Solar Wind Electron Velocity Distribution Research Articles

Statistics of solar wind electron breakpoint energies using machine learning techniques

Solar wind electron velocity distributions at 1 au consist of a thermal “core” population and two suprathermal populations: “halo” and “strahl”. The core and halo are quasi-isotropic, whereas the strahl typically travels radially outwards along the parallel or anti-parallel direction with respect to the interplanetary magnetic field. Using Cluster-PEACE data, we analyse energy and pitch angle distributions and use machine learning techniques to provide robust classifications of these solar wind populations. Initially, we used unsupervised algorithms to classify halo and strahl differential energy flux distributions to allow us to calculate relative number densities, which are of the same order as previous results. Subsequently, we applied unsupervised algorithms to phase space density distributions over ten years to study the variation of halo and strahl breakpoint energies with solar wind parameters. In our statistical study, we find both halo and strahl suprathermal breakpoint energies display a significant increase with core temperature, with the halo exhibiting a more positive correlation than the strahl. We conclude low energy strahl electrons are scattering into the core at perpendicular pitch angles. This increases the number of Coulomb collisions and extends the perpendicular core population to higher energies, resulting in a larger difference between halo and strahl breakpoint energies at higher core temperatures. Statistically, the locations of both suprathermal breakpoint energies decrease with increasing solar wind speed. In the case of halo breakpoint energy, we observe two distinct profiles above and below 500 km s−1. We relate this to the difference in origin of fast and slow solar wind.

The Solar Wind Electron Halo as Produced by Electron Beams Originating in the Lower Corona: Beam Density Dependence

Abstract It has been suggested that the isotropic electron halo observed in the solar wind electron velocity distribution function may originate from nanoflare-accelerated electron beams below 1.1 R ⊙ from the solar surface through the nonlinear electron two-stream instability (ETSI). This model unifies the origins of kinetic waves, the electron halo, and the coronal weak Type III bursts, and establishes a link between the solar wind observables and the electron dynamics in nanoflares. One of the important predictions of this model is that the halo-core temperature ratio is anticorrelated with the density ratio, and the minimum ratio is ∼4, a relic of the ETSI heating and has been found to be consistent with solar wind observations. However, how the density and relative drift of the electron beams determine the thermal properties of solar wind electrons is unclear. In this paper, using a set of particle-in-cell simulations and kinetic theory, we show that a necessary condition for an isotropic halo to develop is that the ratio of beam density n b and the background n 0 be lower than a critical value N c ∼ 0.3. Heating of the core electrons becomes weaker with decreasing beam density, while the heating of halo electrons becomes stronger. As a result, the temperature ratio of the halo and core electrons increases with the decrease of the beam density, explaining the physical meaning of the predicted anticorrelated relation. We apply these results to the current observations and discuss the possible electron beam density produced in the nanoflares.

Clarifying the solar wind heat flux instabilities

In the solar wind electron velocity distributions reveal two counter-moving populations which may induce electromagnetic (EM) beaming instabilities known as heat flux instabilities. Depending on plasma parameters two distinct branches of whistler and firehose instabilities can be excited. These instabilities are invoked in many scenarios, but their interplay is still poorly understood. An exact numerical analysis is performed to resolve the linear Vlasov-Maxwell dispersion and characterize these two instabilities, e.g., growth rates, wave frequencies and thresholds, enabling to identify their dominance for conditions typically experienced in space plasmas. Of particular interest are the effects of suprathermal Kappa-distributed electrons which are ubiquitous in these environments. The dominance of whistler or firehose instability is highly conditioned by the beam-core relative velocity, core plasma beta and the abundance of suprathermal electrons. Derived in terms of relative drift velocity the instability thresholds show an inverse correlation with the core plasma beta for the whistler modes, and a direct correlation with the core plasma beta for the firehose instability. Suprathermal electrons reduce the effective (beaming) anisotropy inhibiting the firehose modes while the whistler instability is stimulated.

Observations of diffusion in the electron halo and strahl

Abstract. Observations of the three-dimensional solar wind electron velocity distribution functions (VDF) using ϕ–θ plots often show a tongue of electrons that begins at the strahl and stretches toward a new population of electrons, termed the proto-halo, that exists near the projection of the magnetic field opposite that associated with the strahl. The energy range in which the tongue and proto-halo are observed forms a “diffusion zone”. The tongue first appears in energy generally near the lower-energy range of the strahl and in the absence of any clear core/halo signature. While the ϕ–θ plots give the appearance that the tongue and proto-halo are derived from the strahl, a close examination of their density suggests that their source is probably the upper-energy core/halo electrons which have been scattered by one or more processes into these populations.

