Electron Velocity Distribution Research Articles

Wave breaking field of relativistically intense electrostatic waves in electronegative plasma with super-thermal electrons

The wave breaking limit of relativistically intense electrostatic waves in an unmagnetised electronegative plasma, where electrons are alleged to attach onto neutral atoms or molecules and thus forming a significant amount of negative ions, has been studied analytically. A nonlinear theory has been developed, using one-dimensional (1D) relativistic multi-fluid model in order to study the roles of super-thermal electrons, negative ion species and the Lorentz factor, on the dynamics of the wave. A generalised kappa-type distribution function has been chosen for the velocities of the electrons, to couple the densities of the fluids. By assuming the travelling wave solution, the equation of motion for the evolution of the wave in a stationary wave frame has been derived and numerical solutions have been presented. Studies have been further extended, using standard Sagdeev pseudopotential method, to discover the maximum electric field amplitude sustained by these waves. The dependence of wave breaking limit on the different input parameters such as the Lorentz factor, electron temperature, spectral index of the electron velocity distribution and on the fraction and the mass ratio of the negative to positive ion species has been shown explicitly. The wavelength of these waves has been calculated for a wide range of input parameters and its dependence on aforementioned plasma parameters have been studied in detail. These results are relevant to understand particle acceleration and relativistic wave breaking phenomena in high intensity laser plasma experiments and space environments where the secondary ion species and super-thermal electrons exist.

Physics-informed neural networks for solving the Boltzmann equation of the electron velocity distribution function in weakly ionized plasmas

The equilibrium electron velocity distribution function (EVDF) and electron transport coefficient in weakly ionized plasmas under crossed DC uniform electric and magnetic fields are calculated via the Boltzmann equation (BE) using physics-informed neural networks (PINNs). The latent solution of the BE is represented by an artificial neural network, and then the neural network is trained to respect the BE. By leveraging automatic differentiation, no mesh generation in velocity space is required, allowing us to calculate the three-dimensional EVDF properly with 0.01% of memory capacity required for the conventional mesh-based method. The EVDF and electron transport coefficients in SF6 calculated from the PINNs are benchmarked by comparing with those calculated from the Monte Carlo simulation (MCS). In most cases, the relative difference between the electron transport coefficient calculated from the PINNs and MCS is found to be within 1%.

On the electron sheath theory and its applications in plasma–surface interactions

In this work, an improved understanding of electron sheath theory is provided using both fluid and kinetic approaches while elaborating on their implications for plasma–surface interactions. A fluid model is proposed considering the electron presheath structure, avoiding the singularity in electron sheath Child–Langmuir law which overestimates the sheath potential. Subsequently, a kinetic model of electron sheath is established, showing considerably different sheath profiles in respect to the fluid model due to non-Maxwellian electron velocity distribution function and finite ion temperature. The kinetic model is then further generalized and involves a more realistic truncated ion velocity distribution function. It is demonstrated that such a distribution function yields a super-thermal electron sheath whose entering velocity at the sheath edge is greater than the Bohm criterion prediction. Furthermore, an attempt is made to describe the electron presheath–sheath coupling within the kinetic framework, showing a necessary compromise between a realistic sheath entrance and the inclusion of kinetic effects. Finally, the secondary electron emissions induced by sheath-accelerated plasma electrons in an electron sheath are analysed and the influence of backscattering is discussed.

