Electron Energy Distribution Function Research Articles

Two-term Boltzmann approximation versus Monte-Carlo simulation: effect of magnetic field

In this paper, we investigate the spatial-local electron energy distribution function (eEDF) interacting with a background gas at the sub-atmospheric pressure in a wide range of applied crossed electric and magnetic fields using the Boltzmann kinetic equation. We compare solutions obtained using two numerical approaches (deterministic two-term approximation and stochastic Monte Carlo method) to identify their applicability in the context of determining drift velocity and reaction constants for electrons. For argon and helium, the upper limit of the reduced electric field applicability of the two-term approximation is discussed. It has been shown that the presence of a magnetic field can reduce this limit. Two explanations are given, one is based on the math of two-term formalism, and the other is based on velocity-space analysis. Two-term approximation fails due to it’s inability to resolve underlying cyclotron oscillation (it should result in an energy variation along the electron’s trajectory). The absence of this feature causes an incorrect estimation of momentum-transfer rate. This results an inaccuracy in the estimation of the angle between electric field and drift velocity.

Application of Optical Emission Spectroscopy to Electron Cyclotron Resonance Ion Sources

Electron Cyclotron Resonance Ion Sources (ECRIS) are widely used for production of highly charged high intensity ion beams for research, medical and industrial applications.ECRIS performances, especially the charge state distribution and beam intensity, depend significantly on the electron energy distribution function that ranges from a few eV to hundreds of keV. Further improvements of ECRIS performances require a deeper and deeper understanding of the plasma heating mechanisms and ion generation by means of opportune plasma diagnostics. Amongst others, optical emission spectroscopy (OES) is the most remarkable for application in ECRIS: it is a non-invasive diagnostics able to operate also in high-voltage conditions and it requires small room for operation. OES has been already tested for plasma diagnostics in proton sources.This work presents the experimental set-up developed for the plasma diagnostics of the Advanced Ion Source for Hadrontherapy (AISHa), an ECRIS for medical applications, together with the strategy applied to relate plasma emission lines in the visible and near-infrared domain to plasma parameters for some ions of interest. Preliminary results and perspectives will be also discussed.

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.

Initial Experimental Results of Producing Multicharged Ions Efficiently by Lower Hybrid Resonance Heating with Exciting Helicon Waves on Electron Cyclotron Resonance Ion Source

Based on experimental results, we considered the accessibility conditions for wave propagation in the magnetized plasma in an electron cyclotron resonance (ECR) ion source (ECRIS), and proposed introducing electromagnetic waves with frequencies lower than those of ECR. We generate the lower hybrid resonance (LHR) in the ECRIS by the electric field of the extra-ordinary mode (X-mode) on the helicon wave which additionally heat the electrons, and then it was conducted to improve the efficiency of multicharged ion generation successfully in over density condition. The electron energy distribution function obtained by the probe measurement shows an increase in the high-energy region in the corresponding LHR region. In this paper, for the first time we describe the initial experimental results on enhanced production of multicharged ions by the LHR of the low-frequency RF electromagnetic waves into the ECRIS.

Study of Electron Energy Distribution Function, Transport Parameters and Instability Analysis of Argon Plasma confined by a Dipole Magnet

This theoretical study is to investigate production and properties of plasma confined by a dipole magnet. A cylindrical permanent magnet (N40 grade) having a surface magnetic field of nearly 1Tesla is simulated to create a dipole magnetic field. Plasma is created by electron cyclotron resonance heating. Heating is accomplished using microwaves operating in continuous mode at 2.45 GHz and electron cyclotron resonance. The investigation is performed in systems of cylindrical geometries at varying pressures (0.5 mTorr – 1.5 mTorr). The electron temperature lies in the range of 1 - 5 eV, is hotter near the magnets and follows a downstream fashion throughout the region.Electron Energy Distribution Function (EEDF) growth investigation throughout the region was done to understand the role of magnetic field confinement. The EEDF was calculated numerically from steady state Boltzmann equation, considering plasma follows druyvesteyn distribution. Followed by analysing transport parameters such as diffusion coefficient, drift velocity, mobility, and recombination rates in plasma. A comparative study for all plots gave been done with respect to pressure. The instability analysis of elastic collisional frequency with inelastic collisions, real frequency and growth factor with wave vector has been also listed in the study.