SOLAR WIND MAGNETIC FLUCTUATIONS AND ELECTRON NON-THERMAL TEMPERATURE ANISOTROPY: SURVEY OF WIND-SWE-VEIS OBSERVATIONS

ABSTRACT The solar wind electron velocity distribution function (eVDF) exhibits a variety of non-thermal features that deviate from thermal equilibrium. These deviations from equilibrium provide a local source for electromagnetic fluctuation emissions, including the commonly observed electron whistler-cyclotron and firehose instabilities. We present a systematic analysis of Wind-SWE-VEIS observations of solar wind electron plasma and associated Wind-MFI observed magnetic fluctuations. For the first time using the full solar wind electron distribution and its moments, without separation of the various electron components, we show clear evidence that the temperature anisotropy threshold of the parallel electron cyclotron anisotropic instability bounds solar wind electrons during slow solar wind periods. We also demonstrate that during periods of slow solar wind, collisions—while infrequent—are the dominant mechanism by which solar wind electrons are constrained, leading to isotropization. During fast solar wind periods, magnetic fluctuations and solar wind anisotropies are enhanced above the parallel whistler anisotropic threshold boundary and collisional effects are significantly reduced. Preliminary calculations further show that the oblique electron whistler mirror anisotropic instability bounds both the slow and fast solar wind. Regardless of speed, the solar wind electron thermal anisotropy appears globally bounded by the parallel electron firehose instability for anisotropies . Our results indicate that collisions, while infrequent, play a necessary role in regulating the solar wind eVDFs. In striking contrast to solar wind ions, solar wind electron plasma, when considered globally as a single eVDF, is only marginally stable with respect to parallel propagating instabilities.

Suprathermal electron distributions in the solar transition region

Suprathermal tails are a common feature of solar wind electron velocity distributions, and are expected in the solar corona. From the corona, suprathermal electrons can propagate through the steep temperature gradient of the transition region towards the chromosphere, and lead to non-Maxwellian electron velocity distribution functions (VDFs) with pronounced suprathermal tails. We calculate the evolution of a coronal electron distribution through the transition region in order to quantify the suprathermal electron population there. A kinetic model for electrons is used which is based on solving the Boltzmann-Vlasov equation for electrons including Coulomb collisions with both ions and electrons. Initial and chromospheric boundary conditions are Maxwellian VDFs with densities and temperatures based on a background fluid model. The coronal boundary condition has been adopted from earlier studies of suprathermal electron formation in coronal loops. The model results show the presence of strong suprathermal tails in transition region electron VDFs, starting at energies of a few 10 eV. Above electron energies of 600 eV, electrons can traverse the transition region essentially collision-free. The presence of strong suprathermal tails in transition region electron VDFs shows that the assumption of local thermodynamic equilibrium is not justified there. This has a significant impact on ionization dynamics, as is shown in a companion paper.

SUPRATHERMAL SOLAR WIND ELECTRONS AND LANGMUIR TURBULENCE

ABSTRACT The steady-state model recently put forth for the solar wind electron velocity distribution function during quiet time conditions, was originally composed of three population electrons (core, halo, and superhalo) with the core remaining nonresonant with any plasma waves while the halo and superhalo separately maintained steady-state resonance with whistler- and Langmuir-frequency range fluctuations, respectively. However, a recent paper demonstrates that whistler-range fluctuations in fact have no significant contribution. The present paper represents a consummation of the model in that a self-consistent model of the suprathermal electron population, which encompasses both the halo and the superhalo, is constructed solely on the basis of the Langmuir fluctuation spectrum. Numerical solutions to steady-state particle and wave kinetic equations are obtained on the basis of an initial trial electron distribution and Langmuir wave spectrum. Such a finding offers a self-consistent explanation for the observed steady-state electron distribution in the solar wind.

