mass ejection (ICME) observed on 1998 August 6 at 1 AU, including particle distributions and wave analysis with the in situ measurements from Wind. Key results are obtained concerning the shock and the shock-ICME interaction at kinetic scales: (1) gyrating ions, which may provide energy dissipation at the shock in addition to wave-particle interactions, are observed around the shock ramp; (2) despite the enhanced proton temperature anisotropy of the shocked plasma, the low plasma beta inside the…
We use magnetic helicity to characterise solar wind fluctuations at proton-kinetic scales from Wind observations. For the first time, we separate the contributions to helicity from fluctuations propagating at angles quasi-parallel and oblique to the local mean magnetic field, $\mathbf{B}_0$. We find that the helicity of quasi-parallel fluctuations is consistent with Alfvén-ion cyclotron and fast magnetosonic-whistler modes driven by proton temperature anisotropy instabilities and the presence of a relative drift between $α$-particles and protons. We also find that the helicity of oblique fluct…
The nature of solar wind turbulence in the dissipation range at scales much smaller than the large MHD scales remains under debate. Here a two-dimensional model based on the hybrid code abbreviated as A.I.K.E.F. is presented, which treats massive ions as particles obeying the kinetic Vlasov equation and massless electrons as a neutralizing fluid. Up to a certain wavenumber in the MHD regime, the numerical system is initialized by assuming a superposition of isotropic Alfvén waves with amplitudes that follow the empirically confirmed spectral law of Kolmogorov. Then turbulence develops and ener…
The first estimation of the incompressible energy cascade rate at magnetohydrodynamic (MHD) scales is obtained in the plasma upstream of the Martian bow shock, using MAVEN observations and an exact relation derived for MHD turbulence. The energy cascade rate is computed for events with and without proton cyclotron wave (PCW) activity, for time intervals when MAVEN was in the solar wind with no magnetic connection to the bow shock. It is shown that the nonlinear cascade of energy at the MHD scales is slightly amplified when PCWs are present in the plasma. The analysis of the normalized cross he…
We present a measurement of the spectral index of density fluctuations between ion and electron scales in solar wind turbulence using the EFI instrument on the ARTEMIS spacecraft. The mean spectral index at 1 AU was found to be -2.75 +/- 0.06, steeper than predictions for pure whistler or kinetic Alfven wave turbulence, but consistent with previous magnetic field measurements. The steep spectra are also consistent with expectations of increased intermittency or damping of some of the turbulent energy over this range of scales. Neither the spectral index nor the flattening of the density spectr…