One-dimensional, hybrid hydrodynamics-Boltzmann model for electron beam generated plasmas produced in low pressure argon

A one-dimensional, hybrid hydrodynamics-Boltzmann model for electron beam (e-beam) generated plasmas in argon at low pressure and a constant magnetic field is developed. The e-beam separates the plasma into two distinct regions: an ionization zone irradiated by the e-beam that creates plasma and reactive species, and a diffusive zone between the e-beam and the chamber wall, where the species diffuse toward the wall. The Boltzmann equation is solved in the ionization zone and the electron energy distribution function is used to calculate rates participating in the species and power balance equations. Comparison of model and experimental data for the radial profiles of the electron density and temperature shows a favorable agreement. All plasma parameters are sensitive to their radial location.

Benchmarking calculations of level energies, transition parameters and electron impact excitation cross sections of S-like Xe38+

Atomic structure parameters for levels corresponding to 2s22p63s23p4, 2s22p63s3p5, 2s22p63s23p23d2, 2s22p63s3p43d and 2s22p63s23p33d configurations of S-like Xe38+ are calculated using the fully relativistic multiconfiguration Dirac-Hatree-Fock (MCDHF) method followed by the subsequent relativistic configuration interaction (RCI) calculations. The parameters evaluated include energies of the lowest 75 levels and E1, M1, E2, and M2 transition parameters among these levels. The effect of the choice of virtual orbitals for generating the wavefunctions is discussed. The accuracy of our line strengths is established through the rigorous calculations of their associated uncertainties using three different methods. Another set of calculations using the many-body perturbation theory (MBPT) to validate the present MCDHF-RCI energies is carried out. Further, the electron impact excitation cross-sections using the relativistic distorted wave (RDW) theory are determined for all transitions from the ground and metastable states in the incident electron energy range from the excitation threshold to 10 keV. For plasma physics applications, the fitting parameters for these cross sections employing two distinct equations tailored for low and high-energy regimes are reported. Moreover, the rate coefficients are determined in the electron temperatures range of 15 eV to 100 eV by taking into account the Maxwellian electron energy distribution function and our computed cross-sections. In addition to addressing the atomic data gap in highly charged Xe ions, the present results are of good accuracy and can serve as benchmark tests for other theoretical evaluations. Moreover, they can also assist in line identification of the complex spectra of highly charged sulphur-like xenon ions.

DYNAMICS OF PLASMA IN A DUAL-FREQUENCY CAPACITIVE DISCHARGE IN AN AR/XE MIXTURE

The spatiotemporal dynamics of the plasma of a symmetrical dual-frequency 81 MHz/1.76 MHz capacitive discharge under the in uence of a low-frequency eld of 1.76 MHz has been studied.Using the method of phase-resolved optical emission spectroscopy, the dynamics of the radiation intensity of argon and xenon in plasma was obtained.The electron energy distribution function at the center of the discharge was measured using a Langmuir probe and the electron density was measured using a microwave probe. The main result is the dynamics of the intensity ratios of the selected argon and xenon lines depending on di erent conditions: at pressures of 40, 200 and 400 mTorr, LF voltage amplitude of 100, 200 and 400 V, input power at 81 MHz of 3 W and 15 W. The dynamics of high-energy electrons is studied based on a two-temperature approximation of the electron energy distribution function.

High-temperature properties of dry air used as arc quenching medium and its mixture with vaporized C2F4 : reaction products and critical reduced electric field strength at 300–3000 K

