Field-aligned Electron Research Articles

Relativistic electron beams accelerated by an interplanetary shock

Context. Collisionless shock waves have long been considered to be among the most prolific particle accelerators in the universe. Shocks alter the plasma they propagate through, and often exhibit complex evolution across multiple scales. Interplanetary (IP) traveling shocks have been recorded in situ for over half a century and act as a natural laboratory for experimentally verifying various aspects of large-scale collisionless shocks. A fundamentally interesting problem in both heliophysics and astrophysics is the acceleration of electrons to relativistic energies (> 300 keV) by traveling shocks. Aims. The reason for an incomplete understanding of electron acceleration at IP shocks is due to scale-related challenges and a lack of instrumental capabilities. This Letter presents the first observations of field-aligned beams of relativistic electrons upstream of an IP shock, observed thanks to the instrumental capabilities of Solar Orbiter. This study presents the characteristics of the electron beams close to the source and contributes to the understanding of their acceleration mechanism. Methods. On 25 July 2022, Solar Orbiter encountered an IP shock at 0.98 AU. The shock was associated with an energetic storm particle event, which also featured upstream field-aligned relativistic electron beams observed 14 min prior to the actual shock crossing. The distance of the beam’s origin was investigated using a velocity dispersion analysis (VDA). Peak-intensity energy spectra were anaylzed and compared with those obtained from a semi-analytical fast-Fermi acceleration model. Results. By leveraging Solar Orbiter’s high temporal resolution Energetic Particle Detector (EPD), we successfully showcase an IP shock’s ability to accelerate relativistic electron beams. Our proposed acceleration mechanism offers an explanation for the observed electron beam and its characteristics, while we also explore the potential contributions of more complex mechanisms.

Kinetic and Shear Alfvén Waves in a Large Guide-field Reconnection at Earth's Magnetopause

A large guide-field (∼1.1B o) reconnection X-line, observed by the Magnetospheric Multiscale spacecraft during an outbound magnetopause crossing, is studied for Alfvén waves. Here B o is the reconnecting field magnitude. The current sheet thickness of the magnetopause was ∼2.6 ion inertial lengths (∼269 km), where field-aligned counter-streaming electrons were observed and Hall electromagnetic fields were identified. A remarkable finding was that a kinetic Alfvén wave (KAW) was seen in the magnetopause upstream region after a shear Alfvén wave (SAW) was encountered in the magnetopause layer. The presence of both the SAW and KAW near the reconnection X-line is for the first time reported. In the spacecraft frame of reference, the SAW has a dominant frequency at ∼0.74 Hz, while the KAW has two dominant frequencies at ∼0.38 and ∼0.64 Hz. The wave energy for KAW and SAW was mostly carried away from the reconnection site by the Poynting flux parallel to the magnetic field. The parallel temperatures for ions and electrons were increased at KAW. The peaks of T ∥/T ⊥ for ions were located near the wave peaks, while the ratio peaks for electrons were near the wave troughs. Our findings suggest that KAWS and SAWs can be generated by asymmetric reconnection with a large guide field.

The force balance of electrons during kinetic anti-parallel magnetic reconnection

Fully kinetic simulations are applied to the study of 2D anti-parallel reconnection, elucidating the dynamics by which the electron fluid maintains force balance within both the ion diffusion region (IDR) and the electron diffusion region (EDR). Inside the IDR, magnetic field-aligned electron pressure anisotropy (pe∥≫pe⊥) develops upstream of the EDR. Compared to previous investigations, the use of modern computer facilities allows for simulations at the natural proton to electron mass ratio mi/me=1836. In this high-mi/me-limit, the electron dynamics change qualitatively, as the electron inflow to the EDR is enhanced and mainly driven by the anisotropic pressure. Using a coordinate system with the x-direction aligned with the reconnecting magnetic field and the y-direction aligned with the central current layer, it is well known that for the much studied 2D laminar anti-parallel and symmetric scenario the reconnection electric field at the X-line must be balanced by the ∂pexy/∂x and ∂peyz/∂z off-diagonal electron pressure stress components. We find that the electron anisotropy upstream of the EDR imposes large values of ∂pexy/∂x within the EDR, and along the direction of the reconnection X-line, this stress cancels with the stress of a previously determined theoretical form for ∂peyz/∂z. The electron frozen-in law is instead broken by pressure tensor gradients related to the direct heating of the electrons by the reconnection electric field. The reconnection rate is free to adjust to the value imposed externally by the plasma dynamics at larger scales.

