Electron Velocity Distribution Function Research Articles

Kinetic and thermodynamic approach to precisely solve the unsteady Rayleigh flow problem of a rarefied homogeneous charged gas under external force influence

Abstract An extension and further development of our previous article [J. Non-equilibrium Thermodyne. 37 (2012), 119–141] is presented. We study the irreversible non-equilibrium thermodynamics (INT) properties of the exact solution to the dilute homogeneously charged gas problem with unsteady Rayleigh flow. In contrast to previous research, the charged gas flows under the influence of an external force, the flat plate oscillates, and the displacement current term is considered, leading to significant advancements in understanding natural plasma dynamics. We are solving the Boltzmann kinetic equation (BKE) Krook model supplemented by Maxwell’s equations. We used a travelling wave and moments method with an electron velocity distribution function (EVDF). To the best of our knowledge, as three new scientific achievements, we introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and fluxes variables, Equations (28–40) and (50–54). Second, we determined, with reasonable accuracy, the thermodynamic equilibrium time of electrons, t equ = 26.7955, under an external force. We clarify the difference between equilibrium EVDF and perturbed EVDF and take advantage of BKE to account for non-equilibrium thermodynamic principles. For diamagnetic and paramagnetic plasmas, the extended Gibbs equation predicts ratios between various contributions to the internal energy change (IEC) is presented. A standard laboratory argon plasma model is used to apply the results.

Role of spontaneous thermal emissions in inflationary laser Raman instability

The role of thermal fluctuations on the stimulated Raman backscattering instability is investigated by means of Vlasov and particle-in-cell (PIC) simulations in a regime of strong linear Landau damping of the Langmuir wave. The instability is initially convective and amplifies thermal noise, leading to a low-amplitude back-scattered laser sideband. Linear Landau damping of the Langmuir sideband modifies and flattens the electron velocity distribution function at the resonant velocity, leading to a gradual decrease in the Landau damping rate and an increase in the convective amplification. The Langmuir wave traps electrons resulting in a rapid nonlinear absolute instability and large amplitude flashes of backscattered light off large amplitude Langmuir waves with trapped electrons, leading to the production of hot electrons. Conditions for simulating realistic thermal noise with Vlasov and PIC simulations are discussed and defined.

Intermittency, bursty turbulence, and ion and electron phase-space holes formation in collisionless current-carrying plasmas

In the previous studies of nonlinear saturation of the Buneman instability caused by high electron drift velocity relative to ions, the phase-space holes and the plateau on the electron velocity distribution function were identified as features of the saturation stage of instability [notably in the paper by Omura et al., J. Geophys. Res. 108, 1197 (2003)]. We have performed a much longer simulation of the Buneman instability and observed a secondary instability. This secondary instability generates fast electron-acoustic waves. By analyzing the phase-space plot of ions and electrons, we show that the fast electron heating and the formation of the plateau of electron velocity distribution function are not due to the quasi-linear diffusion but due to the nonlinear interaction of ion- and electron-acoustic solitary waves (phase-space holes) by exchange of trapped electrons in each wave. We also report the details on the intermittent and bursty nature of turbulence driven by this instability.

Non-Thermal Solar Wind Electron Velocity Distribution Function.

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal "core" population plus a tenuous energetic "halo" population. At first, such a feature was empirically fitted with the kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of the non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi-equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but, unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously emitted thermal fluctuations and the background turbulence leads to the formation of a non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment.

Suprathermal Electron Transport in the Solar Wind: Effects of Coulomb Collisions and Whistler Turbulence

The nature and radial evolution of solar wind electrons in the suprathermal energy range are studied. A wave–particle interaction tensor and a Fokker–Planck Coulomb collision operator are introduced into the kinetic transport equation describing electron collisions and resonant interactions with whistler waves. The diffusion tensor includes diagonal and off-diagonal terms, and the Coulomb collision operator applies to arbitrary electron velocities describing collisions with both background protons and electrons. The background proton and electron densities and temperatures are based on previous turbulence models that mediate the supersonic solar wind. The electron velocity distribution functions and electron heat flux are calculated. Comparison and analysis of the numerical results with analytical solutions and observations in the near-Sun region are made. The numerical results reproduce well the creation of the sunward electron deficit observed in the near-Sun region. The deficit of the electron velocity distribution function below the core Maxwellian fit at low velocities results from Coulomb collisions, and the excess part above the core Maxwellian fit at high velocities is determined by strong wave–particle interactions.

