Electron Energy Distribution Research Articles

Heating mode transitions in capacitively coupled CF4 plasmas at low pressure

Abstract Capacitively coupled plasmas operated in CF4 at low pressure are frequently used for dielectric plasma etching. For such applications the generation of different ion and neutral radical species by energy dependent electron impact ionization and dissociation of the neutral background gas is important. These processes are largely determined by the space and time dependent electron energy distribution function and, thus, by the electron power absorption dynamics. In this work and based on a particle-in-cell/Monte Carlo collision model, we show that the electron heating mode in such plasmas is sensitive to changes of the gap at a constant pressure of 3 Pa. At a gap of 1.5 cm, the dominant mode is found to be a hybrid combination of the Drift-Ambipolar (DA) and the α-mode. As the gap is increased to 2 cm and 2.5 cm, the bulk power absorption and ambipolar power absorption decreases, and the DA mode decays. When the gap reaches 3 cm, the α-mode becomes more prominent, and at a gap of 3.75 cm the α-mode is dominant. These mode transitions are caused by a change of the electronegativity and are found to affect the discharge characteristics. The presence of the DA-mode leads to significant positive electron power absorption inside the bulk region and negative power absorption within the sheaths on time average, as electrons are accelerated from the bulk towards the collapsed sheath. The heating mode transitions result in a change from negative to positive total electron power absorption within the sheaths as the gap increases. When accounting for secondary electron emission, the transition of the heating mode can occur at shorter gaps due to the enhanced plasma density and decreased electronegativity.

Magnetic field and dielectric beads modulate DBD reduced electric field with discharge homogeneity to realize NOx differential conversion

In this paper, the reduced electric field and the discharge homogeneity of DBD were modulated by the magnetic field and the packed ZrO2 beads. Subsequently, the reduced electric field and the discharge homogeneity on discharge performance, de-NOx efficiency and NOx conversion mechanism were evaluated. The experimental results show that the reduced electric field gradually enhances as the magnetic field increases, promoting de-NOx performance. The discharge homogeneity significantly weakens with the length of packed ZrO2 beads increases, inhibiting the de-NOx performance. Compared to the reactor with the packed ZrO2 beads, the de-NOx efficiency of the reactor with a 0.2 T magnetic field can achieve 87.2 %, an improvement of 39.3 %. Meanwhile, the selectivity of NO2 and N2O are reduced by 18.3 % and 21 %, respectively. The de-NOx mechanisms indicate that the reduced electric field affects the electron collision reactions and the relative rate of the NOx conversion reactions by altering the electron energy distribution. The discharge homogeneity alters the degree of plasma mitigation of exhaust gases by regulating the absolute rate of the NOx conversion reactions. The by-product N2O is mainly dependent on the concentration of NO2 and is less sensitive to N2(A3). This work reveals the differential mechanisms of reduced electric field and discharge homogeneity on de-NOx.

Tracking ultrafast non-adiabatic dissociation dynamics of the deuterated water dication molecule.

We applied reaction microscopy to elucidate fast non-adiabatic dissociation dynamics of deuterated water molecules after direct photo-double ionization at 61eV with synchrotron radiation. For the very rare D+ + O+ + D breakup channel, the particle momenta, angular, and energy distributions of electrons and ions, measured in coincidence, reveal distinct electronic dication states and their dissociation pathways via spin-orbit coupling and charge transfer at crossings and seams on the potential energy surfaces. Notably, we could distinguish between direct and fast sequential dissociation scenarios. For the latter case, our measurements reveal the geometry and orientation of the deuterated water molecule with respect to the polarization vector that leads to this rare 3-body molecular breakup channel. Aided by multi-reference configuration-interaction calculations, the dissociation dynamics could be traced on the relevant potential energy surfaces and particularly their crossings and seams. This approach also unraveled the ultrafast time scales governing these processes.

