Electron Distribution Function Research Articles

Quantifying the diffusion of suprathermal electrons by whistler waves between 0.2 and 1 AU with Solar Orbiter and Parker Solar Probe

Context. The evolution of the solar wind electron distribution function with heliocentric distance exhibits different features that are still unexplained, in particular, the fast decrease in the electron heat flux and the increase in the Strahl pitch angle width. Wave-particle interactions between electrons and whistler waves are often proposed to explain these phenomena. Aims. We aim to quantify the effect of whistler waves on suprathermal electrons as a function of heliocentric distance. Methods. We first performed a statistical analysis of whistler waves (occurrence and properties) observed by Solar Orbiter and Parker Solar Probe between 0.2 and 1 AU. The wave characteristics were then used to compute the diffusion coefficients for solar wind suprathermal electrons in the framework of quasi-linear theory. These coefficients were integrated to deduce the overall effect of whistler waves on electrons along their propagation. Results. About 110 000 whistler wave packets were detected and characterized in the plasma frame, including their direction of propagation with respect to the background magnetic field and their radial direction of propagation. Most waves are aligned with the magnetic field and only ∼0.5% of them have a propagation angle greater than 45°. Beyond 0.3 AU, it is almost exclusively quasi-parallel waves propagating anti-sunward (some of them are found sunward but are within switchbacks with a change of sign of the radial component of the background magnetic) that are observed. Thus, these waves are found to be Strahl-aligned and not counter-streaming. At 0.2 AU, we find both Strahl-aligned and counter-streaming quasi-parallel whistler waves. Conclusions. Beyond 0.3 AU, the integrated diffusion coefficients show that the observed waves are sufficient to explain the measured Strahl pitch angle evolution and effective in isotropizing the halo. Strahl diffusion is mainly attributed to whistler waves with a propagation angle of θ ∈ [15.45]°, although their origin has not yet been fully determined. Near 0.2 AU, counter-streaming whistler waves are able to diffuse the Strahl electrons more efficiently than the Strahl-aligned waves by two orders of magnitude.

Laboratory observation of electron energy distribution near three-dimensional magnetic nulls

The acceleration of electrons near three-dimensional (3D) magnetic nulls is crucial to the energy conversion mechanism in the 3D magnetic reconnection process. To explore electron acceleration in a 3D magnetic null topology, we constructed a pair of 3D magnetic nulls in the PKU Plasma Test (PPT) device and observed acceleration of electrons near magnetic nulls. This study measured the plasma floating potential and ion density profiles around the 3D magnetic null. The potential wells near nulls may be related to the energy variations of electrons, so we measured the electron distribution functions (EDFs) at different spatial positions. The axial variation of EDF shows that the electrons deviate from the Maxwell distribution near magnetic nulls. With scanning probes that can directionally measure and theoretically analyze based on curve fitting, the variations of EDFs are linked to the changes of plasma potential under 3D magnetic null topology. The kinetic energy of electrons accelerated by the electric field is 6 eV ( ) and the scale of the region where accelerating electrons exist is in the order of serval electron skin depths.

Development of the ambipolar electric field in a compressed current sheet and the impact on magnetic reconnection

Satellite data analysis of a compressed gyro-scale current sheet prior to magnetic reconnection in the magnetotail shows that electrostatic lower hybrid waves localized to the region of a transverse ambipolar electric field at the centre of the current sheet are driven by $\boldsymbol{E} \times \boldsymbol{B}$ velocity shear and result from compression. The presence and location of shear-driven waves around the centre of the current sheet, where the magnetic field reverses and the density gradient is minimal, is consistent with our model. This is notable because the free energy source is the curvature of the electron $\boldsymbol{E} \times \boldsymbol{B}$ flow and not the density gradient. Laboratory experiments and particle-in-cell (PIC) simulations have shown that shear-driven lower hybrid fluctuations are capable of producing anomalous cross-field transport (viscosity) and resistivity, which can trigger magnetic reconnection. We estimate the terms in the generalized Ohm's Law directly from MMS data as the spacecraft cross a gyro-scale current sheet. Our analysis shows that the wave effects (resistivity, diffusion and viscosity) and pressure anisotropy effects are comparable. We also find that the quasi-static electric field gradient is correlated with a non-gyrotropic electron distribution function, which is consistent with our model. Furthermore, theoretical arguments suggest agyrotropy is an indicator of the possibility for magnetic reconnection to occur.