Recently, electric power equipment manufacturers released a joint statement with the aim of developing high-voltage electrical equipment completely free of fluorinated gases such as fluoroketones and fluoronitriles, which are considered as alternatives to SF6 and artificially produced compounds of F. This paper considers air as a typical gas present naturally in the environment to investigate its high-temperature properties, including an air mixture with C2F4 vapor injected from a polytetrafluoroethylene nozzle, for application as an arc-quenching medium in a high-voltage circuit breaker equipped with a nozzle. Chemical composition results for the reaction products at 300–3000 K show that the admixture of C2F4 vapor causes a decrease in the molar number of O2 contained in the air, owing to the production of O-containing compounds such as CO2 and CO . Additionally, the results reveal that the admixture of C2F4 vapor lead to the production of CF4 as the predominant F-containing compound. Furthermore, the boundary condition for O2 production in terms of O2 molar number XO2 and C2F4 molar number XC2F4 is formulated. Such evaluation of the mixture composition enables the determination of a reduced effective collision ionization coefficient αˉ/N and a critical reduced electric field strength Ecr/N , resulting in αˉ/N = 0. The strength Ecr/N for the mixture with 30%–100% C2F4 molar fraction rises to approximately 150 Td (1 Td = 1 ×10−21 V m2) over 300–3000 K, which is 20–50 Td higher than that for high-temperature air unmixed with C2F4 vapor. The variation in Ecr/N is discussed in terms of predominant electron impact processes and the electron energy distribution function in the mixture.

DC-driven subatmospheric glow discharges in the infrared-stimulated

This paper presents a conceptual framework for experimental research combined with numerical analysis on direct current (DC) glow discharges in microscale planar gas discharge-semiconductor systems (GDSS). In the experimental section, several structural and elemental analyses, including SEM, EDAX, AFM, and near-infrared absorption spectra measurements were carried out for compound semiconductor zinc selenide (ZnSe) cathode sample. Argon (Ar) was charged into the plasma reactor cell of GDSS at pressures of 100 Torr subatmospheric and 760 Torr atmospheric, respectively, by a vacuum pump- gas filling station. Glow discharge light emissions from plasma, excited under three different intensity levels (dark, weak, strong) of infrared beam illumination on ZnSe cathode electrode, were measured by using a phomultiplier tube that is sensitive to UV–Visible wavelengths. In the numerical analysis section, simulation studies were carried out on the two-dimensional gas discharge-semiconductor microplasma system (GDSµPS) cell models using the finite-element method (FEM) solver COMSOL Multiphysics DC plasma program. Calculations and predictions were based on mixture-averaged diffusion drift theory and Maxwellian electron energy distribution function. GDSµPS cell was modeled in a square chamber with planar anode/cathode electrode pair coupled at a 50 μm discharge gap. Single side of ZnSe cathode was finely micro-digitated to increase the effective surface area for enhanced electron emission to the gas discharge cell. The electrical equivalent circuit (EEC) of the proposed model was driven by 1.0 kV DC voltage source. Binary Ar/H2 gas medium in a mixture of 3:2 molar ratio was introduced to the gas discharge chamber at constant 200 Torr subatmospheric pressure. Simulations were run for normal glow discharges to exhibit the electrical fast transient glow discharge behaviours from electron field emission state to self-sustained normal glow discharge state by numerically solving the electron density (ED), electron current density (ECD) and electric potential distribution (EPD) parameters.It is figured out that binary Ar/H2 gas discharge model can undertake a major role in shaping and controlling the spatiotemporal response to transient electro-optical behavior of microplasma-based artificial electromagnetic materials configured for high-efficiency infrared-to-visible wavelength conversion applications.

Transient striations in an inductively coupled plasma during E-to-H transitions

Abstract Azimuthal transient striations are reported for inductively coupled Ar plasma during E-to-H transition at 200 mTorr. In this transient process, the number of striations increases with time, and striations ultimately disappear when the H mode is reached. An integrated model is developed to investigate the mechanism of this phenomenon. This integrated model incorporates a one-dimensional time-dependent fluid model with a perturbation analysis, as well as a circuit model for power coupling with the external radio-frequency driving source. Based on this integrated model, the development of striations is proposed to be a consequence of ionization instability due to the variation in the electron energy distribution function. The model results for the temporal evolution of the number of striations are in good agreement with the observed data.