Multifrequency Analysis of Favored Models for the Messier 87* Accretion Flow

The polarized images of the supermassive black hole Messier 87* (M87*) produced by the Event Horizon Telescope (EHT) provide a direct view of the near-horizon emission from a black hole accretion and jet system. The EHT theoretical analysis of the polarized M87* images compared thousands of snapshots from numerical models with a variety of spins, magnetization states, viewing inclinations, and electron energy distributions, and found a small subset consistent with the observed image. In this article, we examine two models favored by EHT analyses: a magnetically arrested disk with moderate retrograde spin and a magnetically arrested disk with high prograde spin. Both have electron distribution functions that lead to strong depolarization by cold electrons. We ray trace five snapshots from each model at 22, 43, 86, 230, 345, and 690 GHz to forecast future very long baseline interferometry (VLBI) observations and examine limitations in numerical models. We find that even at low frequencies where optical and Faraday rotation depths are large, approximately rotationally symmetric polarization persists, suggesting that shallow depths dominate the polarization signal. However, morphology and spectra suggest that the assumed thermal electron distribution is not adequate to describe emission from the jet. We find 86 GHz images show a ringlike shape determined by a combination of plasma and spacetime imprints, smaller in diameter than recent results from the Global mm-VLBI Array. We find that the photon ring becomes more apparent with increasing frequency, and is more apparent in the retrograde model, leading to large differences between models in asymmetry and polarization structure.

Helium metastable density determination in the COST reference source by absolutely calibrated optical emission spectroscopy

Helium metastable densities in the COST Reference Microplasma Jet are estimated for a variety of He/N2 admixtures and dissipated powers by applying a collisional-radiative model to absolutely calibrated optical emission spectroscopy measurements. This is accomplished by delineating the excitation mechanisms that result in the N2(C–B) and N2+(B–X) emission bands, the latter of which is strongly coupled to the presence of helium metastables. A number of other plasma parameters are established and discussed for each operating condition including the electron energy distribution function, reduced electric field, rate constants, and electron density. With these parameters, the reaction rates for the primary ionization pathways are also calculated, emphasizing the importance of helium metastables for discharge sustainment. Good agreement with the existing literature is found for most plasma parameters and for helium metastable densities, in particular. A clear [N2]−1 relationship between the nitrogen concentration and density of helium metastables is demonstrated, as has been identified in previous studies in analogous atmospheric pressure plasma jets. This validates the efficacy of this optical technique for determining helium metastable densities and establishes it as a viable, and in many cases, more accessible alternative to other means of quantifying helium metastables in low-temperature plasmas.

Machine learning-based prediction of the electron energy distribution function and electron density of argon plasma from the optical emission spectra

Machine learning-based prediction of the electron energy distribution function and electron density of argon plasma from the optical emission spectra

Impact of Scattering Foil Composition on Electron Energy Distribution in a Clinical Linear Accelerator Modified for FLASH Radiotherapy: A Monte Carlo Study.

This study investigates how scattering foil materials and sampling holder placement affect electron energy distribution in electron beams from a modified medical linear accelerator for FLASH radiotherapy. We analyze electron energy spectra at various positions-ionization chamber, mirror, and jaw-to evaluate the impact of Cu, Pb-Cu, Pb, and Ta foils. Our findings show that close proximity to the source intensifies the dependence of electron energy distribution on foil material, enabling precise beam control through material selection. Monte Carlo simulations are effective for designing foils to achieve desired energy distributions. Moving the sampling holder farther from the source reduces foil material influence, promoting more uniform energy spreads, particularly in the 0.5-10 MeV range for 12 MeV electron beams. These insights emphasize the critical role of tailored material selection and sampling holder positioning in optimizing electron energy distribution and fluence intensity for FLASH radiotherapy research, benefiting both experimental design and clinical applications.

Retraction Note to: Determination of Electron Energy Distribution Function in Tokamak Plasma

Retraction Note to: Determination of Electron Energy Distribution Function in Tokamak Plasma

Abnormal transition of the electron energy distribution with excitation of the second harmonic in low-pressure radio-frequency capacitively coupled plasmas

The self-excited second harmonic in radio-frequency capacitively coupled plasma was significantly enhanced by adjusting the external variable capacitor. At a lower pressure of 3 Pa, the excitation of the second harmonic caused an abnormal transition of the electron energy probability function, resulting in abrupt changes in the electron density and temperature. Such changes in the electron energy probability function as well as the electron density and temperature were not observed at the higher pressure of 16 Pa under similar harmonic changes. The phenomena are related to the influence of the second harmonic on stochastic heating, which is determined by both amplitude and the relative phase of the harmonics. The results suggest that the self-excited high-order harmonics must be considered in practical applications of low-pressure radio-frequency capacitively coupled plasmas.