Field reversal in low pressure, unmagnetized radio frequency capacitively coupled argon plasma discharges

In general, the radio frequency (rf) electric field within a sheath points toward the metal electrode in low pressure, unmagnetized rf electropositive capacitively coupled plasma (CCP) glow discharges. This is due to the large ratio of electron to ion mobility and the formation of an ion sheath. In this work, we studied, using fully kinetic particle-in-cell simulations, a reversed electric field induced by the strong secondary electron emission during the phase of sheath collapse in a high-voltage rf-driven low pressure CCP glow discharge. We explored the transition behavior of the formation of field reversal as a function of driving voltage amplitude and found that field reversal starts to form at around 750 V, for a discharge with an electrode spacing of 4 cm at 10 mTorr argon pressure driven at 13.56 MHz. Accordingly, the energy distribution function of electrons incident on the electrode shows peaks from around 3 to 10 eV while varying the driving voltage from 150 to 2000 V, showing potentially beneficial effects in plasma material processing where relatively directional electrons are preferred to solely thermal diffusion electrons.

Source of Radio Emissions Induced by the Galilean Moons Io, Europa and Ganymede: In Situ Measurements by Juno

AbstractAt Jupiter, part of the auroral radio emissions are induced by the Galilean moons Io, Europa and Ganymede. Until now, except for Ganymede, they have been only remotely detected, using ground–based radio–telescopes or electric antennas aboard spacecraft. The polar trajectory of the Juno orbiter allows the spacecraft to cross the range of magnetic flux tubes which sustain the various Jupiter–satellite interactions, and in turn to sample in situ the associated radio emission regions. In this study, we focus on the detection and the characterization of radio sources associated with Io, Europa and Ganymede. Using electric wave measurements or radio observations (Juno/Waves), in situ electron measurements (Juno/JADE–E), and magnetic field measurements (Juno/MAG) we demonstrate that the Cyclotron Maser Instability (CMI) driven by a loss–cone electron distribution function is responsible for the encountered radio sources. We confirmed that radio emissions are associated with Main (MAW) or Reflected Alfvén Wing (RAW), but also show that for Europa and Ganymede, induced radio emissions are associated with Transhemispheric Electron Beam (TEB). For each traversed radio source, we determine the latitudinal extension, the CMI–resonant electron energy, and the bandwidth of the emission. We show that the presence of Alfvén perturbations and downward field–aligned currents are necessary for the radio emissions to be amplified.

Coulomb Blockade in a Nonthermalized Quantum Dot.

We investigate nonequilibrium transport properties of a quantum dot in the Coulomb blockade regime under the condition of negligible inelastic scattering during the dwelling time of the electrons in the dot. Using the quantum kinetic equation we show that the absence of thermalization leads to a double step in the distribution function of electrons on the dot, provided that it is symmetrically coupled to the leads. This drastically changes nonlinear transport through the dot resulting in an additional (compared to the thermalized case) jump in the conductance at voltages close to the charging energy, which could serve as an experimental manifestation of the absence of thermalization.

Investigation of EDF evolution and charged particle transport in E × B plasma based negative ion sources using kinetic simulations

A spatially varying transverse magnetic filter field (TMF) is present in an E times B plasma-based negative ion source to improve negative ion yield. The TMF strength ranges from 1 to 10 mT, causing the plasma electrons to become magnetized while leaving the ions either unmagnetized or partially magnetized. As a consequence, plasma drift, particle trapping, double layer (DL), and instabilities are observed in a negative ion source. The transport of plasma through the TMF is influenced by these phenomena, subsequently affecting the energy distribution functions (EDFs) of both electrons and ions in the plasma. Measurement of EDFs in such systems is a challenging task due to the presence of a strong magnetic field. To address this, a 2D-3V Particle-in-Cell Monte Carlo Collision (PIC MCC) model is employed to study the spatio-temporal evolution of the EDFs separately for electrons and ions. The electron EDF (EEDF) remains Maxwellian, while ion EDF (IEDF) gradually transitions to non-Maxwellian as measurements are taken closer to the TMF region. The present study reveals that the IEDF is more sensitive to the operational conditions compared to the EEDF, as evidenced by the changes observed in both EDFs under different plasma operational conditions.

