Maxwellian Electron Energy Distribution Function Research Articles

A global model and two-dimensional simulation study of a low-pressure inductively coupled CF4 plasma considering non-Maxwellian EEDF

We analyze the discharge characteristics of a low-pressure inductively coupled CF4 plasma using a global model and a two-dimensional (2D) simulation. We first conducted a study comparing the experimental results with the global model, which makes it easier to compare the trend concerning external parameters and less computationally expensive, to validate the chemical reaction data, and then, compared the experimental results with the 2D simulation results. We then analyzed the discharge characteristics by comparing the 2D model results with the global model at various gas pressures and powers. The simulations were performed using COMSOL software, which is based on a fluid model. The electron energy distribution function (EEDF) was solved self-consistently using the Boltzmann equation solver, and then, coupled with the fluid model. The results were more consistent with the experimental results when the EEDF was calculated by solving the Boltzmann equation than for assuming the Maxwellian EEDF. Furthermore, the global model results were similar with the mean values obtained from the 2D model. This indicates that it is efficient to first validate the electron collision cross sections and reaction coefficients using the global model. Our approach is expected to be utilized in the analysis of new gases.

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.

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.

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.

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.

Instability enhanced thermalization of bi-Maxwellian EEDF in multi-dipole confined hot cathode discharge: an experimental observation

In multi-dipole confined hot cathode discharges, the presence of up to three distinct electron species has been observed by performing linear fitting of the Langmuir probe I–V traces. Nevertheless, the fundamental mechanism underlying the generation of hot electrons remains ambiguous. This work presents experimental observations to comprehensively investigate the impact of the instability-enhanced thermalization effect on the thermal equilibrium of both hot and cold electrons. Temperature composition of the electron energy distribution function (EEDF) was measured via a Langmuir probe, while instabilities was measured using a spectrum analyzer. The experimental results confirm the existence of a transition from a three-temperature Maxwellian EEDF composition to a two-temperature Maxwellian EEDF composition as the population of high-energy electrons increases. Furthermore, the process of thermalization between hot and cold electrons is found to be correlated to the effect of instability-enhanced collisions. The intensity of collisional instability also decreases with increased neutral collisionality.

Two-dimensional simulation of non-equilibrium silicon nitride plasma discharge for thin film solar cell deposition

In this work, we model a Two-dimensional (2D) radiofrequency (RF) plasma discharge of hydrogenated silicon nitride (SiH4/NH3/H2) in a capacitive coupled plasma reactor (CCP), using non-Maxwellian electron energy distribution function (EEDF). The purpose is to investigate whether there is a real advantage and a significant contribution in 2D simulation using non-Maxwellian EEDF rather than Maxwellian one for determining the fundamental characteristics of radiofrequency plasma discharge. The results show a comparative study of the 2D evolution of the fundamental characteristics of the RF plasma using Maxwellian and non-Maxwellian EEDF. By considering the criterion of the density and the electronic temperature, the analysis of the results shows that the adoption of the non-equilibrium 2D EEDF makes it possible to obtain an approximation closer to the real conditions and thus a better understanding of the plasma discharge.

Influence of the electron kinetics on Ar/NF3 inductively coupled plasma

A self-consistent two-dimensional axisymmetric fluid plasma model coupled with Maxwell's equations is used to analyze the plasma kinetics of inductively coupled Ar/NF3 low-pressure plasma. We have developed a plasma chemical reaction mechanism for Ar/NF3 plasma and validated the same against the experimental data found in the literature. We analyze two sets of the electron-neutral reaction rate coefficients obtained for assumed Maxwellian and non-Maxwellian electron energy distribution functions. We find that the electron density in the discharge is sensitive to the choice of the electron energy distribution, while the fluorine atoms density is less sensitive. Since the density of atoms is controlled by a balance between production by dissociation reactions and diffusion to the walls, their density is very sensitive to the wall sticking probability.

Electron Impact Excitation of Extreme Ultra-Violet Transitions in Xe7–Xe10 Ions

In the present work, a detailed study on the electron impact excitation of Xe7+, Xe8+, Xe9+ and Xe10+ ions for the dipole allowed (E1) transitions in the EUV range of 8–19 nm is presented. The multi-configuration Dirac–Fock method is used for the atomic structure calculation including the Breit and QED corrections along with the relativistic configuration interaction approach. We have compared our calculated energy levels, wavelengths and transition rates with other reported experimental and theoretical results. Further, the relativistic distorted wave method is used to calculate the cross sections from the excitation threshold to 3000 eV electron energy. For plasma physics applications, we have reported the fitting parameters of these cross sections using two different formulae for low and high energy ranges. The rate coefficients are also obtained using our calculated cross sections and considering the Maxwellian electron energy distribution function in the electron temperature range from 5 eV to 100 eV.