Transmissions of an x-ray free electron laser pulse through Al: Influence of nonequilibrium electron kinetics.

A theoretical model for investigating the radiative transfer of an x-ray free electron laser (XFEL) pulse is developed based on a one-dimensional radiative transfer equation. The population dynamics of energy levels is obtained by rate equationapproximation coupling with the Fokker-Planck equation, in which the electron energy distribution function (EEDF) is self-consistently determined. As an illustrative example, XFEL pulse propagation through a solid-density aluminum (Al) is investigated. The characteristics of the temporal evolution of the x-ray pulse shape, level population, and EEDF are demonstrated. The EEDF usually has two parts in XFEL-Al interactions: the near equilibrium part in the lower energy regions and the nonequilibrium part in the higher energy region. The deep gap between the two parts is quickly filled in the solid-density Al plasma. The pulse shape is distorted and the duration shortens as the x-ray pulse propagates through the Al sample. The x-ray transmission spectra were compared with experimental and other theoretical results, and good agreement was found. There are slight discrepancies between the transmission obtained by solving the Fokker-Planck equationand Maxwellian assumptions because nonequilibrium electrons in the higher energy region account for only a small fraction of the total electrons.

New features in Franck–Hertz experiment with argon: experiment and Monte Carlo simulation

In this work, a homemade apparatus was built to perform the Franck–Hertz experiment with argon. The lowest energy state and the higher energy state of argon can be excited by the Franck–Hertz experiment. The excitation energies of the argon atom are measured by using the setup. The obtained higher excitation energy of argon atoms is 13.73 ± 0.28 eV, for the mixture of higher energy states 3s 23p 53d and 3s 23p 54p. A plate capacitor model was constructed to simulate the inelastic collisions between electrons and argon atoms using the Monte Carlo method. The simulated current curve and electron energy distribution agrees with that of Franck–Hertz experiments, especially the features of higher excited state. The Monte Carlo simulation indicates the deformed electron energy distribution results from the change in excitation proportion of energy levels during the collisions of electrons and argon atoms. Moreover, the new features in Franck–Hertz curve are ascribed to the higher excitation states of argon atoms. The experimental setup has been applied to undergraduate physics experiment teaching in college. Students can perform the Franck–Hertz curve measurement of not only the lowest excited state, but also the higher excited states of argon. In addition, students can do the Monte Carlo simulations for the experimental Franck–Hertz curves and gain a better understanding of electron-argon atom collisions in the experiment. The new designed experiment will make students more familiar with the quantum behavior in atomic physics and quantum mechanics course.

Study on Breakdown Characteristics and Attenuation Characteristics of Air Mixed Gas

Abstract Nowadays, the global demand for environmental protection and energy saving is getting higher and higher. In the past, SF6 gas was regarded as an environmentally unfriendly gas in the circuit breaker with SF6 gas as the insulating medium. In order to save energy and reduce emissions, this paper uses clean and environmentally friendly air as the arc extinguishing medium. The gas mixture studied contains N2, O2 and CO2. Through two approximate values of Boltzmann equation, we obtain the electron energy distribution function of air mixed gas under different electric field reduction conditions. By studying the changes of ionization and adsorption coefficients of particles under various collision conditions, we obtained the conversion breakdown field strength (E/N) Cr of air mixture. An arc attenuation model is built to characterize the arc attenuation characteristics using the prior transport characteristics as input. The arc attenuation process is broken down into three steps: heat recovery, pre-ignition, and arcing. All of these phases are determined by the changes in axial temperature and arc conductance over time. Analysis is done on the air and nitrogen thermal recovery and pre-dielectric recovery phases. This study explores the use of clean dielectrics to ensure optimum performance of primary equipment in the power system, based on current circumstances.