Is the Solar Wind Electron Strahl a Seed Population for the Earth’s Electron Radiation Belt?

1) Since the outer electron radiation belt is lost on occasion, the radiation belt needs seed electrons to rebuild. 2) The clear candidate for that seed population is energetic substorm-injected electrons in the dipolar magnetosphere. 3) The energetic substorm-injected electrons in the dipole come from the suprathermal electron population in the magnetotail plasma sheet, delivered by substorms. Scenario (1)–3) begs the question: Where do these magnetotail suprathermal electrons come from? We are hypothesizing that one source (perhaps the dominant source) is the energetic field-aligned electron strahl in the solar wind, which are electrons fresh from the solar corona.

Whistler waves observed by Solar Orbiter/RPW between 0.5 AU and 1 AU

Context. Solar wind evolution differs from a simple radial expansion, while wave-particle interactions are assumed to be the major cause for the observed dynamics of the electron distribution function. In particular, whistler waves are thought to inhibit the electron heat flux and ensure the diffusion of the field-aligned energetic electrons (Strahl electrons) to replenish the halo population. Aims. The goal of our study is to detect and characterize the electromagnetic waves that have the capacity to modify the electron distribution functions, with a special focus on whistler waves. Methods. We carried out a detailed analysis of 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 from the Search Coil Magnetometer and electric antenna, both part of the Radio and Plasma Waves (RPW) instrumental suite, we detected the electromagnetic waves with frequencies above 3 Hz and determined the statistical distribution of their amplitudes, frequencies, polarization, and k-vector as a function of distance. Here, we also discuss the relevant instrumental issues regarding the phase between the electric and magnetic measurements as well as the effective length of the electric antenna. Results. An overwhelming majority of the observed waves are right-handed circularly polarized in the solar wind frame and identified as outwardly propagating quasi-parallel whistler waves. Their occurrence rate increases by a least a factor of 2 from 1 AU to 0.5 AU. These results are consistent with the regulation of the heat flux by the whistler heat flux instability. Near 0.5 AU, whistler waves are found to be more field-aligned and to have a smaller normalized frequency (f/fce), larger amplitude, and greater bandwidth than at 1 AU.

Whistler wave occurrence and the interaction with strahl electrons during the first encounter of Parker Solar Probe

Aims.We studied the properties and occurrence of narrowband whistler waves and their interaction with strahl electrons observed between 0.17 and 0.26 au during the first encounter of Parker Solar Probe.Methods.We used Digital Fields Board band-pass filtered (BPF) data from FIELDS to detect the signatures of whistler waves. Additionally parameters derived from the particle distribution functions measured by the Solar Wind Electrons Alphas and Protons (SWEAP) instrument suite were used to investigate the plasma properties, and FIELDS suite measurements were used to investigate the electromagnetic (EM) fields properties corresponding to the observed whistler signatures.Results.We observe that the 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. The spacecraft frequencies of the analyzed waves are less than 0.2 electron cyclotron frequency (fce). The occurrence rate of whistler waves was found to be anticorrelated with the solar wind bulk velocity. The study of the duration of the whistler intervals revealed an anticorrelation between the duration and the solar wind velocity, as well as between the duration and the normalized amplitude of magnetic field variations. The pitch-angle widths (PAWs) of the field-aligned electron population referred to as the strahl are broader by at least 12 degrees during the presence of large amplitude narrowband whistler waves. This observation points toward an EM wave electron interaction, resulting in pitch-angle scattering. PAWs of strahl electrons corresponding to the short duration whistlers are higher compared to the long duration whistlers, indicating short duration whistlers scatter the strahl electrons better than the long duration ones. Parallel cuts through the strahl electron velocity distribution function (VDF) observed during the whistler intervals appear to depart from the Maxwellian shape typically found in the near-Sun strahl VDFs. The relative decrease in the parallel electron temperature and the increase in PAW for the electrons in the strahl energy range suggests that the interaction with whistler waves results in a transfer of electron momentum from the parallel to the perpendicular direction.