ASYMPTOTIC THEORY OF SOLAR WIND ELECTRONS

This paper presents a theory for the asymptotically steady-state solar wind electron velocity distribution function (VDF) in a local equilibrium with plasma wave turbulence. By treating the local solar wind electron VDF as a superposition of three populations—the low-energy Maxwellian core electrons with an energy range of tens of eV, the intermediate –103 eV energy-range halo electrons, and the high –105 eV energy-range superhalo electrons—the present paper puts forth a model in which the halo electrons are in dynamical steady state with the pervasive whistler fluctuations, while the superhalo electrons maintain dynamical steady-state equilibrium with the Langmuir fluctuations, known as the quasi-thermal noise. Customary models of the solar wind electrons include only the Maxwellian core and the halo (plus highly field-aligned strahl). While the present paper does not consider the strahl population in the discussion, the highly energetic superhalo component, which is observed to be present in all solar conditions, is explicitly taken into account as part of the total solar wind electron model. Comparisons with STEREO and WIND spacecraft observations are also made.

THE ORIGIN OF NON-MAXWELLIAN SOLAR WIND ELECTRON VELOCITY DISTRIBUTION FUNCTION: CONNECTION TO NANOFLARES IN THE SOLAR CORONA

The formation of the observed core-halo feature in the solar wind electron velocity distribution function is a long-time puzzle. In this letter based on the current knowledge of nanoflares we show that the nanoflare-accelerated electron beams are likely to trigger a strong electron two-stream instability that generates kinetic Alfv\'en wave and whistler wave turbulence, as we demonstrated in a previous paper. We further show that the core-halo feature produced during the origin of kinetic turbulence is likely to originate in the inner corona and can be preserved as the solar wind escapes to space along open field lines. We formulate a set of equations to describe the heating processes observed in the simulation and show that the core-halo temperature ratio of the solar wind is insensitive to the initial conditions in the corona and is related to the core-halo density ratio of the solar wind and to the quasi-saturation property of the two-stream instability at the time when the exponential decay ends. This relation can be extended to the more general core-halo-strahl feature in the solar wind. The temperature ratio between the core and hot components is nearly independent of the heliospheric distance to the sun. We show that the core-halo relative drift previously reported is a relic of the fully saturated two stream instability. Our theoretical results are consistent with the observations while new tests for this model are provided.

ASYMMETRIC SOLAR WIND ELECTRON DISTRIBUTIONS

The present paper provides a possible explanation for the solar wind electron velocity distribution functions possessing asymmetric energetic tails. By numerically solving the electrostatic weak turbulence equations that involve nonlinear interactions among electrons, Langmuir waves, and ion-sound waves, it is shown that different ratios of ion-to-electron temperatures lead to the generation of varying degrees of asymmetric tails. The present finding may be applicable to observations in the solar wind near 1 AU and in other regions of the heliosphere and interplanetary space.

Radial evolution of nonthermal electron populations in the low‐latitude solar wind: Helios, Cluster, and Ulysses Observations

We have performed a statistical study of a substantial amount of solar wind electron velocity distribution functions (eVDFs). In our data set, we combine measurements acquired onboard three spacecrafts (Helios, Cluster II, and Ulysses) in the low ecliptic latitudes covering the heliocentric distance from 0.3 up to 4 AU. In this study, we focus on the nonthermal properties of the measured eVDFs in both the slow and the fast solar wind regimes. The aim of the present study is (1) to provide, for the first time, an analytical model to fit separately all three components of the solar wind eVDFs (i.e., the core, the halo, and the strahl) and (2) to study the fractional densities of the three electron components and also the non‐Maxwellian character of the high‐energy eVDF tails as a function of the radial distance from the sun. Basically, our study is incremental to the previous studies of the fast solar wind and primarily extends their conclusions on a large number of slow wind observations in the ecliptic plane. We confirm that the halo and the strahl relative densities vary in an opposite way. The relative number of strahl electrons is decreasing with radial distance, whereas the relative number of halo electrons is increasing. The fractional density of the core population remains roughly constant. These findings suggest that there are mechanisms in the solar wind that scatter the strahl electrons into the halo. Also, we find that the relative importance of the nonthermal electrons in the fast solar wind is slightly higher compared to the slow wind.