On fundamental inconsistencies in a commonly used modification of a fluid model for glow discharge

This work considers the fundamental contradictions in the concept of one of the most well-known and widely used modifications of the fluid model for simulation of a glow discharge (GD), the ‘local mean energy approximation’ (LMEA). In this model, it is proposed to determine the kinetic coefficients in the electron particle and energy balance equations as functions of the electron mean energy (temperature) rather than local electric field, using a one-to-one correspondence between these parameters through the electron Boltzmann equation. It is shown that the scope of applicability of this model, like any other modification of the fluid model, is limited by the local mode of formation of the electron energy distribution function (EEDF). Therefore, as demonstrated by the examples of typical 1D and 2D problems for a GD in argon, its extension to the region of nonlocal EEDF is in no way justified and leads not only to serious errors in the results, but also to a logically intractable situation in attempts to apply the main postulate of the LMEA model to the region of a weak (or even reverse) electric field in a negative glow plasma. At the same time, the apparent reliability of calculations within the framework of the LMEA model for a number of parameters, in our opinion, only slows down progress in modeling of gas discharge plasma.

Time-dependent electron Boltzmann equation for hypersonic plasmas

The electron kinetics in hypersonic plasmas is modeled by solving the time-dependent electron Boltzmann equation for the electron energy distribution function (EEDF). This plasma is created by strong shock compression of the gas in front of a vehicle moving with hypersonic speed. The main source of energy for the electrons is gas heating due to elastic collisions and second-kind collisions (de-excitation) from vibrationally excited states of N2. We established that the electron energy distribution function is most sensitive to vibrational level populations. At mid-altitudes (tens of kilometers), the electron temperature equilibrates with the vibrational temperature on a microsecond timescale. The electron distribution function reaches steady state on a comparable timescale. Numerical simulations of air plasma showed that the electron energy distribution function is far from Maxwellian and the collision rates differ by orders of magnitude from those computed with a Maxwellian distribution. The two most important parameters for the electron kinetics and the electron energy distribution function are the vibrational temperature and ionization degree.

Electron correlation effects in electron promotion processes during binary atomic collisions at solid surfaces

We report energy distributions of electrons emitted by Aluminum and Magnesium surfaces under the impact of singly charged neon ions with energies in the range 100–5000 eV, focusing on the Auger decay of electronic excitations produced during binary atomic collisions. The autoionization spectra of the projectiles show several peaks that are identified and assigned to specific collisional excitation processes. The data provide evidence for electron correlation effect that occur while the colliding atoms are still coupled in the quasi-molecular system and results in two-electron transitions.

Self-consistent calculation of the optical emission spectrum of an argon capacitively coupled plasma based on the coupling of particle simulation with a collisional-radiative model

We report the development of a computational framework for the calculation of the optical emission spectrum of a low-pressure argon capacitively coupled plasma (CCP), which is based on the coupling of a particle-in-cell/Monte Carlo collision simulation code with a diffusion-reaction-radiation code for Ar I excited levels. In this framework, the particle simulation provides the rates of the direct and stepwise electron-impact excitation and electron-impact de-excitation for 30 excited levels, as well as the rates of electron-impact direct and stepwise ionization. These rates are used in the solutions of the diffusion equations of the excited species in the second code, along with the radiative rates for a high number of Ar-I transitions. The calculations also consider pooling ionization, quenching reactions, and radial diffusion losses. The electron energy distribution function and the population densities of the 30 excited atomic levels are computed self-consistently. The calculations then provide the emission intensities that reproduce reasonably well the experimentally measured optical emission spectrum of a symmetric CCP source operated at 13.56 MHz with 300 V peak-to-peak voltage, in the 2–100 Pa pressure range. The accuracy of the approach appears to be limited by the one-dimensional nature of the model, the treatment of the radiation trapping through the use of escape factors, and the effects of radiative cascades from higher excited levels not taken into account in the model.

Influence of energy transfer processes on the rovibrational characteristics of CO2 in low-temperature conversion plasma with Ar and He admixture.