Effects of non‐thermality and plasma parameters on dust‐ion‐acoustic shock waves

AbstractThe nonlinear characteristics of dust‐ion‐acoustic shock waves (DIASHWs) in a plasma consisting of charge‐fluctuating dust, inertial ions, and non‐Maxwellian electrons is examined. In particular, the electron velocity distribution function (VDF) is assumed to follow Kappa and Cairns distributions. In this regard, a reductive perturbation (RP) approach (in a weakly nonlinear limit) is used to derive the corresponding Burger's equation, and, from its solution, the effects of various physical parameters, for example, non‐thermal indices, number density, and temperature ratios, on the properties of shock waves are investigated. It is observed that the magnitude of the shock reduces as ion‐electron temperature ratio increases and vice versa. Furthermore, when the ion to electron (equilibrium) density ratio increases, the shock profile gets steepened. The resultant potential amplitude as well as the shock width is also shown to be strongly related to the spectral indices, namely κ and α in the case of Kappa‐ and Cairns‐distributed electrons, respectively. Hence, the potential distribution is strongly affected by the non‐thermal nature of the electron VDF. The relevant Maxwellian results are recovered in the limiting cases, namely κ → ∞ and α → 0. The present study will be useful in understanding the nonlinear propagation of DIASHWs in non‐thermal (space and laboratory) plasmas.

Electron velocity distribution on the abrupt change in source–drain current of GaN devices

An analytical model of the channel electron energy distribution in an on-state GaN transistor has been proposed based on the assumption that drift velocities of channel electrons obey the two-dimensional Maxwell–Boltzmann distribution. The validity of such an assumption was confirmed by Monte Carlo simulation. It was found that there could be a larger number of high-energy channel electrons whose energy is higher than the intervalley energy between [Formula: see text] and [Formula: see text] valleys in a GaN transistor with a high electron temperature. The fraction of hot electrons with its energy higher than the intervalley energy between [Formula: see text] and [Formula: see text] valleys to the total channel electrons can easily reach 50% when the electron temperature is higher than 3000 K. Such an electron temperature in a GaN transistor had been determined in experiments. Thus, hot electrons in the [Formula: see text] valley can transit into [Formula: see text] valleys. It suggests that intervalley transitions could be one possible physical origin of the abrupt change in the source−drain current in GaN devices. The proposed model can well explain how an abrupt change in the source–drain current in GaN transistor experiments depends on the voltage-dependent gate, the trap, etc.

Wave Emission of Nonthermal Electron Beams Generated by Magnetic Reconnection

Magnetic reconnection in solar flares can efficiently generate nonthermal electron beams. The energetic electrons can, in turn, cause radio waves through microscopic plasma instabilities as they propagate through the ambient plasma along the magnetic field lines. We aim at investigating the wave emission caused by fast-moving electron beams with characteristic nonthermal electron velocity distribution functions (EVDFs) generated by kinetic magnetic reconnection: two-stream EVDFs along the separatrices and in the diffusion region, and perpendicular crescent-shaped EVDFs closer to the diffusion region. For this purpose, we utilized 2.5D fully kinetic Particle-In-Cell code simulations in this study. We found the following: (1) the two-stream EVDFs plus the background ions are unstable to electron/ion (streaming) instabilities, which cause ion-acoustic waves and Langmuir waves due to the net current. This can lead to multiple-harmonic plasma emission in the diffusion region and the separatrices of reconnection. (2) The perpendicular crescent-shaped EVDFs can cause multiple-harmonic electromagnetic electron cyclotron waves through the electron cyclotron maser instabilities in the diffusion region of reconnection. Our results are applicable to diagnose the plasma parameters, which are associated to magnetic reconnection in solar flares by means of radio wave observations.

