Halo Electrons Research Articles

REVISED MODEL OF THE STEADY-STATE SOLAR WIND HALO ELECTRON VELOCITY DISTRIBUTION FUNCTION

ABSTRACT A recent study discussed the steady-state model for solar wind electrons during quiet time conditions. The electrons emanating from the Sun are treated in a composite three-population model—the low-energy Maxwellian core with an energy range of tens of eV, the intermediate ∼102–103 eV energy-range (“halo”) electrons, and the high ∼103–105 eV energy-range (“super-halo”) electrons. In the model, the intermediate energy halo electrons are assumed to be in resonance with transverse EM fluctuations in the whistler frequency range (∼102 Hz), while the high-energy super-halo electrons are presumed to be in steady-state wave–particle resonance with higher-frequency electrostatic fluctuations in the Langmuir frequency range (∼105 Hz). A comparison with STEREO and WIND spacecraft data was also made. However, ignoring the influence of Langmuir fluctuations on the halo population turns out to be an unjustifiable assumption. The present paper rectifies the previous approach by including both Langmuir and whistler fluctuations in the construction of the steady-state velocity distribution function for the halo population, and demonstrates that the role of whistler-range fluctuation is minimal unless the fluctuation intensity is arbitrarily raised. This implies that the Langmuir-range fluctuations, known as the quasi thermal noise, are important for both halo and super-halo electron velocity distribution.

Runaway electrons and magnetic island confinement

The breakup of magnetic surfaces is a central feature of ITER planning for the avoidance of damage due to runaway electrons. Rapid thermal quenches, which lead to large accelerating voltages, are thought to be due to magnetic surface breakup. Impurity injection to avoid and to mitigate both halo and runaway electron currents utilizes massive gas injection or shattered pellets. The actual deposition is away from the plasma center, and the breakup of magnetic surfaces is thought to spread the effects of the impurities across the plasma cross section. The breakup of magnetic surfaces would prevent runaway electrons from reaching relativistic energies were it not for the persistence of non-intercepting flux tubes. These are tubes of magnetic field lines that do not intercept the walls. In simulations and in magnetic field models, non-intercepting flux tubes are found to persist near the magnetic axis and in the cores of magnetic islands even when a large scale magnetic surface breakup occurs. As long as a few magnetic surfaces reform before all of the non-intercepting flux tubes dissipate, energetic electrons confined and accelerated in these flux tubes can serve as the seed electrons for a transfer of the overall plasma current from thermal to relativistic carriers. The acceleration of electrons is particularly strong because of the sudden changes in the poloidal flux that naturally occur in a rapid magnetic relaxation. The physics of magnetic islands as non-intercepting flux tubes is studied. Expressions are derived for (1) the size of islands required to confine energetic runaway electrons, (2) the accelerating electric field in an island, (3) the increase or reduction in the size of an island by the runaway electron current, (4) the approximate magnitude of the runaway current in an island, and (5) the time scale for the evolution of an island.

Characterizing cometary electrons with kappa distributions

AbstractThe Rosetta spacecraft has escorted comet 67P/Churyumov‐Gerasimenko since 6 August 2014 and has offered an unprecedented opportunity to study plasma physics in the coma. We have used this opportunity to make the first characterization of cometary electrons with kappa distributions. Two three‐dimensional kappa functions were fit to the observations, which we interpret as two populations of dense and warm (density = 10 cm−3, temperature = 2 × 105 K, invariant kappa index = 10−>1000), and rarefied and hot (density = 0.005 cm−3, temperature = 5 × 105 K, invariant kappa index = 1–10) electrons. We fit the observations on 30 October 2014 when Rosetta was 20 km from 67P, and 3 AU from the Sun. We repeated the analysis on 15 August 2015 when Rosetta was 300 km from the comet and 1.3 AU from the Sun. Comparing the measurements on both days gives the first comparison of the cometary electron environment between a nearly inactive comet far from the Sun and an active comet near perihelion. We find that the warm population density increased by a factor of 3, while the temperature cooled by a factor of 2, and the invariant kappa index was unaffected. We find that the hot population density increased by a factor of 10, while the temperature and invariant kappa index were unchanged. We conclude that the hot population is likely the solar wind halo electrons in the coma. The warm population is likely of cometary origin, but its mechanism for production is not known.