Formation of suprathermal electron distributions in the quiet solar corona

Context. Solar wind electron velocity distribution functions (VDFs) show enhanced levels of suprathermal electrons as compared to a Maxwellian distribution. Previous studies show that the suprathermal tails of solar wind VDFs can be fitted by kappa distributions, and that a coronal origin of the suprathermal electrons is possible. Aims. The generation of suprathermal electrons by resonant interaction with whistler waves in the corona is investigated under quiet solar conditions without any flare activity. The magnetic field geometry is that of a closed magnetic loop. The electron-whistler interaction is described within the framework of quasilinear theory, that leads to pitch-angle diffusion of the electrons in the reference frame of the waves. Methods. A study of electron VDFs requires a kinetic description of the electrons. The model used in this paper is based on a numerical solution of the Boltzmann-Vlasov equation for the electrons, considering Coulomb collisions and wave-electron interaction. The waves are assumed to enter the simulation box with a given power-law spectrum, which evolves inside the box due to wave propagation and absorption by the electrons. Starting from a nearly Maxwellian initial electron VDF, the temporal evolution of the VDF is calculated until a final steady state has been reached. Results. The results show that a population of suprathermal electrons develops in a closed coronal loop. The electron VDF can be approximated by a power-law in the energy range of 4-10 keV. The power-law index is in agreement with the solar wind observations. For lower energy, the electrons are thermalized in the dense model coronal loop, and the efficiency of the acceleration mechanism decreases for higher energies. The energy range of the simulation box has to be chosen sufficiently large, and the influence of the loop geometry on the results is also studied. Conclusions. These numerical studies show that the quiet solar corona is capable of producing suprathermal electron VDFs with similar characteristics to those observed in the solar wind. This study is focused on a closed region in the solar corona, but if such an electron population is present in the corona, it should also appear in the solar wind.

Modification of the solar wind electron velocity distribution at interplanetary shocks

We analyze a small selection of interplanetary shocks of moderate strength, observed by instruments aboard the Wind spacecraft. We find electron signatures of heating and acceleration that are similar to those found at Earth's high Mach number bow shock. Upstream, velocity distributions have the signature of shock‐accelerated electrons with the characteristic time of flight velocity cutoff with bump‐on‐tail reduced distributions observed in coincidence with Langmuir waves. Downstream, the distributions broaden with the stronger shocks showing flat‐topped distributions and accompanying beams, such as are seen on the high entropy side of Earth's bow shock. We apply the Liouville mapping analysis of Hull et al. [1998, 2001] to one of the interplanetary shocks and compute the deHoffman‐Teller electrostatic potential across the shock using the electron moments to map the observed upstream distribution to the downstream region. The mapping successfully reproduces the inflated phase density and beam signatures of the observed downstream electron velocity distribution.

Generation of Suprathermal Electrons by Resonant Wave‐Particle Interaction in the Solar Corona and Wind

Observations of solar wind electron velocity distribution functions (VDFs) reveal pronounced deviations from a Maxwellian with enhanced numbers of suprathermal electrons. It is shown that these suprathermal tails of the electron VDFs can originate from the solar corona. A model for the acceleration of suprathermal electrons based on resonant interaction with whistler waves is presented. Quasi-linear theory describes this interaction as pitch-angle diffusion in the reference frame of the waves. The waves are assumed to be generated below the coronal base and to propagate antisunward through the corona. Under plasma conditions with high whistler wave phase speeds, the resonant interaction causes electrons to be accelerated from relatively small sunward velocities parallel to the background magnetic field to high speeds perpendicular to the magnetic field. Such plasma conditions are found in the solar corona. A kinetic model is developed to study this acceleration mechanism and the evolution of an electron VDF from the coronal base up into interplanetary space. The kinetic model includes not only the resonant interaction with whistler waves but also Coulomb collisions and the mirror force the electrons experience in the opening magnetic structure of a coronal funnel. The wave absorption of the electrons is also considered to guarantee energy conservation. Kinetic results for the coronal funnel and solar wind are presented. The electron VDFs show deviations from a Maxwellian that are in coincidence with theoretical expectations. The whistler waves generate suprathermal electrons. Toward interplanetary space, the mirror force focuses the electrons toward a narrow "strahl." A comparative study without whistler waves shows that the waves considerably enhance the suprathermal electron fluxes in interplanetary space at 1 AU, as they are observed in the solar wind.

On the long-tail solar wind electron velocity distribution

We show that the core-halo solar wind velocity distribution function can be understood in terms of a simple phenomenological model of general applicability in which the core has a Maxwellian or normal distribution and the halo a log-normal distribution. Furthermore, in the presence of structures in the interplanetary medium capable of interacting with the electrons, the model predicts a transition at the highest velocities to a secondary halo distribution.