Analysis of parameters of coaxial dielectric barrier discharges in argon flow at atmospheric pressure

This work deals with the numerical and experimental investigation of atmospheric pressure dielectric barrier discharges (DBDs). In the experiment, the current and voltage of DBD sustained in an argon flow in coaxial discharge cell are measured. Numerical models are based on the drift-diffusion theory of gas discharges. Different modelling approaches, where the electron kinetics is determined on the basis of the Maxwellian electron energy distribution function (EEDF), vs models with more realistic EEDF obtained from the solution of the electron Boltzmann equation are implemented. The effect of energy loss due to heating of the gas is considered.

Arbitrary EEDF determination of atmospheric-pressure plasma by applying machine learning to OES measurement

A new method to determine the arbitrary electron energy distribution function (EEDF) from the optical emission spectroscopic measurement in atmospheric-pressure plasma is introduced. The optical emission spectroscopy (OES) continuum emission spectrum, dominated by electron-neutral bremsstrahlung radiation, is analyzed to inspect the usefulness of the conventional OES measurement range for EEDF determination. The EEDF is reconstructed from the OES continuum radiation spectrum by applying machine learning to solve the bremsstrahlung emissivity equation inversely. Through iterative statistical analysis, the presented genetic algorithm can locate the EEDF reliably. Verification of the algorithm shows that theoretical Maxwellian and Druyvesteynian EEDFs can be partially reconstructed from a realistic OES measurement range. Furthermore, preliminary experimental EEDF results of an argon dielectric barrier discharge (DBD) OES measurement are given. The electron energy range and resolution of the determined EEDF are discussed. The results in this paper show potential for accurate determination of the arbitrary EEDF in atmospheric-pressure plasma using simple OES equipment.

Measurement of electron temperature and density of atmospheric-pressure non-equilibrium argon plasma examined with optical emission spectroscopy

The electron temperature T e and density N e of atmospheric-pressure non-equilibrium dielectric barrier discharge argon (Ar) plasma are measured with optical emission spectroscopy. Continuum emission due to bremsstrahlung is applied to the analysis of the electron temperature and density with the spectrometric system in the visible wavelength range calibrated absolutely. The assumption of the Maxwellian electron energy distribution function (EEDF) results in T e ≃ 0.29 eV and N e ≃ 1.1 × 1016 cm−3, whereas the Druyvesteyn EEDF leads to the result T e ≃ 0.79 eV and N e ≃ 1.4 × 1014 cm−3. To confirm the validity of these values, several line intensities of the excited states of the Ar atom are observed experimentally and compared with the theoretical population densities calculated by the Ar collisional–radiative (CR) model that includes atomic collisional processes. It is confirmed that the order of the observed excited-state number densities agrees well with that calculated numerically by the CR model with the Druyvesteyn EEDF, while the Maxwellian EEDF gives poor results.

Impact of impurity seeding on the electron energy distribution function in the COMPASS divertor region

In the COMPASS tokamak, series of experiments were performed aimed at studying the impact of nitrogen, neon, and argon impurity seeding on the electron energy distribution function (EEDF) in the divertor region. The experiments were conducted in D-shaped, L-mode, deuterium plasmas. In order to obtain the radial distribution of the floating potential, ion saturation current, electron temperatures, and densities, the current-voltage characteristics were measured by Langmuir probes embedded in the COMPASS tokamak divertor. The properties of the plasma in the divertor region were measured before and during impurity seeding. Before the N2 seeding, the EEDF was bi-Maxwellian with a low-energy electron fraction with temperatures 3.5–5 eV, and a higher-energy one with temperatures in the range of 10 eV to 23 eV. During seeding with an increasing number of molecules per second, the EEDF changed from bi-Maxwellian to Maxwellian and the electron temperature decreased. The time-evolution was studied of the change in the EEDF during N2 seeding. When the seeding was carried out by a valve in the private flux region, the duration of the transition from a bi-Maxwellian to a Maxwellian EEDF was about 10–15 ms. When the N2 seeding took place through a low-field side valve, the transition from a bi-Maxwellian to a Maxwellian EEDF took longer −25–45 ms. The temporal evolution was also analyzed of the plasma parameters’ radial profiles when neon and argon were puffed using a valve in the divertor low-field side. The application is discussed of the probe measurements’ results to calculating the parallel heat-flux densities in the divertor region of the COMPASS tokamak.