Characterization of the TJ-II stellarator plasma by means of reciprocating Langmuir probes

Experiments were conducted in deuterium plasma in the TJ-II stellarator by means of swept Langmuir probes mounted on reciprocating probes manipulators. The results were processed using the four-parameter fit, as well as the triple-probe and the first-derivative probe techniques. The parameters determined were the floating potential, the ion saturation current density, the electron temperature and density, and the plasma potential. The results were obtained for two plasma heating techniques – electron cyclotron resonance heating (ECRH) and neutral beam injection (NBI) heating. In the case of ECRH, employing the first-derivative probe technique resulted in finding that the electron-energy distribution function (EEDF) was not Maxwellian, but rather a bi-Maxwellian one with thermal (14-25 eV) and cold (4-5 eV) electrons. In comparison, during NBI heating we found a Maxwellian EEDF with the electron temperature being around 5 eV and slightly increasing in the confined plasma, but always remaining below 15 eV. We present a detailed analysis and discussion of the data for the plasma parameters as acquired by different techniques of using the reciprocating probe manipulator.

On the coupling effect in the RF-biased inductively coupled plasma with the synchronous control

The coupling effects between the bias power and the inductive power in the RF-biased inductively coupled plasma with synchronous control are investigated by measuring electron energy distribution function using a compensated Langmuir probe. With synchronous control, the inductive power and the bias power are driven at an identical phase and frequency. The experimental results show that the inductive power lowers the self-bias voltage, while the bias power changes the plasma density by introducing extra power absorption and dissipation. The bias power also enhances the electron beam confinement, leading to an increase in electron density at a low pressure. Furthermore, in the E and H mode transition, with the bias power increasing, the hysteresis power reduces, and the electron density jump decreases.

Hollow cathode effect in radio frequency hollow electrode discharge in argon

Radio frequency capacitively coupled plasma source (RF-CCP) with a hollow electrode can increase the electron density through the hollow cathode effect (HCE), which offers a method to modify the spatial profiles of the plasma density. In this work, the variations of the HCE in one RF period are investigated by using a two-dimensional particle-in-cell/Monte-Carlo collision (PIC/MCC) model. The results show that the sheath electric field, the sheath potential drop, the sheath thickness, the radial plasma bulk width, the electron energy distribution function (EEDF), and the average electron energy in the cavity vary in one RF period. During the hollow electrode sheath’s expansion phase, the secondary electron heating and sheath oscillation heating in the cavity are gradually enhanced, and the frequency of the electron pendular motion in the cavity gradually increases, hence the HCE is gradually enhanced. However, during the hollow electrode sheath’s collapse phase, the secondary electron heating is gradually attenuated. In addition, when interacting with the gradually collapsed hollow electrode sheaths, high-energy plasma bulk electrons in the cavity will lose some energy. Furthermore, the frequency of the electron pendular motion in the cavity gradually decreases. Therefore, during the hollow electrode sheath’s collapse phase, the HCE is gradually attenuated.

Spectral analysis and kinetic modeling of radioluminescence in air and nitrogen.

In this article we present a quantitative analysis of the second positive system of molecular nitrogen and the first negative system of the molecular nitrogen cation excited in the presence of ionizing radiation. Optical emission spectra of atmospheric air and nitrogen surrounding 210Po sources were measured from 250 to 400 nm. Multi-Boltzmann and non-Boltzmann vibrational distribution spectral models were used to determine the vibrational temperature and vibrational distribution function of the emitting N2(C3Πu) and N2+(B2Σ+u) states. A zero-dimensional kinetic model, based on the electron energy distribution function (EEDF) and steady-state excitation and de-excitation of N2(X1Σ+g), N2+(B2Σ+u), N2+(X2Σ+g), N4+, O2+, and N2(C3Πu, v), was developed for the prediction of the relative spectral intensity of both the N2+(B2Σ+u → X2Σ+g) emission band and the vibrational bands of N2(C3Πu → B3Πg) for comparison with the experimental data.

Enhanced plasma jet generation through numerical integration and dielectric influence analysis

This paper reports a study on the production of plasma jets that are out of equilibrium through numerical solutions of electron energy distribution function using a self-consistent methodology. The approach includes the integration of the continuity, momentum, and Poisson equations, which allows the use of the mean electron energy to fit the transport and source coefficients. The paper concurrently presents an analysis of cold plasma generation in a tube. This investigation utilizes COMSOL Multiphysics software to simulate the electric field, potential, and electron density in space. Moreover, the study examines how the dielectric’s permittivity impacts plasma propagation. The simulated outcomes are compared with experimental and numerical results. As electron density, ionization rate and electric potential vary during plasma propagation on a dielectric surface, and the permittivity of dielectric materials increases, it promotes an increase in electron density around it. This, in turn, accelerates the ionization front, indicating efficient polarization and accumulation of electric charges, specifically electrons, near the dielectric surface.