Implications of Kappa Suprathermal Halo of the Solar Wind Electrons

The electron velocity distributions measured in-situ in space plasmas reveal two central populations, a low-energy and highly dense (quasi-)thermal core, and a more diffuse but hotter suprathermal halo. Even if the core contributes much more to the total number density than the suprathermal particles, the energetic electrons play an important role in the higher moments. Using a dataset of more than 120,000 solar wind observations of electron distributions, measured in the ecliptic between 0.35 and 3.3 AU, we investigate here the main characteristics of the halo population and its potential influence on the core, and macroscopic properties of electrons, i.e., number density (n), bulk velocity (u), temperature (T) and temperature anisotropy (T⊥/Τ//). The analysis indicates that the parameters exhibit interdependence trends characterized by correlations between certain of these parameters and the kappa exponent (κ) corresponding to the power law of the halo population tail. The links between low kappa and low number densities (of both the core and halo populations) confirm that Coulomb collisions can be quite ineffective even at low radial distances if the density of the plasma is sufficiently low. Moreover, halo populations with lower values of κ are also associated to higher temperature anisotropies, and to higher bulk velocity. An interdependence between core and halo populations is also suggested by an apparent (inverse) correlation between their density and temperature ratios. We further show relations between the parameters fitting the sum of a Maxwellian core and a Kappa halo, and those of a global (single) Kappa fit that incorporates both the core and halo components. Such a global Kappa is used in an exospheric model of the solar wind, to predict the influence of suprathermal electrons on the characteristics of the solar wind. These results should stimulate future detailed analysis of these relationships and correlations, which may contribute to a realistic modeling of the solar wind and the formation and evolution of suprathermal populations.

Design of Thomson scattering diagnostic system on linear magnetized plasma device

In addition to the magnetic confinement fusion plasma, Thomson scattering has been applied to measure electron density and temperature of low-temperature plasmas. Based on a linear magnetized plasma device, a set of Thomson scattering diagnostic system is designed to diagnose the plasma with and eV. Due to low plasma temperature and density, this diagnostic system needs high spectral resolution and collection efficiency to meet the requirements of electron velocity distribution function measurements. Through the bench test, it is confirmed that the spectral resolution reaches 0.01 nm, and theoretical collection efficiency is high enough to obtain a Thomson scattering spectrum by 1000 accumulations.

Electron Weibel instability induced magnetic fields in optical-field ionized plasmas

Generation and amplification of magnetic fields in plasmas is a long-standing topic that is of great interest to both plasma and space physics. The electron Weibel instability is a well-known mechanism responsible for self-generating magnetic fields in plasmas with temperature anisotropy and has been extensively investigated in both theory and simulations, yet experimental verification of this instability has been challenging. Recently, we demonstrated a new experimental platform that enables controlled initialization of highly nonthermal and/or anisotropic plasma electron velocity distributions via optical-field ionization. Using an external electron probe bunch from a linear accelerator, the onset, saturation, and decay of the self-generated magnetic fields due to electron Weibel instability were measured for the first time to our knowledge. In this paper, we will first present experimental results on time-resolved measurements of the Weibel magnetic fields in non-relativistic plasmas produced by Ti:Sapphire laser pulses (0.8 μm) and then discuss the feasibility of extending the study to a quasi-relativistic regime by using intense CO2 (e.g., 9.2 μm) lasers to produce much hotter plasmas.

The Role of Core and Strahlo Electrons Properties on the Whistler Heat-Flux Instability Thresholds in the Solar Wind

There is wide observational evidence that electron velocity distribution functions (eVDF) observed in the solar wind generally present enhanced tails and field-aligned skewness. These properties may induce the excitation of electromagnetic perturbations through the whistler heat-flux instability (WHFI), that may contribute to a non-collisional regulation of the electron heat-flux values observed in the solar wind via wave-particle interactions. Recently, a new way to model the solar wind eVDF has been proposed: the core-strahlo model. This representation consist in a bi-Maxwellian core plus a Skew-Kappa distribution, representing the halo and strahl electrons as a single skewed distribution. The core-strahlo model is able to reproduce the main features of the eVDF in the solar wind (thermal core, enhanced tails, and skewness), with the advantage that the asymmetry is controlled by only one parameter. In this work we use linear kinetic theory to analyze the effect of solar wind electrons described by the core-strahlo model, over the excitation of the parallel propagating WHFI. We use parameters relevant to the solar wind and focus our attention on the effect on the linear stability introduced by different values of the core-to-strahlo density and temperature ratios, which are known to vary throughout the Heliosphere. We also obtain the stability threshold for this instability as a function of the electron beta and the skewness parameter, which is a better indicator of instability than the heat-flux macroscopic moment, and present a threshold conditions for the instability that can be compared with observational data.