Numerical Modeling of Non-equilibrium Plasma Discharge of Hydrogenated Silicon Nitride (SiH4/NH3/H2)

In this work, we model a radiofrequency discharge of hydrogenated silicon nitride in a capacitive coupled plasma reactor using Maxwellian and non-Maxwellian electron energy distribution function. The purpose is to investigate whether there is a real advantage and a significant contribution using non-Maxwellian electron energy distribution function rather than Maxwellian one for determining the fundamental characteristics of a radiofrequency plasma discharge. The results show the evolution of the non-Maxwellian electron energy distribution function, the mobility and the diffusion coefficient required to determine the fundamental characteristics of the radiofrequency plasma discharge of a hydrogenated silicon nitride deposit at low pressure and low temperature, between the two electrodes of the capacitive coupled plasma reactor. By comparing these results using non-Maxwellian electron energy distribution function with those calculated using the Maxwellian one, we conclude that the use of non-Maxwellian electronic energy distribution function is more efficient for describing the evolution of a radiofrequency plasma discharge in a capacitive reactor, which will improve the quality of the deposition of thin films.

Global model of cold atmospheric He + air plasmas: A comparison of Maxwellian and non-Maxwellian EEDFs

The electron energy distribution function (EEDF) of cold atmospheric plasmas (CAPs) is often assumed to be Maxwellian, but it is actually non-Maxwellian, as calculated from the Boltzmann equation. To determine the impact of the Maxwellian assumption, two global models with Maxwellian and non-Maxwellian EEDFs are developed for the He + air CAPs, and the resulting discharge characteristics and reactive species are compared. With the increasing air concentration from 100 to 50 000 ppm in He + air feeding gas, the simulation results of both global models display similar trends, and the orders of the densities of both global models are similar for the reactive species and each air concentration scenario. However, the Maxwellian assumption leads to lower electron temperature, weaker electronegativity, less power dissipation to Ion Joule heating, higher densities, and lagging peak points for most types of reactive species compared to using the non-Maxwellian EEDF. These findings indicate that the Maxwellian assumption is capable of capturing the main physicochemical features of He + air CAPs, but it can lead to large calculation errors at the quantitative level.

Time and space-resolved experimental investigation of the electron energy distribution function of a helium capacitive discharge at atmospheric pressure

Using a collisional radiative model coupled with optical emission spectroscopy (OES) of helium n = 3 levels, the electron temperature (Te) of an atmospheric-pressure capacitively coupled radiofrequency (AP-CCRF) discharge in helium is determined with space and time resolution. When the AP-CCRF discharge is sustained in the mode, Te varies from 0.2 to 7.2 eV. In this case, high values of Te (>5 eV) occur only during a brief instant (<10 ns) in the high-voltage sheath. When the AP-CCRF discharge is sustained in the mode, Te varies from 0.3 to 0.4 eV during the complete cycle. The physical meaning of these electron temperatures are then analyzed by considering possible departure from the Maxwellian electron energy distribution function (EEDF). As a first approximation to non-Maxwellian distribution functions, a two-parameter EEDF was used to fit the OES data. This approach yields an overpopulation of high energy electrons with respect to the Maxwellian form in the mode and the opposite trend in the mode.

A kinetic model for investigating the dielectric properties of rocket exhaust dusty plasmas

The electron kinetic model of rocket exhaust dusty plasma is developed based on the Boltzmann equation. Additional electron-dust elastic and inelastic collision processes are included in the kinetic equation except for the electron-neutral collisions. The dust surface potential and electron density are calculated according to the dust charging balance equation and the quasineutrality condition. The electron energy distribution function (EEDF) is calculated by solving the kinetic equation numerically. It shows that the obtained EEDF results for different dust densities deviate from the Maxwellian distribution obviously. In addition, the dielectric properties of rocket exhausts based on the obtained non-Maxwellian EEDFs are analyzed for different dust and plasma parameters. It is shown that the relative permittivity based on the EEDFs obtained from the kinetic model is larger than that based on Maxwellian distribution, while for the conductivity and attenuation constant, they become smaller. As for the influence of dust particles on the dielectric properties, a high ratio of dust and neutral density (10−9) leads to a smaller absolute value of relative permittivity, electrical conductivity, and attenuation constant for both Maxwellian distribution and EEDF obtained from the kinetic model. When the ratio is low (10−10), the dust particles almost have no influence on the dielectric properties. Meanwhile, it can be seen that the existence of dust particles makes the difference in dielectric properties obtained from the calculated EEDFs and Maxwellian distribution smaller.