Loss cone effects and monotonic sheath conditions of a partially magnetized plasma sheath

In this Letter, we propose the conditions for monotonic plasma sheaths adjacent to a floating wall in the presence of an applied, oblique magnetic field. The electron velocity distribution function (VDF) at the sheath edge obtained from a kinetic model exhibits a loss cone shaped truncation. Using an approximation of the truncated VDF, we derive an analytical framework of the sheath edge condition (i.e., Bohm condition), namely, the relation of ion injection velocity and sheath potential drop as a function of the magnetic field angle. The results show that the sheath edge velocity and total potential drop decrease for a steady-state sheath, which eventually collapses when the magnetic field lines become parallel to the wall.

The Regulation of the Solar Wind Electron Heat Flux by Wave–Particle Interactions

The solar wind electrons carry a significant heat flux into the heliosphere. The weakly collisional state of the solar wind implicates collisionless processes as the primary factor that constrains nonthermal features of the velocity distribution function (VDF), including the heat flux. Previous observational work suggests that the electron VDF sometimes becomes unstable to the whistler wave, but reliance on model VDFs (e.g., drifting bi-Maxwellians) has proven insufficient for an exact description of the behavior of the solar wind electrons—in particular, the regulation of the heat flux. The characterization of these processes requires methods to obtain fine details of the VDF and quantification of the impact of kinetic processes on the VDF. We employ measurements of the electron VDF by Solar Orbiter’s Solar Wind Analyser and of the magnetic field by the Radio and Plasma Waves instrument to study an unstable solar wind electron configuration. Through a Hermite–Laguerre expansion of the VDF, we implement a low-pass filter in velocity space to remove velocity space noise and obtain a VDF suitable for analysis. With our method, we directly measure the instability growth rate and the rate of change of the electron heat flux through wave–particle interactions.

Study of the Electron Velocity Distribution Function in Weakly Ionized Radiofrequency Plasma

Study of the Electron Velocity Distribution Function in Weakly Ionized Radiofrequency Plasma

Excitation characterization of whistler waves and electrostatic oscillation in asymmetric magnetic reconnection

Utilizing the 2.5D Particle-in-Cell (PIC) method, we observe that large-amplitude whistler waves are present near the separatrix on the magnetospheric side and in the outflow region during asymmetric magnetic reconnection. Minimum variance analyses confirm their quasi-parallel and anti-parallel propagation to the background magnetic field, respectively, and their accuracy is validated through parallel Poynting fluxes (S∥). The excited whistler waves have intermittent property due to the evolution and movement of the reconnection layer. Wave-Particle Interaction Analysis (WPIA) reveals a pronounced energy conversion between the waves and electrons. Our simulation results demonstrate that whistler waves near the separatrix are excited by the cyclotron resonance duo to the instability of electron beam by analyzing the electron velocity distribution functions (VDFs). Meanwhile, the electrostatic oscillation is generated by the positive parallel drift of electron beam. However, the whistler waves in the outflow region are excited by the Landau resonance duo to anisotropic instability distributions of electron beam-mode.

Spacecraft Floating Potential Measurements for the Wind Spacecraft

Analysis of 8,804,545 electron velocity distribution functions, observed by the Wind spacecraft near 1 au between 2005 January 1 and 2022 January 1, was performed to determine the spacecraft floating potential, ϕ sc. Wind was designed to be electrostatically clean, which helps keep the magnitude of ϕ sc small (i.e., ∼5–9 eV for nearly all intervals) and the potential distribution more uniform. We observed spectral enhancements of ϕ sc at frequencies corresponding to the inverse synodic Carrington rotation period with at least three harmonics. The two-dimensional histogram of ϕ sc versus time also shows at least two strong peaks, with a potential third, much weaker peak. These peaks vary in time, with the intensity correlated with solar maximum. Thus, the spectral peaks and histogram peaks are likely due to macroscopic phenomena like coronal mass ejections (solar cycle dependence) and stream interaction regions (Carrington rotation dependence). The values of ϕ sc are summarized herein and the resulting data set is discussed.

Measurements of electron velocity distribution function in microwave cathode plume by incoherent laser Thomson scattering

This paper reports the development of a method of using incoherent laser Thomson scattering (LTS) to directly measure the electron velocity distribution function (EVDF) within a plasma plume. In this method, a 532 nm wavelength laser is injected into a plasma and Thomson scattering is detected with a CCD camera and a triple-monochromator. First, the measurement settings (e.g., laser power, number of integrations, and data analysis) were validated through a comparison between a microwave cathode and a hollow cathode. The results indicate that lower laser power is required as the photo-ionization from the metastable state particles increases the Thomson scattering. Second, the EVDFs of the microwave cathode at the plume were investigated for various anode currents and propellant flow rates. The results suggest that the non-Maxwellian EVDF was clearly observed at the low propellant flow rate, and the propellant flow rate is a more important parameter for the non-Maxwellian EVDFs than the anode current.