Three-dimensional modeling of intense unipolar THz pulses formation during their amplification in nonequilibrium extended Xe plasma channel

We develop a three-dimensional (3D) fully self-consistent model for analysis of an ultrashort THz pulse propagation and amplification in a nonequilibrium plasma channel formed in xenon by a femtosecond UV laser pulse. The model is based on the self-consistent solution of a second order wave equation in the cylindrical geometry and the kinetic Boltzmann equation for the electron velocity distribution function (EVDF) at different points of the spatially inhomogeneous nonequilibrium plasma channel. We analyze the wide range of plasma and seed pulse parameters and reveal the optimal regimes for producing high intensity outgoing THz fields as well as highly unipolar THz pulses within the proposed mechanism. It is demonstrated that the process of EVDF relaxation in plasma limits the amplification of THz pulses at the level of ∼10^{7}W/cm^{2}. Both focusing features of nonequilibrium plasma and the possibility of producing THz pulses with a high degree of unipolarity are confirmed for the case of 3D geometry.

Characteristics of an Annular Electron Flow Formed by an Electron Gun With a Field Emitter

Characteristics of annular electron flow formed in electron gun with a multitip field emitter were determined experimentally and by numerical simulations, and the possibility to achieve electron beam current up to 75 mA was demonstrated. The gun performance was stable in technical vacuum conditions—at the pressure of ~10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−7</sup> torr. Electron velocity distributions in a flow on transverse and longitudinal components were determined. It was shown that the relative root-mean-square transverse velocity spread varied with radial coordinate within the annular beam wall from ca. 6% to 30%, while the total spread in the electron flow was about 60%.

Gap Formation Around 0.5Ωe in the Whistler‐Mode Waves Due To the Plateau‐Like Shape in the Parallel Electron Distribution: 2D PIC Simulations

AbstractThe power gap around 0.5Ωe (where Ωe is the equatorial electron gyrofrequency) of whistler‐mode waves is commonly observed in the Earth's inner magnetosphere, but its generation mechanism is still under debate. By performing two‐dimensional particle‐in‐cell simulations in a uniform background magnetic field, we investigate the spectral properties of whistler‐mode waves excited by temperature anisotropic electrons. The waves have positive growth rates in a wide range of normal angles (θ ≈ 0°–35°), resulting in the generation of both parallel and nonparallel waves. Although the nonparallel wave modes are weaker than the parallel ones, they can cause the plateau‐like shape around 0.5 VAe (where VAe represent the electron Alfven speed) in the parallel direction of electron velocity distribution. The plateau‐like electron component can then lead to severe damping in the waves around 0.5Ωe via the cyclotron resonance, and the power gap is formed. This mechanism is called as “spectrum bite”. Our study sheds fresh light on the well‐known gap formation at ∼0.5Ωe in the whistler‐mode waves, which is ubiquitously detected near the equator in the inner magnetosphere.

The bipolar charge plasma spectrometer (BCPS) based on the 2π-field-of-view double-channel electrostatic analyzer.