QUIET-TIME SUPRATHERMAL (∼0.1–1.5 keV) ELECTRONS IN THE SOLAR WIND

ABSTRACT We present a statistical survey of the energy spectrum of solar wind suprathermal (∼0.1–1.5 keV) electrons measured by the WIND 3DP instrument at 1 AU during quiet times at the minimum and maximum of solar cycles 23 and 24. After separating (beaming) strahl electrons from (isotropic) halo electrons according to their different behaviors in the angular distribution, we fit the observed energy spectrum of both strahl and halo electrons at ∼0.1–1.5 keV to a Kappa distribution function with an index κ and effective temperature T eff. We also calculate the number density n and average energy E avg of strahl and halo electrons by integrating the electron measurements between ∼0.1 and 1.5 keV. We find a strong positive correlation between κ and T eff for both strahl and halo electrons, and a strong positive correlation between the strahl n and halo n, likely reflecting the nature of the generation of these suprathermal electrons. In both solar cycles, κ is larger at solar minimum than at solar maximum for both strahl and halo electrons. The halo κ is generally smaller than the strahl κ (except during the solar minimum of cycle 23). The strahl n is larger at solar maximum, but the halo n shows no difference between solar minimum and maximum. Both the strahl n and halo n have no clear association with the solar wind core population, but the density ratio between the strahl and halo roughly anti-correlates (correlates) with the solar wind density (velocity).

Spontaneous emission of electromagnetic and electrostatic fluctuations in magnetized plasmas: Quasi-parallel modes

The present paper is devoted to the theoretical and numerical analysis of the spontaneously emitted electromagnetic fluctuations characterized by quasi-parallel wave vectors relative to the ambient magnetic field. The formulation is based upon the Klimontovich plasma kinetic theory. The comparative study is carried out between the spontaneously emitted field fluctuation spectrum constructed on the basis of a single Maxellian velocity distribution function (VDF) and the spectrum that arises from multi-component electron VDFs similar to those found in the solar wind. Typical solar wind electron VDF is composed of a Gaussian core and kappa distributions of halo and super-halo components. Of these, the halo and super-halo populations represent tenuous but energetic components. It is found that the energetic electrons make important contributions to the total emission spectrum. It is also found that the halo electrons are largely responsible for the emission spectrum in the whistler frequency range, whereas the more energetic super-halo electrons emit quasi-longitudinal fluctuations in the Langmuir frequency range, thus validating the recent quasi-steady state model of the solar wind electrons put forth by the present authors [Kim et al., Astrophys. J. 806, 32 (2015); Yoon et al., Astrophys. J. 812, 169 (2015)].

STRAHL FORMATION IN THE SOLAR WIND ELECTRONS VIA WHISTLER INSTABILITY

This Letter puts forth a possible explanation for the formation of a solar wind strahl electron distribution function by means of local wave–particle interactions. A solar wind electron consists of a core and the hot electrons, which possess a net drift speed with respect to the core. According to the present model, pitch angle scattering of the initially isotropic drifting halo occurs when the enhanced whistler waves are excited by mildly anisotropic core electrons. The pitch angle scattering primarily affects the halo moving in the anti-sunward direction, resulting in pitch angle diffusion across the 90° gap through a nonlinear scattering process, and consequently leading to a reduction in the net drift speed of halo electrons. The remaining portion of the anti-sunward moving halo, which is not affected by pitch angle scattering, simply appears to form a field-aligned strahl in the electron velocity distribution. The present scenario of local generation of the strahl is demonstrated by the particle-in-cell simulation.

Solar Wind Electron Energization by Plasma Turbulence

The solar wind electrons are made of the low-energy Maxwellian core, intermediate-energy halo, field-aligned strahl, and the highly-energetic super-halo electrons. The present paper discusses a model in which the halo electrons interact with the whistler fluctuation via cyclotron wave-particle resonance, and the super-halo electrons interact through Landau resonance with the Langmuir fluctuation, thus maintaining a local steady state.