Theoretical model of the nonlinear resonant interaction of whistler-mode waves and field-aligned electrons

The nonlinear resonant interaction of intense whistler-mode waves and energetic electrons in the Earth's radiation belts is traditionally described by theoretical models based on the consideration of slow–fast resonant systems. Such models reduce the electron dynamics around the resonance to the single pendulum equation that provides solutions for the electron nonlinear scattering (phase bunching) and phase trapping. Applicability of this approach is limited to not-too-small electron pitch-angles (i.e., sufficiently large electron magnetic moments), whereas model predictions contradict to the test particle results for small pitch-angle electrons. This study is focused on such field-aligned (small pitch-angle) electron resonances. We show that the nonlinear resonant interaction can be described by the slow–fast Hamiltonian system with the separatrix crossing. For the first cyclotron resonance, this interaction results in the electron pitch-angle increase for all resonant electrons, contrast to the pitch-angle decrease predicted by the pendulum equation for scattered electrons. We derive the threshold value of the magnetic moment of the transition to a new regime of the nonlinear resonant interaction. For field-aligned electrons, the proposed model provides the magnitude of magnetic moment changes in the nonlinear resonance. This model supplements existing models for not-too-small pitch-angles and contributes to the theory of the nonlinear resonant electron interaction with intense whistler-mode waves.

Scattering of Energetic Electrons by Heat-flux-driven Whistlers in Flares

Abstract The scattering of electrons by heat-flux-driven whistler waves is explored with a particle-in-cell simulation relevant to the transport of energetic electrons in flares. This simulation is initiated with a large heat flux produced by 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 the waves are dominantly driven by the low-energy electrons, including the cold return current beam, the energetic electrons resonate with and are scattered by the whistlers on timescales of the order of a hundred electron cyclotron times. Peak whistler amplitudes of and angles of ∼60° with respect to the background magnetic field are observed. Electron perpendicular energy is increased, while the field-aligned electron heat flux is suppressed. The resulting scattering mean-free-paths of energetic electrons are small compared with the typical scale size of energy-release sites in flares, which might lead to the effective confinement of energetic electrons required for the production of very energetic particles.

Effect of Field-Line Curvature on the Ionospheric Accessibility of Relativistic Electron Beam Experiments

Magnetosphere-ionosphere coupling is a particularly important process that regulates and controls magnetospheric dynamics such as storms and substorms. However, in order to understand magnetosphere-ionosphere coupling it is necessary to understand how regions of the magnetosphere are connected to the ionosphere. It has been proposed that this connection may be established by firing electron beams from satellites that can reach an ionospheric footpoint creating detectable emissions. This type of experiment would greatly aid in identifying the relationship between convection processes in the magnetotail and the ionosphere and how the plasma sheet current layer evolves during the growth phase preceding substorms. For practical purposes, the use of relativistic electron beams with kinetic energy on the order of 1 MeV would be ideal for detectability. However, Porazik et al. \cite{Porazik2014} has shown that, for relativistic particles, higher order terms of the magnetic moment are necessary for consideration of the ionospheric accessibility of the beams. These higher order terms are related to gradients in the magnetic field and curvature and are typically unimportant unless the beam is injected along the magnetic field direction, such that the zero order magnetic moment is small. In this article, we address two important consequences related to these higher order terms. First, we investigate the consequences for satellites positioned in regions subject to magnetotail stretching and demonstrate systematically how curvature affects accessibility. We find that curvature can reduce accessibility for beams injected from the current sheet, but can increase accessibility for beams injected just above the current sheet. Second, we investigate how detectability of ionospheric precipitation of variable energy field-aligned electron beams could be used as a constraint on field-line curvature, which would be valuable for field-line reconstruction and/or stability analysis.