The shape of the electron and muon lateral distribution functions of extensive air showers

The shape of the electron and muon lateral distribution functions of extensive air showers

Hybrid Fluid Model for Calculating Electron Transport in Air in Strong Electric Fields

The hybrid fluid model for calculating electron transport in air is presented. Within the model, the transport of electrons with energies less than 300 eV is calculated based on the drift-diffusion equation, and in the high-energy range, it is calculated using a set of multigroup equations for the first two moments of the electron distribution function: the balance equations for concentrations and electron flux densities. The hybrid model presented is intended to be used for numerical simulations of electric discharge processes in air proceeding with the participation of runaway electrons. The results of numerical simulations of electron transport in air in homogeneous and inhomogeneous electric fields, which were performed using the hybrid model, were compared with the corresponding results of simulations obtained using the Monte Carlo method.

κmonty: a Monte Carlo Compton scattering code including non-thermal electrons

ABSTRACT Low-luminosity active galactic nuclei are strong sources of X-ray emission produced by Compton scattering originating from the accretion flows surrounding their supermassive black holes. The shape and energy of the resulting spectrum depend on the shape of the underlying electron distribution function (DF). In this work, we present an extended version of the grmonty code, called κmonty. The grmonty code previously only included a thermal Maxwell–Jütner electron DF. We extend the grmonty code with non-thermal electron DFs, namely the κ and power-law DFs, implement Cartesian Kerr–Schild coordinates, accelerate the code with mpi, and couple the code to the non-uniform adaptive mesh refinement grid data from the general relativistic magnetohydrodynamics code bhac. For the Compton scattering process, we derive two sampling kernels for both DFs. Finally, we present a series of code tests to verify the accuracy of our schemes. The implementation of non-thermal DFs opens the possibility of studying the effect of non-thermal emission on previously developed black hole accretion models.

Attenuation characteristics analysis of the THz circularly polarized waves in inhomogeneous fully ionized dusty plasma using FPL model

When the hypersonic vehicle is flying, the plasma in the area near the stagnation point of the front end of the vehicle can be approximately seen as the fully ionized dusty plasma. Due to the existence of dust particles, dusty plasma affects the communication quality of the hypersonic vehicle. In this paper, the general Boltzmann equation applicable to dusty plasmas containing electrons and the Fokker–Planck–Landau collision model are combined to derive a general formula for the electron distribution function of fully ionized dusty plasmas. Considering the contribution of the collision effect and charging effect to the dispersion relationship of fully ionized dusty plasma, the dielectric constant of fully ionized dusty plasma under an external magnetic field is solved. The Wentzel–Kramers–Brillouin method is used to calculate the attenuation coefficient (α) of the THz wave in fully ionized dusty plasma, and the influence of the external magnetic field strength and other dusty plasma parameters on the attenuation characteristics of the THz circularly polarized wave is analyzed. The research results show that the α of the THz left-hand circularly polarized wave decreases with the increase in the external magnetic field strength, while the α of the THz right-hand circularly polarized wave increases. In addition, increasing the dust particle radius, dust particle density, and electron density in a certain frequency range can increase the α of the THz circularly polarized waves. These research results provide theoretical guidance for the exploration of the interaction mechanism between the THz waves and fully ionized dusty plasma.

Influence of the ambipolar field on the formation of electron phase flows in the positive column of a glow discharge in a nitrogen-like gas

The formation of the electron energy distribution function (EEDF) and phase flows of electrons in the plasma of a positive column of a glow discharge in a model gas with strong vibrational excitation, similar to molecular nitrogen, is analyzed in a wide pressure range. It is found that the traditional local approximation for calculating the EEDF can only be used at medium gas pressures, when the characteristic size of the plasma volume exceeds electron energy relaxation length in the entire range of electron energies. With a decrease in gas pressure, a new phenomenon is discovered—merging the phase flow streamlines into a single line on the coordinate-energy phase plane in the energy region of the of vibrational excitation threshold. It is shown that the combination of a strong electron sink at the threshold of vibrational excitation and the deceleration of electrons in an ambipolar field lead to a practical ‘vanishing’ of the component of the phase electron flux upward in energy. As a result, the streamlines of electron phase flow approach to some approximately straight line of constant kinetic energy close to the threshold energy of vibrational excitation. The formation of this feature on the phase plane correlates with the predominant escape to the walls of electrons with kinetic energy equal to the threshold of vibrational excitation.