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 interplay of Kappa and core populations in the solar wind: Electromagnetic electron cyclotron instability

AbstractRecently, a realistic parameterization was proposed for the kinetic anisotropy and the resulting instabilities in the solar wind plasma. This parameterization is based on observations of the particle velocity distribution, which always comprises a Maxwellian population at low energies, viz. the core, and a suprathermal halo in the tail of the distribution which is best described by the Kappa (power law) models. The cyclotron instability, driven by an anisotropic electron halo, was found to be inhibited by the finite thermal spread in the core, and this effect is highly dependent on the halo‐core relative density. In this paper, the interplay between the Kappa and Maxwellian populations is further investigated for more complex (less idealized) situations when both the core and halo temperatures are anisotropic. Growth of this instability is markedly stimulated by the core anisotropy. The wave numbers that are stable for an isotropic core become unstable even for small anisotropies of this population. Just a modest increase of the core anisotropy from Ac=T⊥/T∥=1.2 to 2 causes the growth rates to enhance by 1 order of magnitude, and the range of unstable wave numbers to extend considerably. When the anisotropies in the core and halo are comparable, the growth rate exhibits two distinct peaks, the first driven by the halo at lower wave numbers and the second driven by the core. However, the first peak is inhibited by the suprathermal populations, while the second peak is sustained, suggesting a more intricate connection between the core and Kappa populations.

Analysis of the substructure within a complex magnetic cloud on 3–4 September 2008

Abstract. In this paper we have analyzed a substructure found within a leading part of a north–south-oriented magnetic cloud (MC) observed on 3–4 September 2008 in the near-Earth solar wind by multiple spacecraft (ACE, Wind, THEMIS B and C). The MC was preceded by a stream interface (SI) and followed by a high-speed stream (HSS). The identified substructure featured a strong depletion of suprathermal halo electrons and showed distinct magnetic field and plasma signatures. It occurred where suprathermal electron flow within a cloud changed from bidirectional to unidirectional, indicating change in the field line connectivity to the Sun. We found that the substructure maintained roughly its integrity from the first Lagrangian point to the vicinity of the Earth's bow shock in the front edge of the MC, but revealed small changes in the structure which could be explained either by temporal evolution or spatial configuration of the spacecraft.

Shocklets, SLAMS, and field‐aligned ion beams in the terrestrial foreshock

We present Wind spacecraft observations of ion distributions showing field‐aligned beams (FABs) and large‐amplitude magnetic fluctuations composed of a series of shocklets and short large‐amplitude magnetic structures (SLAMS). The FABs are found to have Tb ~ 80 − 850 eV, Vb/Vsw ~ 1. 3 − 2. 4, T⊥,b/T∥,b ~ 1–8, and nb/no ~ 0.2–11%. Saturation amplitudes for ion/ion resonant and non‐resonant instabilities are too small to explain the observed SLAMS amplitudes. We show two examples where groups of SLAMS can act like a local quasi‐perpendicular shock reflecting ions to produce the FABs, a scenario distinct from the more common production at the quasi‐perpendicular bow shock. The SLAMS exhibit a foot‐like magnetic enhancement with a leading magnetosonic whistler train, consistent with previous observations. Strong ion and electron heating are observed within the series of shocklets and SLAMS with temperatures increasing by factors ≳ 5 and ≳ 3, respectively. Both the core and halo electron components show strong perpendicular heating inside the feature.

Electromagnetic waves and electron anisotropies downstream of supercritical interplanetary shocks

We present waveform observations of electromagnetic lower hybrid and whistler waves with fci ≪ f < fce downstream of four supercritical interplanetary shocks using the Wind search coil magnetometer. The whistler waves were observed to have a weak positive correlation between δB and normalized heat flux magnitude and an inverse correlation with Teh/Tec. All were observed simultaneous with electron distributions satisfying the whistler heat flux instability threshold and most with T⊥ h/T∥ h > 1.01. Thus, the whistler mode waves appear to be driven by a heat flux instability and cause perpendicular heating of the halo electrons. The lower hybrid waves show a much weaker correlation between δB and normalized heat flux magnitude and are often observed near magnetic field gradients. A third type of event shows fluctuations consistent with a mixture of both lower hybrid and whistler mode waves. These results suggest that whistler waves may indeed be regulating the electron heat flux and the halo temperature anisotropy, which is important for theories and simulations of electron distribution evolution from the Sun to the Earth.