South‐North Hemispheric Asymmetry of the FAE Distribution Around the Cusp Region: Cluster Observation

AbstractCluster data from late July to early October were used to study the distribution of field‐aligned electron (FAE) events around the two cusps. An FAE event was defined as electron parallel flux >3 × 108 (cm2 s)−1. The total number of FAE events around the two cusps was basically identical, but downward FAE events prevailed in the south and upward FAE events in the north. In the southern cusp, the peak of the FAE events distribution versus altitude was about 1.3 RE higher and the peak of the FAE events distribution versus invariant latitude (ILAT) was about 4° ILAT lower. Only the downward FAEs around the southern cusp had a second ILAT peak, which was located about 11° higher than the main peak. The normalized number of FAEs showed nearly the same features as the unnormalized number of the FAEs events. These results indicated a north‐south asymmetry of the FAE distribution around the two cusps. Some causes for the asymmetry are discussed, the main ones being the asymmetry of the magnetospheric configuration resulting from geomagnetic dipolar tilt and solar wind flows, the interplanetary magnetic field asymmetry related to the magnetosphere, and the difference of ionospheric conductivity in the two hemispheres. Various solar wind‐magnetosphere interaction processes, such as quasi‐viscous interaction and reconnection, are responsible for the asymmetry, too. The second distribution peak (at higher ILAT) of the downward FAE events around the southern cusp corresponded to high solar wind speed and may be associated with the northward interplanetary magnetic field Bz field‐aligned current at low altitude. This requires further studies, however.

Field-aligned Boltzmann electric triple layer in a low-pressure expanding plasma

A deep and narrow potential structure has been measured along the last magnetic field line to exit the source tube of an expanding plasma device. The potential structure is identified as an electric triple layer and features a potential dip with Full Width Half Maximum ∼70 Debye lengths (16 mm), depth of ∼25 V () and its width and magnitude are seen to decrease with increases in argon pressure. The triple layer acts as a potential barrier for field-aligned electron transport, decelerating hot electrons exiting the plasma source before reaccelerating into the expansion chamber those that are able to overcome the triple layer potential, explaining the topography of high density plasma conics published previously. Measurements of the electron energy probability function at locations upstream and downstream of the potential structure show two-temperature electron populations with break energies of 41.5 V and 22 V, respectively, values that are consistent with the plasma potential measurements along the field line. Under these experimental conditions, the dielectric wall of the source tube charges to significantly negative potentials and the proximity of the field line to this negatively charged wall appears to be the cause for the triple layer.

Mapping the Lunar Wake Potential Structure With ARTEMIS Data.

The refilling of the lunar wake is relatively well explained by the theory of 1-D plasma expansion into a vacuum; however, the field-aligned wake potential is not a directly measured quantity, and thus, a statistical analysis of wake potentials at high altitudes has not been previously performed. In this study, we obtain the wake potential by comparing the field-aligned electron distributions inside and outside of the lunar wake measured by the two probes of the Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) mission. The derived potentials from ARTEMIS data vary with solar wind electron temperature and bulk flow velocity as the theory predicts. We also expand the 1-D plasma theory to 2-D in the plane of the interplanetary magnetic field and the solar wind velocity to examine how a tilted interplanetary magnetic field affects the wake potential structure. As the expansion time for the two sides of the wake differs, a wake potential asymmetry is developed in our model. This asymmetry is confirmed by the data-derived wake potentials. Moreover, ambipolar electric fields are obtained from both the modeled and data-derived wake potentials and show good agreement. Lastly, we examine the effects of the solar wind strahl-electron population on the wake potential structure, which appears to cause a net potential difference across the lunar shadow. This may imply that the disturbance of the wake plasma expansion extends farther outside the wake than previous plasma-expansion theories have predicted.