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.

High Te discrepancies between ECE and Thomson diagnostics in high-performance JET discharges

The present paper is dedicated to the study of the discrepancies encountered in electron temperature (Te) measurements carried out with electron cyclotron emission (ECE) and Thomson scattering (TS) diagnostics in the core of the JET tokamak. A large database of discharges has been collected, including high-performance scenarios performed with deuterium only and deuterium–tritium mixtures. Discrepancies have been found between core Te measurements taken with an X-mode ECE interferometer (TECE) and a LIDAR TS system (TLID) for Te>5 keV. Depending on the plasma scenario, TECE has been found to be systematically higher or lower than TLID. Discrepancies have also been observed between the peaks of the ECE spectrum in the second (X2) and third (X3) harmonic domains, even in high optical thickness conditions. These discrepancies can be interpreted as evidence of the presence of non-Maxwellian features in the electron energy distribution function (EEDF). In order to investigate the relation between the shape of the EEDF and the measured discrepancies, a model for bipolar perturbations of Maxwellian EEDF has been developed. The model allows analytical calculations of ECE absorption and emission coefficients; hence, the comparison of modeled ECE spectra with experimental data. The different experimental results observed for the various JET scenarios have been found to be qualitatively reproducible by adapting the model parameters, suggesting that bipolar distortions of the bulk EEDF could play a role in giving rise to the reported discrepancies between ECE and TS measurements.

Double-sided electron energy analyzer for measurement of non-Maxwellian electron energy distributions.

A double-sided electron energy analyzer is developed for studies of magnetic reconnection. It can measure electron energy distribution functions along two directions opposite to each other at the same time. Each side is composed of a floating reference grid, an energy selector grid, and a collector plate. The voltage of the selector grid is swept from -40 to 0V with respect to the reference grid with a frequency of 1MHz. This fast sweeping is required to resolve sub-Alfvénic changes in plasma quantities of the Magnetic Reconnection Experiment, where the typical Alfvénic time is a few microseconds. The reliability of the energy analyzer is checked in Maxwellian plasmas away from the reconnection region. In this case, the electron temperature computed from the electron energy distribution function agrees with measurements of a reference triple Langmuir probe. When it is located near the reconnection region, the temperatures of the tail electron population from both sides, facing into the electron flow and facing away from it, exceed the bulk electron temperature measured by the Langmuir probe by a factor of about 2.

First-principles simulation of optical emission spectra for low-pressure argon plasmas and its experimental validation

Various spectral line emissions are often used for the experimental characterization of low-temperature plasmas. For a better understanding of the relation between the plasma characteristics and optical emission spectra, first-principle numerical simulations for low-pressure radio-frequency driven capacitively-coupled plasmas (CCPs) of argon have been performed by coupling one-dimensional particle-in-cell/Monte Carlo collision (PIC/MCC) simulations with a global collisional-radiative model (CRM). The only ionization and excitation mechanisms included in the PIC/MCC simulations of this study are the electron-impact ionization and excitations of the ground-state Ar atoms, as done commonly, whereas the electron-impact ionization of metastable states and other ionization mechanisms are also included in the CRM to account for the optical emission spectra. The PIC/MCC coupled CRM provides the emission spectra, which are then compared with experimental data obtained from the corresponding Ar CCPs with a gas pressure ranging from 2 Pa to 100 Pa. The comparison has shown good agreement for pressures up to about 20 Pa but increasingly notable deviations at higher pressures. The deviation is ascribed to the missing consistency between the PIC/MCC simulations and CRM at higher pressures, where the ionization from the metastable states is more dominant than that from the ground states, indicating a significant change in the electron energy distribution function due to the electron collisions with excited Ar atoms at higher pressures.