Using Direct Laboratory Measurements of Electron Temperature Anisotropy to Identify the Heating Mechanism in Electron-Only Guide Field Magnetic Reconnection.

Anisotropic electron heating during electron-only magnetic reconnection with a large guide magnetic field is directly measured in a laboratory plasma through insitu measurements of electron velocity distribution functions. Electron heating preferentially parallel to the magnetic field is localized to one separatrix, and anisotropies of 1.5 are measured. The mechanism for electron energization is identified as the parallel reconnection electric field because of the anisotropic nature of the heating and spatial localization. These characteristics are reproduced in a 2D particle-in-cell simulation and are also consistent with numerous magnetosheath observations. A measured increase in the perpendicular temperature along both separatrices is not reproduced by our 2D simulations. This work has implications for energy partition studies in magnetosheath and laboratory reconnection.

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.

Precision electron measurements in the solar wind at 1 au from NASA’s Wind spacecraft

Context. The non-equilibrium characteristics of electron velocity distribution functions (eVDFs) in the solar wind are key to understanding the overall plasma thermodynamics as well as the origin of the solar wind. More generally, they are important in understanding heat conduction and energy transport in all weakly collisional plasmas. Solar wind electrons are not in local thermodynamic equilibrium, and their multicomponent eVDFs develop various non-thermal characteristics, such as velocity drifts in the proton frame and temperature anisotropies as well as suprathermal tails and heat fluxes along the local magnetic field direction. Aims. This work aims to characterize precisely and systematically the nonthermal characteristics of the eVDF in the solar wind at 1 au using data from the Wind spacecraft. Methods. We present a comprehensive statistical analysis of solar wind electrons at 1 au using the electron analyzers of the 3D-Plasma instrument on board Wind. This work uses a sophisticated algorithm developed to analyze and characterize separately the three populations – core, halo and strahl – of the eVDF up to super-halo energies (2 keV). This algorithm calibrates these electron measurements with independent electron parameters obtained from the quasi-thermal noise around the electron plasma frequency measured by Wind’s Thermal Noise Receiver (TNR). The code determines the respective set of total electron, core, halo, and strahl parameters through non-linear least-square fits to the measured eVDF, properly taking into account spacecraft charging and other instrumental effects, such as the incomplete sampling of the eVDF by particle detectors. Results. We use four years, approximately 280 000 independent measurements, of core, halo, and strahl electron parameters to investigate the statistical properties of these different populations in the slow and fast solar wind. We discuss the distributions of their respective densities, drift velocities, temperature, and temperature anisotropies as functions of solar wind speed. We also show distributions with solar wind speed of the total density, temperature, temperature anisotropy, and heat flux of the total eVDF, as well as those of the proton temperature, proton-to-electron temperature ratio, proton-β and electron-β. Intercorrelations between some of these parameters are also discussed. Conclusions. The present data set represents the largest, high-precision collection of electron measurements in the pristine solar wind at 1 au. It provides a new wealth of information on electron microphysics. Its large volume will enable future statistical studies of parameter combinations and their dependences under different plasma conditions.

An improved calculation scheme of electron flow in a propagator method for solving the Boltzmann equation

In order to accurately evaluate the electron acceleration process in the calculation of the time evolution of the electron velocity distribution function (EVDF) based on the Boltzmann equation, an improved scheme blending upwind and central differences is introduced into the propagator method (PM). While the previous PM based on the upwind scheme needs fine cells to obtain an accurate EVDF at low electric fields, the improved PM is robust against coarse cells, which allows the reduction of cell resolution. Calculations of the EVDF in Ar under RF electric fields demonstrated that the blending scheme can provide satisfactorily accurate results even with cells about tenfold larger than the upwind case at low reduced electric fields below 1 Td, which leads to much shorter computational time because the reduction in the number of cells satisfactorily compensates for the complexity of the blending scheme. This technique has been built into a new user-friendly PM software named BOSPROM.

Inertial and anisotropic pressure effects on cross-field electron transport in low-temperature magnetized plasmas

In this paper, a one-dimensional (1D) particle-in-cell Monte Carlo collision (PIC-MCC) model is developed to investigate the effects of anisotropic pressure and inertial terms due to non-Maxwellian velocity distribution functions on cross-field electron transport. The conservation of momentum is evaluated by taking the moments of the first-principles gas-kinetic equation. A steady-state discharge is obtained without any low-frequency ionization oscillations by considering an anomalous electron scattering profile. The results obtained from the 1D PIC-MCC model are compared with fluid models, including the quasi-neutral drift-diffusion (DD), non-neutral DD, and full fluid moment models. The discharge current obtained from the PIC-MCC model is in good agreement with the fluid models. The cross-field electron transport due to the inertial terms, i.e. the gradient of axial and azimuthal drift, is evaluated. Moreover, PIC-MCC simulation results show non-zero, anisotropic, off-diagonal pressure tensor terms due to asymmetric non-Maxwellian electron velocity distribution function, potentially contributing to cross-field electron transport.