In this paper, we propose a bipolar charge plasma spectrometer based on the double-channel electrostatic analyzer for simultaneously measuring thermal ions and electrons with a 2π hemispherical field-of-view. Both ions and electrons within the wide field-of-view enter the spectrometer, pass through the variable geometric factor channel, and are then separated by the double-channel electric fields. Two microchannel plates are accommodated at the exit of the analyzer for ion and electron detection. The main performance of the spectrometer has been obtained from on-ground calibration. With the electrostatic deflectors and the cylindrically symmetric structure, the spectrometer provides simultaneous measurements of thermal ion and electron velocity distributions with a shared field-of-view of 360° (azimuth angle) by 90° (elevation angle) and a broad energy range for both ions and electrons. The ion analyzer constant and the electron analyzer constant are 11.1 and 9.7, respectively. The detecting energy range of 33.3-44.4 keV for ions and 29.1-38.8 keV for electrons can be obtained by using the sweeping electrostatic analyzer voltage range of 3-4000 V. The ion and electron energy resolutions are 9.6% and 6.1%, respectively. The variable geometric factor function provides a large geometric factor adjusting range for both ion and electron measurements by two orders of magnitude, which fulfills the requirements of a large dynamic flux range for simultaneous measurements of space thermal plasma in the solar wind and magnetosphere.

Intermolecular Coulombic Decay in Liquid Water.

We report the first observation of intermolecular Coulombic decay (ICD) in liquid water following inner-valence ionization. By combining a monochromatized tabletop high-harmonic source with a liquid microjet, we record electron-electron coincidence spectra at two photon energies that identify the ICD electrons, together with the photoelectrons originating from the 2a_{1} inner-valence band of liquid water. Our results confirm the importance of ICD as a source of low-energy electrons in bulk liquid water and provide quantitative results for modeling the velocity distribution of the slow electrons that are thought to dominate radiation damage in aqueous environments.

Isentropic plasma sheath model for improved fidelity

A model is developed for a collisionless plasma sheath assuming isentropic electrons in contrast to the standard isothermal electron assumption. This approach is enabled by the approximation of a Maxwellian electron velocity distribution function across the sheath, which is justified by near wall measurements. The conservation of entropy leads to a modified Boltzmann relation and a modified Bohm criterion. The predicted floating sheath potential is in excellent agreement with experimental data. Takamura's model for a space-charge limited plasma sheath near an emissive surface is also modified for isentropic electrons and with that modification agrees well with numerical results from a full fluid plasma model.

Analysis of secondary emission mechanism in electron avalanches propagating in cylindrical nanoruptures in liquid water

Recently, a bouncing-like mechanism for electron multiplication inside long nano-ruptures during the early stages of nanosecond discharge in liquid water has been proposed in (Bonaventura 2021 Plasma Sources Sci. Technol. 30 065023). This mechanism leads to the formation of electron avalanches within nano-ruptures caused by strong electrostrictive forces. The avalanche propagation is a self-sustaining process: the electrons emitted from the water surface to the cavity support the propagation of the avalanche and the avalanche itself is a source of the parent electrons impinging on the surface of the nano-rupture and causing secondary emission. We analyze the process of the electron secondary emission directly from the simulation results of the electron avalanche propagation. This allow us to perform an in situ study of the secondary emission and related physical processes. We present the results of an extensive parametric study performed using the state-of-the-art simulation toolkit Geant4-DNA for modeling electron-liquid water interactions. It is shown that the typical lifetime of an electron in an avalanche is about 0.1 to 0.2 picoseconds and that the electron experiences about 4 bounces before ending up in liquid water. In addition, it is shown that the secondary electrons are formed in a layer adjacent to the nano-rupture surface that is only a few nanometres thin. The secondary electron velocity distribution at the moment of the electron birth, the velocity space of electrons (re-)emitted from the water, and the velocity space of electrons at the moment of their impact to the cavity surface are analyzed in detail. Electron bouncing and secondary electron generation efficiency are quantified using the secondary emission coefficient, the secondary emission efficiency, and the effective energy consumed to produce new electrons.

