Electron Distribution Function Research Articles

The Adiabatic 1D Kinetic Equilibrium of the Electron Diffusion Region During Anti‐Parallel Magnetic Reconnection

AbstractAn earlier model of the electron distribution function accounts for the pressure anisotropy that develops in the inflow regions during anti‐parallel magnetic reconnection. However, the model is not applicable to the electron diffusion region (EDR), where the electron magnetic moments break as an adiabatic invariant. The earlier model is here generalized through the use of the current‐sheet adiabatic invariant of a 1D current layer, to become applicable also to the EDR. The new generalized model reproduces the main features of the EDR and its vicinity observed in a fully kinetic simulation, formally proving the 1D equilibrium relationship between the upstream electron pressure anisotropy and the EDR electron jets.

A New Type of Jovian Hectometric Radiation Powered by Monoenergetic Electron Beams

AbstractIn this study, we statistically analyze the Jovian auroral radio sources detected in situ by Juno/Waves at frequencies f below the electron cyclotron frequency fce. We first conduct a survey of Juno/Waves data over 1–40 MHz from 2016 to 2022. The 15 detected HectOMetric (HOM) sources all lie within 1–5 MHz and are both less frequent than the radio sources commonly observed slightly above fce and clustered in the southern hemisphere, within ∼90–270° longitudes. We analyze these emission regions with a growth rate analysis in the framework of the Cyclotron Maser Instability (CMI), which we apply to JADE‐E high cadence electron measurements. We show that the f < fce emissions correspond to crossed radio sources, ∼300 km wide. They are located in a hot and highly depleted auroral plasma environment, along flux tubes colocated with upward field‐aligned current and at the equatorward edge of the main auroral oval. The wave amplification is consistent with the CMI and its free energy source consists of a shell‐type electron distribution function (EDF) with characteristic energies of 0.2–5keV. More energetic, 5–50 keV, shell‐type EDFs were systematically observed at higher latitudes but without any radio counterpart. Various parameters for the f < fce HOM sources, reminiscent of the ones at Earth/Saturn, are compared. Other CMI‐unstable EDFs, primarily loss cone ones, are systematically observed during the same intervals, giving rise to emission observed at fce < f < fce + 0.5%. Our analysis thus reveals that different portions of the same EDF can be CMI‐unstable and simultaneously amplify radio waves below and above fce.

Numerical characterization of capacitively coupled plasma driven by tailored frequency modulated radio frequency source

Capacitively coupled plasma (CCP) is widely used in plasma etching and deposition processes because of its low cost, simple structure, and easy generation of a uniform plasma in large areas. Conventional CCPs are operated under a fixed frequency power source; however, CCPs driven by a variable frequency power source are poorly understood. In this paper, numerical simulations of CCPs driven by frequency modulated (FM) radio frequency (RF) sources within the frequency range of 2 MHz–18 MHz are carried out with a particle-in-cell/Monte Carlo collision model. Our research indicates that the CCP driven by an FM RF source can maintain a stable glow discharge and form a time-dependent plasma. Plasma density, electron and ion current, energy and heating rate, ion flux, and energy on the electrodes fluctuate consistently with the FM period. The electron and ion energy distribution function can also be modulated by the frequency variation of the FM source. A multi-peak structure that varies and shifts with frequency variation is observed in the ion energy distribution function. In addition, by fixing the chirp period while varying the start or end frequency of the chirp signal (start frequency from 0.4 to 6 MHz, or end frequency from 18 to 48 MHz), effective modulations can be produced on the electron density, electron energy, and the shape of the EEPF and IEDF.

Presheath-like structures and effusive particle losses for biased probes at and near I–V electron saturation

A theory for presheath-like structures near probes biased at and above the plasma potential is developed for collisionless plasmas with an electron-neutral mean free path on the order of the chamber scale. The theory predicts presheath-like perturbations to the plasma that result from the free streaming of electrons and an effusion loss process from the chamber at the electrode. For these situations, a loss-cone-like velocity distribution function for electrons is predicted where the loss angle of the depletion region corresponds to the angular size of the electrode at a specified distance. The angle of the loss cone becomes 180° at the sheath edge. In comparison with a previous collisional electron presheath model that required electrons satisfy a Bohm criterion at the sheath edge [Scheiner et al., Phys. Plasmas 22, 123520 (2015)], the present work suggests that no such condition is needed for collisionless low pressure plasmas in the ≲10 mTorr range. The theory predicts the generation of a density depletion of roughly 0.5ne and an electron velocity moment of tens of percent of the electron thermal speed by the sheath edge in a presheath with a potential drop of less than Ti/e. The range of this presheath perturbation is determined by the electrode geometry instead of the collisional mean free path. These predictions are tested against previously published particle in cell simulations and are found to be in good agreement.