Control of Spectral and Polarization Properties of Quasiunipolar Terahertz Pulses in Strongly Nonequilibrium Magnetized Plasma Channels

The possibility to control both spectral and polarization properties of seed THz pulses in strongly nonequilibrium elongated magnetized plasma channels formed via intense UV femtosecond laser pulses in nitrogen (air) is analyzed. The physical mechanism of THz pulse control is based on cyclotron resonance, which can strongly reconstruct electrodynamical plasma features and, in particular, its ability to amplify the radiation of different spectral bands and polarization states. In particular, the formation of quasiunipolar pulses with a non-zero electric area and a specific polarization state is discussed. This study is based on the self-consistent solution of the kinetic Boltzmann equation for the electron velocity distribution function (EVDF) in the plasma channel and the second-order wave equation for THz pulse propagation.

Numerical strategy for solving the Boltzmann equation with variable E/N using physics-informed neural networks

A novel strategy to solve the Boltzmann equation with variable reduced electric field by using an artificial neural network (ANN) is introduced, where is the electric field and is the gas number density. In this method, the ANN learns the electron velocity distribution function (EVDF) for arbitrary in the Boltzmann equation. Thus, the ANN can calculate the EVDFs in the training range of without additional training. For validation of the ANN, the EVDFs in each Ar and SF6 gas were calculated with the trained ANN. The electron energy distribution function and electron transport coefficients calculated from the EVDF quantitatively agree with those from another ANN for a single and those from a Monte Carlo simulation, proving the validity of the present method.

Detailed composition of iron ions in interplanetary coronal mass ejections based on a multipopulation approach

Context. Coronal mass ejections (CMEs) are extremely dynamical, large-scale events in which plasma – but not only the coronal plasma – is ejected into interplanetary space. If a CME is detected in situ by a spacecraft located in the interplanetary medium, it is then called an interplanetary coronal mass ejection (ICME). This solar activity has been studied widely since coronagraphs were first flown into space in the early 1970s. Aims. Charge states of heavy ions reflect important information about the coronal temperature profile due to the freeze-in effect and it is estimated that iron ions freeze in at heights of ∼5 solar radii. However, the measured charge-state distribution of iron ions cannot be composed of only one single group of plasma. To identify the different populations of iron charge-state composition of ICMEs and determine their sources, we developed a model that independently uses two, three, and four populations of iron ions to fit the measured charge-state distribution in ICMEs detected by the Advanced Composition Explorer (ACE) at 1 AU. Methods. Three parameters are used to identify a certain population, namely freeze-in temperature, relative abundance, and kappa value (κ), which together describe the potential non-Maxwellian kappa distributions of coronal electrons. Our method chooses the reduced chi-squared to describe the goodness of fit of the model to the observations. The parameters of our model are optimized with the covariance-matrix-adaptation evolution strategy (CMA-ES). Results. Two major types of ICMEs are identified according to the existence of hot material, and both, that is, the cool type and the hot type, have two main subtypes. Different populations in those types have their own features related to freeze-in temperature and κ. The electron velocity distribution function usually contains a significant hot tail in typical coronal material and hot material, while the Maxwellian distribution appears more frequently in mid-temperature material. Our model is also suitable for all types of solar wind and the existence of hot populations as well as the change of temperatures of individual populations may indicate boundaries between ICMEs and individual solar wind streams.

Multi-dimensional incoherent Thomson scattering system in PHAse Space MApping (PHASMA) facility.

A multi-dimensional incoherent Thomson scattering diagnostic system capable of measuring electron temperature anisotropies at the level of the electron velocity distribution function (EVDF) is implemented on the PHAse Space MApping facility to investigate electron energization mechanisms during magnetic reconnection. This system incorporates two injection paths (perpendicular and parallel to the axial magnetic field) and two collection paths, providing four independent EVDF measurements along four velocity space directions. For strongly magnetized electrons, a 3D EVDF comprised of two characteristic electron temperatures perpendicular and parallel to the local magnetic field line is reconstructed from the four measured EVDFs. Validation of isotropic electrons in a single magnetic flux rope and a steady-state helicon plasma is presented.