Electron-only reconnection and associated electron heating and acceleration in PHASMA

Using incoherent Thomson scattering, electron heating and acceleration at the electron velocity distribution function (EVDF) level are investigated during electron-only reconnection in the PHAse Space MApping (PHASMA) facility. Reconnection arises during the merger of two kink-free flux ropes. Both push and pull type reconnection occur in a single discharge. Electron heating is localized around the separatrix, and the electron temperature increases continuously along the separatrix with distance from the X-line. The local measured gain in enthalpy flux is up to 70% of the incoming Poynting flux. Notably, non-Maxwellian EVDFs comprised of a warm bulk population and a cold beam are directly measured during the electron-only reconnection. The electron beam velocity is comparable to, and scales with, electron Alfvén speed, revealing the signature of electron acceleration caused by electron-only reconnection. The observation of oppositely directed electron beams on either side of the X-point provides “smoking-gun” evidence of the occurrence of electron-only reconnection in PHASMA. 2D particle-in-cell simulations agree well with the laboratory measurements. The measured conversion of Poynting flux into electron enthalpy is consistent with recent observations of electron-only reconnection in the magnetosheath [Phan et al., Nature 557, 202 (2018)] at similar dimensionless parameters as in the experiments. The laboratory measurements go beyond the magnetosheath observations by directly resolving the electron temperature gain.

The Kinetic Expansion of Solar-wind Electrons: Transport Theory and Predictions for the Very Inner Heliosphere

Abstract We propose a transport theory for the kinetic evolution of solar-wind electrons in the heliosphere. We derive a gyro-averaged kinetic transport equation that accounts for the spherical expansion of the solar wind and the geometry of the Parker spiral magnetic field. To solve our three-dimensional kinetic equation, we develop a mathematical approach that combines the Crank–Nicolson scheme in velocity space and a finite-difference Euler scheme in configuration space. We initialize our model with isotropic electron distribution functions and calculate the kinetic expansion at heliocentric distances from 5 to 20 solar radii. In our kinetic model, the electrons evolve mainly through the combination of ballistic particle streaming, the magnetic mirror force, and the electric field. By applying fits to our numerical results, we quantify the parameters of the electron strahl and the core part of the electron velocity distributions. The strahl fit parameters show that the density of the electron strahl is around 7% of the total electron density at a distance of 20 solar radii, the strahl bulk velocity and strahl temperature parallel to the background magnetic field stay approximately constant beyond a distance of 15 solar radii, and β ∥s (i.e., the ratio of the strahl parallel thermal pressure to the magnetic pressure) is approximately constant with heliocentric distance at a value of about 0.02. We compare our results with data measured by the Parker Solar Probe. Furthermore, we provide theoretical evidence that the electron strahl is not scattered by the oblique fast-magnetosonic/whistler instability in the near-Sun environment.

Kinetic and thermodynamic examinations for the unsteady couette flow problem of a plasma using the BGK cylindrical model

We aim to investigate the kinetic and irreversible thermodynamic treatment of the Couette flow of gaseous plasma (GP) confined between two coaxial rotating circular rigid cylinders. The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann kinetic equation (BKE) is solved by applying the perturbation method coupled with the moments' approach with a two-stream Maxwellian distribution function (MDF). Nonlinear partial differential equations are precisely solved. As an actual application, we are considering the laboratory Argon GP. An interesting comparison between the non-equilibrium electron velocity distribution function (EVDF) and the equilibrium EVDF is made carefully with 3-Dimensional graphics in various time values. We found that the system goes to an equilibrium state (ES) with time compatible with Le Chatelier's principles. Moreover, we determined with very high precision the value of the system equilibrium time, which is tequ.≅2.4. That great advantage cannot be reached by solving other macroscopic magnetohydrodynamic models. The relations between the various macroscopic variables of the GP are studied. The irreversible non-equilibrium thermodynamics (NT) properties of the system are presented. We present the extended Gibbs equation (EGE) for the internal energy variation (IEV) in cylindrical geometry for GP for the first time, to the best of our knowledge. We have shown that our model is compatible with the H-theorem of Boltzmann and the Onsager-Casimir relations. The various participations in IEV are introduced. The significance of this search is due to its vast implementations in various fields, such as in GP physics, electrical engineering, medicine, biological systems, and numerous commercial and industrial deployments.