Observations of large‐amplitude, narrowband whistlers at stream interaction regions

We present the first solar wind observations of large‐amplitude, narrowband waveforms in the frequency range 10–100 Hz, consistent with the whistler mode. These whistlers are only observable in high time resolution electric field waveform data provided by the Time Domain Sampler (TDS) instrument on STEREO. Amplitudes range from a few to >40 mV/m peak‐to‐peak, one to three orders of magnitude larger than any previous observations of whistler mode waves in the solar wind. The whistlers are obliquely propagating with a large electrostatic component and are right‐hand elliptically polarized in the spacecraft frame. The whistlers occur in groups that are strongly correlated with stream interaction regions (SIRs). The groups persist from a few seconds to minutes and are observed at 88% of SIRs and 17% of shocks from available data. A more detailed look shows that the whistler groups are observed near sudden disturbances of the solar wind magnetic field and plasma. We suggest that, owing to the oblique and narrowband nature of these waves, an electron or ion beam instability may be responsible for their creation. Test particle simulations show that the waves can interact strongly with halo (>60 eV) electrons. Test electrons were scattered by tens of degrees and energized/deenergized by up to 50% in a few tens of milliseconds. Thus these whistlers may play an important role in the dynamics of solar wind electrons within SIRs and near some shocks.

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.

A one dimensional, electrostatic Vlasov model for the generation of suprathermal electron tails in solar wind conditions

Space and laboratory collisionless plasmas are most often out of local thermodynamic equilibrium. In particular, their charged particle velocity distributions usually differ from simple Maxwellian distributions and exhibit a great variety of anisotropies and components such as suprathermal beams and tails. Here we propose a new model responsible for a “local” origin of electron suprathermal tails. The model is based on adding a high and a low frequency external forcing to the Vlasov‐Poisson system of equations. The first one represents mainly the thermal noise electric field generated by charge separation effects. The second one represents the energy injection resulting from the energy cascade generated by the large scale fluid (MHD) turbulence. We find that in typical solar wind conditions, our model could be the base of a full three dimensional, electromagnetic model capable of explaining the local generation of the electron halo population observed on the electron distribution function.

Perpendicular scattering for electron beams by the electron/electron instability in solar electron bursts

Energy dependence of electron pitch angle distributions in solar electron bursts is studied using both particle‐in‐cell simulations of the electron/electron instability and a time‐of‐flight model for streaming electrons. The simulations show that the electron/electron instability leads to a maximum of electron pitch angle width in electron kinetic energy. The energy where the maximum appears varies with electron beam parameters. The simulations further show that the maximum electron pitch angle width increases with increasing electron beam density. The time‐of‐flight effect which leads to positive slopes in electron velocity distributions implies that the probability of electron/electron instability growth in the solar wind depends on electron kinetic energy because of the presence of an electron halo distribution. It is concluded that the electron/electron instability induced by the time‐of‐flight effect is likely to yield a maximum electron pitch angle width near 1 keV.