Particle acceleration during merging-compression plasma start-up in the Mega Amp Spherical Tokamak

Magnetic reconnection occurred during merging-compression plasma start-up in the Mega Amp Spherical Tokamak (MAST), resulting in the prompt acceleration of substantial numbers of ions and electrons to highly suprathermal energies. Accelerated field-aligned ions (deuterons and protons) were detected using a neutral particle analyser at energies up to about 20 keV during merging in early MAST pulses, while nonthermal electrons have been detected indirectly in more recent pulses through microwave bursts. However no increase in soft x-ray emission was observed until later in the merging phase, by which time strong electron heating had been detected through Thomson scattering measurements. A test-particle code CUEBIT is used to model ion acceleration in the presence of an inductive toroidal electric field with a prescribed spatial profile and temporal evolution based on Hall-MHD simulations of the merging process. The simulations yield particle distributions with properties similar to those observed experimentally, including strong field alignment of the fast ions and the acceleration of protons to higher energies than deuterons. Particle-in-cell modelling of a plasma containing a dilute field-aligned suprathermal electron component suggests that at least some of the microwave bursts can be attributed to the anomalous Doppler instability driven by anisotropic fast electrons, which do not produce measurable enhancements in soft x-ray emission either because they are insufficiently energetic or because the nonthermal bremsstrahlung emissivity during this phase of the pulse is below the detection threshold. There is no evidence of runaway electron acceleration during merging, possibly due to the presence of three-dimensional field perturbations.

Ions shear flow and electron field-aligned current produce ion acoustic waves in the oxygen-hydrogen ionospheric plasma

It is pointed out that the ion acoustic waves (IAWs) are excited either by field-aligned shear flows or electron parallel current in oxygen-hydrogen (O-H) plasma of upper ionosphere. The purely growing D'Angelo instability becomes ion acoustic wave instability in the presence of second kind of ions within the framework of multi-fluid plasma model. On the other hand, kinetic theory is used to show that the growth rate of current driven ion acoustic wave overcomes the ion Landau damping. Out of four real roots corresponding to negative shear flow, the two roots can become unstable. Thus, ion acoustic waves at different but very low real frequencies appear in O-H plasma of ionosphere due to parallel shear flow and current, which is in agreement with satellite observations.

Weakly turbulent plasma processes in the presence of inverse power-law velocity tail population

Observations show that plasma particles in the solar wind frequently display power-law velocity distributions, which can be isotropic or anisotropic. Particularly, the velocity distribution functions of solar wind electrons are frequently modeled as a combination of a background Maxwellian distribution and a non-thermal distribution which is known as the “halo” distribution. For fast solar wind conditions, highly anisotropic field-aligned electrons, denominated as the “strahl” distribution, are also present. Motivated by these observations, the present paper considers a tenuous plasma with Maxwellian ions, and electrons described by a summation of an isotropic Maxwellian distribution and an isotropic Kappa distribution. The formalism of weak turbulence theory is utilized in order to discuss the spectra of electrostatic waves that must be present in such a plasma, satisfying the conditions of quasi-equilibrium between the processes of spontaneous fluctuations and of induced emission. The kappa index and relative density of the Kappa electron distribution are varied. By taking into account the effects due to electromagnetic waves into the weak turbulence formalism, we investigate the electromagnetic spectra that satisfy the conditions of “turbulent equilibrium,” and also the time evolution of the wave spectra and of the electron distribution, which occurs in the case of the presence of an electron beam in the electron distribution.