Electron velocity distributions near interplantary shocks

Solar wind electron velocity distributions measured across interplanetary shocks using the Los Alamos plasma analyzer on ISEE 3 have been studied to understand electron heating mechanisms for weak and intermediate strength collisionless shocks. This study thus complements earlier studies of electron heating at the earth's bow shock, an example of a highly supercritical collisionless shock. At the weakest interplanetary shocks (downstream to upstream density ratio N(d/u) ≲ 2 and velocity difference V(d‐u) ≲ 70 km/s), heating perpendicular to the magnetic field B predominates over parallel heating. Such heating may be a consequence of conservation of magnetic moment across the shock. At the stronger interplanetary shocks (N(d/u) ≳ 2 and V(d‐u) ≳ 70 km/s), heating parallel to B is dominant and the downstream velocity distributions are flat‐topped, similar to what is observed downstream of the earth's bow shock. This similarity suggests that electron heating in all collisionless shocks with N(d/u) ≳ 2 and V(d‐u) ≳ 70 km/s results in part from an acceleration parallel to B produced by the macroscopic shock electric field, followed by beam driven plasma instabilities.

Lower hybrid waves in the solar wind

We demonstrate that the frequently observed broad band low frequency electrostatic noise in the solar wind generally has a dominant lower hybrid component. These modes are probably produced by the anisotropic halos of the solar wind electron velocity distributions exhibiting "heat flux" profiles and thus, are accompanied by broad band, "hybrid‐like" whistler waves. When the electron temperature is much larger than the ion temperature, these modes can also co‐exist with the ion acoustic waves. Since lower hybrid modes propagate nearly normal to the interplanetary magnetic field lines, the ions can be transversely accelerated by these waves and attain the observed anisotropic and/or loss‐cone‐like distributions.

Plasma electron signature of magnetic connection to the Earth's bow shock: ISEE 3

Enhanced fluxes of low‐energy electrons backstreaming from the earth's bow shock have been identified at ISEE 3. When present, these fluxes modify ambient solar wind electron velocity distributions f(υ) in characteristic ways that depends on whether ISEE 3 is near the edge of, or within the interior of the earth's electron foreshock. Near the edge, energy peaks in f(υ) are observed. Such distributions should be locally unstable to electron plasma oscillations. Well within the interior of the foreshock, enhanced fluxes of electrons with energies up to the maximum detected by the Los Alamos electron analyzer (∼1 keV) are observed over the full backward hemisphere. These electrons can be modelled with an asymptotic power law distribution having index in the range 4 ≲ pbs ≲ 6. At intermediate energies (∼20–50 eV), twin angular peaks are observed centered on the magnetic field direction . Also observed at these times are depressions in f(υ) at energies less than ∼20 eV that are centered on . Such distributions having a perpendicular temperature greater than their parallel temperature may be locally unstable to the generation of whistler waves. Analysis of a particularly clean example of connection to the bow shock is consistent with the possibility that the observed electron fluxes emerge from the forward foot of the electron heating region within the bow shock where the electron density and temperature are larger than that of the unperturbed upstream solar wind by a factor of ∼1.2. This analysis also indicates that the electrostatic potential within the forward foot of the shock is between ∼5 and 50 V more positive than that within plasma far upstream at ISEE 3. However, these interpretations depend on the assumption of nearly scatter‐free propagation, which may not hold. Using parameters derived from model fits to measured velocity distributions, we estimate ∼10−4 of the incident solar wind electrons are accelerated by the bow shock back into the upstream region with energies greater than 1 keV.

Solar wind electrons

Average characteristics of solar wind electron velocity distributions as well as the range and nature of their variations are presented. The measured distributions are generally symmetric about the heat flux direction and are adequately parameterized by the superposition of a nearly bi-Maxwellian function which characterizes the low-energy electrons and a bi-Maxwellian function which characterizes a distinct, ubiquitous component of higher-energy electrons. An alternate self-consistent description of the higher-energy component is presented in terms of an unbound population of hot electrons with energy greater than some breakpoint energy of ≃60 V. The largest-scale parameter variations appear to come most often in association with high-speed streams. The salient electron parameter variations associated with these structures are presented and discussed. The mechanism by which interplanetary electrons conduct heat is convection of the hot component relative to the bulk speed. Arguments are presented which favor the local regulation of the solar wind heat flux at 1 AU.