Solar wind electron distribution functions inside magnetic clouds

This paper presents a study of the kinetic properties of the electron velocity distribution functions within interplanetary magnetic clouds, since they are the dominant thermal component and can contribute as much as 50% of the total electron pressure within the clouds. The study is based on high time resolution data from the Goddard Space Flight Center Wind Solar Wind Experiment vector electron and ion spectrometer. Studies on interplanetary magnetic clouds have shown observational evidence of anticorrelation between the total electron density and temperature, which suggests a polytrope law Pe = αneγ for electrons with the constant γ ≈ 0.5 < 1. This anticorrelation and small γ values are interpreted in the context of the presence of highly non‐Maxwellian electron distributions (i.e., nonthermal tails) within magnetic clouds. We have revisited some of the magnetic cloud events previously studied to quantify the nature of the nonthermal electrons by modeling the electron velocity distribution function using Maxwellian and kappa‐like distribution functions to characterize the kinetic nonthermal effects. The results show that the electron density‐temperature anticorrelation is not a unique feature of magnetic clouds. Within magnetic clouds, κ values are generally small, in the range of 1.6–5.4; however, such small values are also typical of regions outside the clouds. We have shown that the density‐temperature anticorrelation of the electron moments is persistently consistent with similar density‐temperature anticorrelation in the electron halo component of the velocity distribution function and essentially little or no correlation was obtained for the core component. This result clearly shows that the temperature and density of the suprathermal components play a significant role in the temperature‐density anticorrelation because of a relative enhancement of the halo component abundance to the total density.

The IMPACT Solar Wind Electron Analyzer (SWEA)

SWEA, the solar wind electron analyzers that are part of the IMPACT in situ investigation for the STEREO mission, are described. They are identical on each of the two spacecraft. Both are designed to provide detailed measurements of interplanetary electron distribution functions in the energy range 1∼3000 eV and in a 120°×360° solid angle sector. This energy range covers the core or thermal solar wind plasma electrons, and the suprathermal halo electrons including the field-aligned heat flux or strahl used to diagnose the interplanetary magnetic field topology. The potential of each analyzer will be varied in order to maintain their energy resolution for spacecraft potentials comparable to the solar wind thermal electron energies. Calibrations have been performed that show the performance of the devices are in good agreement with calculations and will allow precise diagnostics of all of the interplanetary electron populations at the two STEREO spacecraft locations.

Experimental and numerical characterization of ion-cyclotron heated protons on the Alcator C-Mod tokamak

Energetic minority protons with ∼100 keV effective temperature are routinely created in Alcator C-Mod plasmas with the application of ion-cyclotron-range-of-frequency (ICRF) heating. A multichannel compact neutral particle analyzer (CNPA) is used to make measurements of these distributions in Alcator C-Mod's unique and reactor-relevant operating space via active and passive charge-exchange techniques. A radially injected 50 keV diagnostic hydrogen neutral beam is used for active analysis. Using a detailed model that accounts for beam, halo and impurity electron donors, core proton temperatures of ∼30–120 keV are directly measured for the first time in lower density (ne0 ∼ (0.8–1.5) × 1020 m−3) Alcator C-Mod plasmas with up to only ∼0.5 MW of ICRF power. The model found that the minority proton temperatures are peaked spatially away from r/a = 0, even for an on-axis resonance. Additionally, noticeable phase-space anisotropy is seen as expected for ICRF heating. The measured effective temperatures also scale approximately with the Stix parameter. The CNPA temperature measurements are compared with several leading simulation packages such as the TORIC/FPPRF and AORSA/CQL3D full-wave/Fokker–Planck (FW/FP) solvers. Preliminary comparisons with the AORSA/CQL3D code which include results from a new synthetic diagnostic show good agreement and demonstrate that accurate tracking of the minority distribution during iterations of the FW and FP solvers is required to simulate Alcator C-Mod's energetic minority populations with accuracy. Physically, poor wave focusing and preferential heating of trapped energetic protons are found to move the fast proton temperature profiles off-axis. These FW/FP analyses represent the first comparison between predictions of these detailed codes and core minority tail experimental measurements on Alcator C-Mod.

Numerical studies on the structure of the cosmic ray electron halo in starburst galaxies

The structure of the cosmic ray electron halo of a starburst galaxy depends strongly on the nature of galactic wind and the configuration of the magnetic field. We have investigated these dependencies by solving numerically the propagation of electrons originating in starburst galaxies, most likely in supernova remnants. The calculations are made for several models for the galactic winds and for the configuration of the magnetic fields for comparison with observations. Our simulation of a quasi-radio halo reproduces both the extended structure of ∼9 kpc and the subtle hollow structure near the polar region of the radio halo that are observed in the starburst galaxy NGC 253. These findings suggest the existence of strong galactic wind in NGC 253.