Kaguya observations of the lunar wake in the terrestrial foreshock: Surface potential change by bow-shock reflected ions

There forms a tenuous region called the wake behind the Moon in the solar wind, and plasma entry/refilling into the wake is a fundamental problem of the lunar plasma science. High-energy ions and electrons in the foreshock of the Earth’s magnetosphere were detected at the lunar surface in the Apollo era, but their effects on the lunar night-side environment have never been studied. Here we show the first observation of bow-shock reflected protons by Kaguya (SELENE) spacecraft in orbit around the Moon, confirming that solar wind plasma reflected at the terrestrial bow shock can easily access the deepest lunar wake when the Moon stays in the foreshock (We name this mechanism ‘type-3 entry’). In a continuous type-3 event, low-energy electron beams from the lunar night-side surface are not obvious even though the spacecraft location is magnetically connected to the lunar surface. On the other hand, in an intermittent type-3 entry event, the kinetic energy of upward-going field-aligned electron beams decreases from ∼ 80 eV to ∼ 20 eV or electron beams disappear as the bow-shock reflected ions come accompanied by enhanced downward electrons. According to theoretical treatment based on electric current balance at the lunar surface including secondary electron emission by incident electron and ion impact, we deduce that incident ions would be accompanied by a few to several times higher flux of an incident electron flux, which well fits observed downward fluxes. We conclude that impact by the bow-shock reflected ions and electrons raises the electrostatic potential of the lunar night-side surface.

TEC variations and ionospheric disturbances during the magnetic storm in March 2015 observed from continuous GPS data in the Southeast Asia region

TEC variations and ionospheric disturbances during the magnetic storm in March 2015 observed from continuous GPS data in the Southeast Asia region

Instability of field-aligned electron–cyclotron waves in a magnetic mirror plasma with anisotropic temperature

Dispersion characteristics have been analysed for field-aligned electron–cyclotron waves (also known as right-hand polarized waves, extraordinary waves or whistlers) in a cylindrical magnetic mirror plasma including electrons with anisotropic temperature. It is shown that the instability of these waves is possible only in the range below the minimal electron–cyclotron frequency, which is much lower than the gyrotron frequency used for electron–cyclotron resonance power input into the plasma, under the condition where the perpendicular temperature of the resonant electrons is larger than their parallel temperature. The growth rates of whistler instability in the two magnetized plasma models, where the stationary magnetic field is either uniform or has a non-uniform magnetic mirror configuration, are compared.

Transient, small-scale field-aligned currents in the plasma sheet boundary layer during storm time substorms.

We report on field‐aligned current observations by the four Magnetospheric Multiscale (MMS) spacecraft near the plasma sheet boundary layer (PSBL) during two major substorms on 23 June 2015. Small‐scale field‐aligned currents were found embedded in fluctuating PSBL flux tubes near the separatrix region. We resolve, for the first time, short‐lived earthward (downward) intense field‐aligned current sheets with thicknesses of a few tens of kilometers, which are well below the ion scale, on flux tubes moving equatorward/earthward during outward plasma sheet expansion. They coincide with upward field‐aligned electron beams with energies of a few hundred eV. These electrons are most likely due to acceleration associated with a reconnection jet or high‐energy ion beam‐produced disturbances. The observations highlight coupling of multiscale processes in PSBL as a consequence of magnetotail reconnection.

Spontaneous focusing of plasma flow in a weak perpendicular magnetic field

Structure formation of high-beta plasma flow in a perpendicular magnetic field is investigated in the ion kinetic regime by a fully kinetic particle-in-cell simulation. We demonstrate that directional plasma flow is spontaneously focused to form a sharp density structure. The primary focusing process comes from field-aligned electron inflow associated with the whistler mode and plasma confinement due to a self-generated magnetic field. The resulting concave magnetic field lines modulate ion gyration to cause a secondary focusing process with significant plasma concentration. Required conditions for these processes are determined by a dimensionless parameter α ≡ βi0(ΔW/ρi0), where βi0, ΔW, and ρi0 denote the plasma kinetic beta, window size, and ion gyration radius, respectively. The focusing process is apparent for small α, whereas diamagnetic expansion is dominant for large α. This condition describes a transition between diamagnetic cavity formation and the focusing process.