Thermalisation time of electron swarms in xenon for uniform electric fields

We have calculated the thermalisation time for an electron swarm in gaseous xenon using a multi-term time-dependent Boltzmann equation (BE), for a range of instantaneously applied reduced electric fields 1 Td < E/N < 1000 Td. Starting from a Maxwellian electron energy distribution function (EEDF) at room temperature for a given E/N, the time-evolution of the EEDF and associated electron swarm parameters (drift velocity We, mean energy 〈ε〉, ionisation coefficient ki, excitation coefficient kex) are followed as they converge to steady-state values. For all values of E/N considered, the individual swarm parameters are found to converge at different rates. For E/N > 5 Td, they converge in order We (fastest), 〈ε〉, kex, and ki (slowest). The time taken for the slowest swarm parameter to converge to an acceptable level (e.g. to within 10% of its steady-state value) is used universally as the benchmark for evaluating the thermalisation time τth. This time is found to be strongly dependent on the value of the reduced electric field E/N, dropping by almost 5 orders of magnitude for increasing E/N fields 1 Td < E/N < 1000 Td. As a key outcome from this work, the calculated thermalisation times τth·p are expressed as a general formula, as a function of both the reduced electric field E/N and a user defined convergence level between 1% and 20%. We show that ballpark estimates of thermalisation times, based on the inverse of the collision frequency for energy dissipation 1/νe(ε) at typical average electron energies, are likely to be unreliable if applied to the heating phase. We also undertake a brief analysis of the cooling phase when the electric field is instantaneously removed from the plasma (i.e. field-free) after it evolves to steady-state conditions during the previous heating phase. Finally, we compare calculated thermalisation times with the typical risetimes of the voltage pulse waveforms for several experimental ‘nanosecond’ pulse excited plasma discharge devices.

Kinetics of Deuterium Gas-Discharge Plasma in the Resonator of a Neutron Generator in Electron-Cyclotron Resonance Mode

The results of numerical simulation of the microwave discharge kinetics in molecular deuterium in electron-cyclotron resonance mode are presented for a description of the physical processes in the resonator of a neutron generator. The calculations have been carried out in an approximation of homogeneous electric and magnetic fields, as well as the Maxwellian electron energy distribution function. In the kinetic scheme, the reactions of excitation, dissociation, ionization, and recombination of deuterium atoms and molecules, as well as elastic collisions, were taken into account. As a result, the time dependences of the number density and temperature of the plasma components at different electric and magnetic field intensities and the initial number density of molecular deuterium are obtained. The values of the fields corresponding to the minimum ionization time are determined, and the maximum ion current extracted from the microwave discharge is estimated.

Electron density and temperature in an atmospheric-pressure helium diffuse dielectric barrier discharge from kHz to MHz

Diffuse dielectric barrier discharges are generated over a very wide range of frequencies. According to the targeted frequency, the glow, Townsend-like, hybrid, Ω and RF-α modes are sustained. In this paper, the electrical characterization of the discharge cell together with an electrical model are used to estimate the electron density from current and voltage measurements for excitation frequencies ranging from 50 kHz to 15 MHz. The electron density is found to vary from 1014 to 1017 m−3 over this frequency range. In addition, a collisional-radiative model coupled with optical emission spectroscopy is used to evaluate the electron temperature (assuming Maxwellian electron energy distribution function) in the same conditions. The time and space-averaged electron temperature is found to be about 0.3 eV in both the low-frequency and high-frequency ranges. However, in the medium-frequency range, it reaches almost twice this value as the discharge is in the hybrid mode. The hybrid mode is similar to the atmospheric-pressure glow discharge usually observed in helium DBDs at low frequency with the major difference being that the plasma is continuously sustained and is characterized by a higher power density.