Impacts of nonthermal emission on the images of a black hole shadow and extended jets in two-temperature GRMHD simulations

The recent 230\,GHz observations from the Event Horizon Telescope (EHT) collaboration are able to image the innermost structure of the M87 galaxy showing the shadow of the black hole, a photon ring, and a ring-like structure that agrees with thermal synchrotron emission from the accretion disc. However, at lower frequencies, M87 is characterized by a large-scale jet with clear signatures of nonthermal emission. It is necessary to explore the impacts of nonthermal emission on black hole shadow images and extended jets, especially at lower frequencies. In this study, we aim to compare models with different electron heating prescriptions to one another and to investigate how these prescriptions and nonthermal electron distributions may affect black hole shadow images and the broadband spectrum energy distribution (SED) function. We performed general relativistic radiative transfer (GRRT) calculations in various two-temperature general relativistic magnetohydrodynamic (GRMHD) models utilizing different black hole spins and different electron heating prescriptions coupled with different electron distribution functions (eDFs). Through a comparison with GRRT images and SEDs, we found that when considering a variable kappa eDF, the parameterized prescription of the $R- electron temperature model with h $ = 1 is similar to the model with electron heating in the morphology of images, and the SEDs at a high frequency. This is consistent with previous studies using the thermal eDF. However, the nuance between them could be differentiated through the diffuse extended structure seen in GRRT images, especially at a lower frequency, and the behavior of SEDs at low frequency. The emission from the nearside jet region is enhanced in the case of electron heating provided by magnetic reconnection and it will increase if the contribution from the regions with stronger magnetization is included or if the magnetic energy contribution to kappa eDF mainly in the magnetized regions is considered. Compared with the thermal eDF, the peaks of the SEDs shift to a lower frequency when we consider nonthermal eDF.

Generation of relativistic electrons at the termination shock in the solar flare region

Solar flares are accompanied by an enhanced emission of electromagnetic waves from the radio up to the gamma -ray range. The associated hard X-ray and microwave radiation is generated by energetic electrons. These electrons play an important role, since they carry a substantial part of the energy released during a flare. The flare is generally understood as a manifestation of magnetic reconnection in the corona. The so-called standard CSHKP model is one of the most widely accepted models for eruptive flares. The solar flare event on September 10, 2017 offers us a unique opportunity to study this model. The observations from the Expanded Owens Valley Solar Array (EOVSA) show that approx 1.6 times 104 electrons with energies $>$ 300 keV are generated in the flare region. There are signatures in solar radio and extreme ultraviolet (EUV) observations as well as numerical simulations that a “termination shock” (TS) appears in the magnetic reconnection outflow region. Electrons accelerated at the TS can be considered to generate the loop-top hard X-ray sources. In contrast to previous studies, we investigate whether the heating of the plasma at the TS provides enough relativistic electrons needed for the hard X-ray and microwave emission observed during the solar X8.2 flare on September 10, 2017. We studied the heating of the plasma at the TS by evaluating the jump in the temperature across the shock by means of the Rankine-Hugoniot relationships under coronal circumstances measured during the event on September 10, 2017. The part of relativistic electrons was calculated in the heated downstream region. In the magnetic reconnection outflow region, the plasma is strongly heated at the TS. Thus, there are enough energetic electrons in the tail of the electron distribution function (EDF) needed for the microwave and hard X-ray emission observed during the event on September 10, 2017. The generation of relativistic electrons at the TS is a possible mechanism of explaining the enhanced microwave and hard X-ray radiation emitted during flares.

How electrons still guard the space: Electron number distribution functions based on QTAIM∩ELF intersections.

Despite the importance of the one-particle picture provided by the orbital paradigm, a rigorous understanding of the spatial distribution of electrons in molecules is still of paramount importance to chemistry. Considerable progress has been made following the introduction of topological approaches, capable of partitioning space into chemically meaningful regions. They usually provide atomic partitions, for example, through the attraction basins of the electron density in the quantum theory of atoms in molecules (QTAIM) or electron-pair decompositions, as in the case of the electron localization function (ELF). In both cases, the so-called electron distribution functions (EDFs) provide a rich statistical description of the electron distribution in these spatial domains. Here, we take the EDF concept to a new fine-grained limit by calculating EDFs in the QTAIM ∩ ELF intersection domains. As shown in AHn systems based on main group elements, as well as in the CO, NO, and BeO molecules, this approach provides an exquisitely detailed picture of the electron distribution in molecules, allowing for an insightful combination of the distribution of electrons between Lewis entities (such as bonds and lone pairs) and atoms at the same time. Besides mean-field calculations, we also explore the impact of electron correlation through Hartree-Fock (HF), density functional theory (DFT) (B3LYP), and CASSCF calculations.

Kinetic plasma-wall interaction using immersed boundary conditions

The interaction between a plasma and a solid surface is studied in a (1D-1V) kinetic approach using immersed boundary conditions and penalization to model the wall. Two solutions for the penalized wall region are investigated that either allow currents to flow within the material boundary or not. Essential kinetic aspects of sheath physics are recovered in both cases and their parametric dependencies investigated. Importantly, we show how the two approaches can be reconciled when accounting for relevant kinetic effects. Non-Maxwellian features of the ion and electron distribution functions are essential to capture the value of the potential drop in the sheath. These features lead to a sheath heat transmission factor for ions 60% larger than usually predicted and 35% for electrons. The role of collisions is discussed and means of incorporating minimally-relevant kinetic sheath physics in the gyrokinetic framework are discussed.

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.