Feasibility of the EDICAM camera for runaway electron detection in JT-60SA disruptions

The visible camera system EDICAM (Event Detection Intelligent Camera), recently installed on JT-60SA, is simulated to assess whether it can be used for measuring synchrotron radiation from relativistic runaway electrons. In this simulation, the SOFT synthetic synchrotron diagnostic framework is used to compute the synthetic synchrotron camera images from a JT-60SA-like disruption modelled with the DREAM disruption simulation code. In the studied scenario, a large amount of argon is added to the plasma, and a disruption is simulated by starting a prescribed exponential temperature drop and finishing with further cooling provided by the argon in a self-consistent simulation of the current quench. The background plasma evolution is calculated by DREAM self-consistently with the fast electron population, which is modelled kinetically. The resulting runaway electron distribution function along with the parameters of the EDICAM visible camera system are used as an input to the SOFT framework to assess the feasibility of the camera for runaway electron detection. We find that the runaway electron beam formed in the disruption can produce synchrotron radiation observable by the EDICAM system, thus enabling the use of the EDICAM for the characterization of runaway electron beams.

Monte Carlo study of electron–electron scattering effects in FET channels

In this work, we study the effect of electron–electron scattering on the high-energy tail of the electron distribution function in FET channels. A new Monte Carlo algorithm for solving a two-particle kinetic equation in the presence of a position-dependent electric field is proposed. In stationary bulk simulations, no visible effect of electron–electron scattering on the distribution function and consequently on its moments is observed. In stationary device simulations, however, a clear effect on the high-energy tail can be seen. The enhancement of the tail relative to the thermal tail is found to scale with the electron concentration.

Nonlinear saturation of whistler modes driven by runaway electrons

Runaway electrons exhibit kinetic instabilities with potentially beneficial consequences. The anomalous Doppler resonance between the electrons and whistler modes is a primary underlying mechanism. These instabilities require a first-principle nonlinear theoretical analysis, which would ultimately enable assessment of their impact on disruption mitigation and diagnostics, especially in ITER-relevant conditions. This paper presents recent progress in developing the required theoretical framework for isolated nonlinear resonances. By employing the generic bump-on-tail model, we predict the wave saturation levels in both near-threshold and strongly driven regimes. Remarkably, for the waves of interest, the parallel component of the wave vector dictates the parallel momentum of the resonant particles. This feature, together with the expected wave saturation level, provides a complete description of the resonance impact on the runaway electron distribution function. We show that the parametric dependence of the nonlinearly saturated mode provides a way to recover certain features of the runaway momentum distribution function.

Electrostatic lower hybrid turbulence due to magnetic islands and particle heating in magnetopause reconnection regions

This investigation presents a model to understand the magnetopause turbulence in the lower hybrid frequency range at reconnection regions as observed by the magnetospheric multiscale mission. We have modeled 3D electrostatic lower hybrid wave (LHW) in cold magnetized plasma in the presence of magnetic islands. In this model, we have developed the modified nonlinear Schrödinger equation, contemplating that nonlinear effects are due to ponderomotive force. The dynamical equation of the system thus obtained is solved using numerical simulation techniques. The simulation results illustrate the formation and evolution of localized structures and the current sheets. Due to the nonlinear effects and magnetic reconnection, the current sheets become turbulent with time. A semi-analytical model is also given to illustrate the scale size of current sheets. The turbulent power spectra have also been studied. The spectral index of the power spectrum is found to be −2.7 (approximately) in the perpendicular direction and −2.2 (approximately) in the parallel direction, indicating anisotropy. Using the Folker–Plank diffusion equation with the new velocity space diffusion coefficient, we find the distribution function of energetic electrons due to these turbulent structures. We propose that LHW may be responsible for plasma heating in magnetopause.