The influence of argon and helium on the rovibrational kinetics of carbon dioxide (CO2) and CO in low-temperature conversion plasma is investigated. With this objective, a combined experimental and computational study is conducted, applying quantum cascade laser infrared absorption spectroscopy to a pulsed DC CO2 glow discharge with varying noble gas admixture and modeling it with a two-term Boltzmann solver. Time-resolved rovibrational temperatures and dissociation fractions are presented, exhibiting an increase in rotational-vibrational non-equilibrium and an increasing CO2 conversion with argon (Ar) and helium (He) admixtures. Results are discussed in the context of energy transfer processes for collisions involving electrons, corroborated by electron-kinetic modeling, and heavy particle collisions. With noble gas addition, an increase in the electron number density, promoting excitation, and the high-energy tail of the electron energy distribution function are found. Penning ionization processes are proposed as an explanation for the increase in conversion, showing higher conversion for Ar due to the lower excitation thresholds and, therefore, larger state population. In the context of rovibrational kinetics, processes leading to the gain or loss of vibrational energy of CO2 are analyzed, pointing out subtle differences in, for example, relaxation rate coefficients between Ar and He. However, the cooling of the gas through conductive heat transfer is identified as the most important influence of the Ar and He admixture, as it keeps the relaxation rate for vibrational quenching low.

Modeling Study of Chemical Kinetics and Vibrational Excitation in a Volumetric DBD in Humid Air at Atmospheric Pressure

A zero-dimensionl model is developed to study the chemical kinetics of a volumetric dielectric barrier discharge (DBD) reactor operating with humid air at atmospheric pressure. This work focuses on the relation between molecular vibrational excitation, the plasma reactor input power and the number densities of several species that are known to play an important role in biomedical applications (e.g. O3,NO,NO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{3},\ extrm{NO, NO}_{2}$$\\end{document}, ...). A preliminary study is carried out to observe the influence of water molecules on the electron energy distribution function for different values of water concentration and reduced electric field. A simplified approach is then adopted to quantify the contribution of vibrationally-excited O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{2}$$\\end{document} molecules to NO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{NO}$$\\end{document} formation. The results obtained using our detailed model suggest that for the physical conditions considered in this work O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{2}$$\\end{document} vibrational kinetics can be neglected without compromising the overall accuracy of the simulation. Finally, a reaction set is coupled with an equivalent circuit model to simulate the E-I characteristic of a typical DBD reactor. Different simulations were carried out considering different values of the average plasma input power densities. A particular focus was given to the influence of the Zeldovich mechanism on O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{3}$$\\end{document} and NOX\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{NO}_\ extrm{X}$$\\end{document} production performing simulations where this reaction is not considered. The obtained results are shown and the role of vibrationally excited N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{N}_{2}$$\\end{document} molecules is discussed. The simulation results indicate also that N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{N}_{2}$$\\end{document} vibrational excitation, and more precisely the Zeldovich mechanism, has a larger effect on O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{3}$$\\end{document} and NOX\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{NO}_\ extrm{X}$$\\end{document} production at intermediate input power levels.

Reducing the computational complexity of implicit schemes in the modeling of kinetic inelastic collisions in a partially ionized plasma

AbstractModeling the time evolution of atomic number densities and the kinetic (non‐Maxwellian) electron energy distribution function under the action of electron impact collisions by classical approaches requires an implicit time‐stepping scheme to maintain numerical stability. The resulting linear system that must be iteratively solved at each time step incorporates a dense (nonsparse) matrix. For variables being propagated, the computational cost is . We present an alternative approach with a computational cost of , which is the same order as the computational cost of an explicit method for propagating a system of this type. The approach relies on a combination of classical iterative derivative evaluations, combinatorial approximations, and some ideas from deep machine learning.

Plasma properties in the vicinity of the last closed flux surface in hydrogen and helium fusion plasma discharges

The origin of the bi-Maxwellian electron energy distribution function (EEDF) observed in the scrape-off layer (SOL) of tokamak plasmas by means of Langmuir probes is still under discussion. It has been assumed that the ionization of hydrogen and deuterium neutrals by thermal electrons penetrating the SOL from the bulk plasma is the main reason for the appearance of a second Maxwellian. To validate this assumption, radial measurements of the electron temperatures and densities, or the plasma properties in helium plasmas in the GOLEM tokamak and the TJ-II stellarator were performed. The radial profiles of the low-temperature electron group densities follow the trend of the calculated radial profiles of the electron sources arising from the ionization of neutrals in both deuterium and helium plasmas in TJ-II. The difference in the radial location where the bi-Maxwellian EEDF appears can be explained by the difference in the rate coefficients for ionization of deuterium and helium. The results of probe measurements in GOLEM and the WEST tokamak divertor, at one radial location in the SOL, are compatible with the hypothesis concerning the ionization of neutral atoms and the type of the EEDF.