Kinetic Equilibrium of Two-dimensional Force-free Current Sheets

Force-free current sheets are local plasma structures with field-aligned electric currents and approximately uniform plasma pressures. Such structures, widely found throughout the heliosphere, are sites for plasma instabilities and magnetic reconnection, the growth rate of which is controlled by the structure’s current-sheet configuration. Despite the fact that many kinetic equilibrium models have been developed for one-dimensional force-free current sheets, their two-dimensional (2D) counterparts, which have a magnetic field component normal to the current sheets, have not received sufficient attention to date. Here, using particle-in-cell simulations, we search for such 2D force-free current sheets through relaxation from an initial, magnetohydrodynamic equilibrium. Kinetic equilibria are established toward the end of our simulations, thus demonstrating the existence of kinetic force-free current sheets. Although the system currents in the late equilibrium state remain field aligned as in the initial configuration, the velocity distribution functions of both ions and electrons systematically evolve from their initial drifting Maxwellians to their final time-stationary Vlasov state. The existence of 2D force-free current sheets at kinetic equilibrium necessitates future work in discovering additional integrals of motion of the system, constructing the kinetic distribution functions, and eventually investigating their stability properties.

Electrostatic upper-hybrid mode instability driven by a ring electron distribution

Quasi electrostatic fluctuations in the upper-hybrid frequency range are commonly detected in the planetary magnetospheric environment. The origin of such phenomena may relate to the instability driven by a loss-cone feature associated with the electrons populating the dipole-like magnetic field. The present paper carries out a one-dimensional electrostatic particle-in-cell simulation accompanied by a reduced quasilinear kinetic theoretical analysis to investigate the dynamics of the upper-hybrid mode instability driven by an initial ring electron distribution function, which is a form of loss-cone distribution. A favorable comparison is found between the two approaches, which shows that the reduced quasilinear theory, which is grounded in the concept of a model of the particle distribution function that is assumed to maintain a fixed mathematical form except that the macroscopic parameters that define the distribution are allowed to evolve in time, can be an effective tool in the study of plasma instabilities, especially if it is guided by and validated against the more rigorous simulation result.

RAIKOU (来光): A General Relativistic, Multiwavelength Radiative Transfer Code

We present a general relativistic radiative transfer code RAIKOU (来光) for multiwavlength studies of spectra and images including the black hole shadows around Kerr black holes. Important radiative processes in hot plasmas around black holes, i.e., (cyclo-)synchrotron, bremsstrahlung emission/absorption, and Compton/inverse-Compton scattering, are incorporated. The Maxwell–Jüttner and single/broken power-law electron distribution functions are implemented to calculate the radiative transfer via both thermal and nonthermal electrons. Two calculation algorithms are implemented for studies of the images and broadband spectra. An observer-to-emitter ray-tracing algorithm, which inversely solves the radiative transfer equation from the observer screen to emitting plasmas, is suitable for an efficient calculations of the images, e.g., the black hole shadows observed by the Event Horizon Telescope, and spectra without Compton effects. On the other hand, an emitter-to-observer Monte Carlo algorithm, by which photons are transported with a Monte Carlo method including the effects of Compton/inverse-Compton scatterings, enables us to compute multiwavelength spectra, with their energy bands broadly ranging from radio to very high energy gamma-ray. The X-ray black hole shadows, which are formed via synchrotron emission and inverse-Compton scattering processes and will be observed in the future X-ray interferometry missions, can be also computed with this algorithm. The code is generally applicable to accretion flows around Kerr black holes with relativistic jets and winds/coronae with various mass accretion rates (i.e., radiatively inefficient accretion flows, super-Eddington accretion flows, and others). We demonstrate an application of the code to a radiatively inefficient accretion flow onto a supermassive black hole.

Electron heating in kinetic-Alfvén-wave turbulence.

We report analytical and numerical investigations of subion-scale turbulence in low-beta plasmas using a rigorous reduced kinetic model. We show that efficient electron heating occurs and is primarily due to Landau damping of kinetic Alfvén waves, as opposed to Ohmic dissipation. This collisionless damping is facilitated by the local weakening of advective nonlinearities and the ensuing unimpeded phase mixing near intermittent current sheets, where free energy concentrates. The linearly damped energy of electromagnetic fluctuations at each scale explains the steepening of their energy spectrum with respect to a fluid model where such damping is excluded (i.e., a model that imposes an isothermal electron closure). The use of a Hermite polynomial representation to express the velocity-space dependence of the electron distribution function enables us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.