Electron Energy Distribution Function Research Articles

Local enhancement of electron heating and neutral species generation in radio-frequency micro-atmospheric pressure plasma jets: the effects of structured electrode topologies

The effects of structured electrode topologies on He/O2 radio frequency micro-atmospheric pressure plasma jets driven at 13.56 MHz are investigated by a combination of 2D fluid simulations and experiments. Good qualitative agreement is found between the computational and experimental results for the 2D spatio-temporally resolved dynamics of energetic electrons measured by phase resolved optical emission spectroscopy, 2D spatially resolved helium metastable densities measured by tunable diode laser absorption spectroscopy and 2D spatially resolved atomic oxygen densities measured by two photon absorption laser induced fluorescence. The presence of rectangular trenches of specific dimensions inside the electrodes is found to cause a local increase of the electron power absorption inside and above/below these surface structures. This method of controlling the electron energy distribution function via tailored surface topologies leads to a local increase of the metastable and atomic oxygen densities. A linear combination of trenches along the direction of the gas flow is found to result in an increase of the atomic oxygen density in the effluent, depending linearly on the number of trenches. These findings are explained by an enhanced Ohmic electric field inside each trench, originating from (a) the low electron density, and, consequently, the low plasma conductivity inside the trenches, and (b) the presence of a current focusing effect as a result of the electrode topology.

Simulation of the spatio-temporal evolution of the electron energy distribution function in a pulsed hollow-cathode discharge

This article presents the 2D simulation results of a nanosecond pulsed hollow cathode discharge obtained through a combination of fluid and kinetic models. The spatio-temporal evolution of the electron energy distribution function (EEDF) of the plasma column and electrical characteristics of the nanosecond pulsed hollow cathode discharge at a gas pressure of 5 Torr are studied. The results show that the discharge development starts with the formation of an ionization front at the anode surface. The ionization front splits into two parts in the cathode cavity while propagating along its lateral surfaces. The ionization front formation leads to an increase in the fast isotropic EEDF component at its front, as well as in the anisotropic EEDF component. The accelerated electrons enter the cathode cavity, which significantly contributes to the formation of the high-energy EEDF component and EEDF anisotropy.

Kinetic simulations of ignited mode cesium vapor thermionic converters

Cesium vapor thermionic converters are an attractive method of converting high-temperature heat directly to electricity, but theoretical descriptions of the systems have been difficult due to the multi-step ionization of Cs through inelastic electron–neutral collisions. This work presents particle-in-cell simulations of these converters, using a direct simulation Monte Carlo collision model to track 52 excited states of Cs. These simulations show the dominant role of multi-step ionization, which also varies significantly based on both the applied voltage bias and pressure. The electron energy distribution functions are shown to be highly non-Maxwellian in the cases analyzed here. A comparison with previous approaches is presented, and large differences are found in ionization rates due especially to the fact that previous approaches have assumed Maxwellian electron distributions. Finally, an open question regarding the nature of the plasma sheaths in the obstructed regime is discussed. The one-dimensional simulations did not produce stable obstructed regime operation and thereby do not support the double-sheath hypothesis.

ABSOLUTE INTENSITIES OF HELIUM LINES AND SPACE RESOLVED ELECTRON DENSITIES AND ENERGIES IN DISCHARGE WITH A HOLLOW CATHODE IN HE:H2O GAS MIXTURE

In a discharge with a hollow cathode the electron energy distribution functions (EEDFs), electron concentration, and absolute intensities of pure helium and helium mixtures with water vapor at pressures of 2-3 mbar were measured. It was shown that under the experiment conditions, the EEDFs were significantly different from the Maxwellian function since the amount of high-energy electrons in the energy range of 7-24 eV was much larger. As the concentration of water molecules in plasma increased, the amount of high-energy electrons decreased. The absolute intensities of a number of helium lines were calculated in coronal model approximation. It was determined that the lines reasonably agreed with the experimental measurements of the absolute intensities.

Analysis of the electron energy distribution function and its transport coefficient in SF6-CO2 applied gas mixtuers

The Boltzmann transport equation is used to calculate the electron energy distribution function (EEDF) and the transport coefficient in pure sulfur hexafluoride (SF6) and pure Carbon dioxide (CO2) and their mixtures. The electron swarm parameters are evaluated in the range of These parameters namely are: The Diffusion coefficient of electrons and mean electron energy. The motion of electrons in plasma gas (SF6) and mixing it with (CO2) under an applied uniform electric field is simulated by using the numerical solution ofBoltzmann's transport equation technique. The numerical solutions are utilized within the international computer code kinema-Elendif and written in Fortran 77 language software. The calculated distribution function is found to be remarked non-Maxwillian that has energy variations which reflect the import electron-molecule energy exchange processes.

Numerical simulation of a partially anisotropic electron distribution function in a pulsed discharge with a hollow cathode

In this paper, we propose a convenient method for calculating the electron energy distribution function (EEDF) in a gas-discharge plasma, where the presence of high-energy electrons results in the formation of a partial EEDF anisotropy. A detailed description of this method is provided. The performance of the proposed method is demonstrated to calculate the EEDF of plasma column of a high-voltage nanosecond discharge in argon with an extended hollow cathode. The applicability assessment of the proposed method calculating the EEDF in the plasma column of pulsed discharge sustained by the 50 Hz pulse and gas pressure from 5 to 40 Torr is given. It was shown that high-energy electrons were effectively formed in this type of discharge with an increase in the EEDF in the high-energy region. This technique can also be usefully employed for other types of discharges where fast electrons are formed.

The Determination of Deposition Parameters for Carbon-Based Materials in an Inductively Coupled Plasma System Using COMSOL

A 2-D axisymmetric fluid model simulation of inductively coupled discharges of a methane plasma is presented. The continuity equations for charged species and electron energy are solved with COMSOL Multiphysics. A constant frequency and gas pressure, 13.56 MHz and 0.02 Torr, respectively, are used. Initially, a coil power of 100 W is used, but this is later adjusted to include various coil powers up to 600 W. A Boltzmann equation solver is used to calculate the electron energy distribution function (EEDF) and reduced electron mobility. The effects of increased coil power are investigated, and the results indicate that increases in power increases moderately the electron temperature and charge densities. The growth rate of carbon across the substrate holder is mapped to determine a growth profile for the system.

Dielectric Breakdown Properties of He-H2 Mixtures for High Temperature Superconducting Power Devices

In this study, the electron energy distribution function (EEDF), the electron swarm parameters , the effective ionization coefficients, and the critical field strength (dielectric strength) in binary He-H2 gas mixture which is used as cryogenic for high-temperature superconducting power applications, are evaluated using two-term solution of the Boltzmann equation over the range of E/N ( the electric field to gas density) from 1 to 100 Td ( 1 Td=10-17 Vcm2) at temperature 77 K and pressure 2MPa, taking into account elastic ( momentum transfer) and inelastic cross-sections. Using the electron energy distribution function (EEDF) electron swarm parameters (electron drift velocity, mean electron energy, diffusion coefficient, electron mobility, ionization and attachment coefficient) are calculated. At low reduced electric field strength E/N, the EEDF is close to Maxwellian distribution, at high E/N, due to vibrational excitation of H2, the calculated distribution function is non-Maxwellian. Besides, the Boltzmann equation analysis showed as the small mole fraction of H2 in the He-H2 mixture is increased, the electron energy distribution function EEDF shifts to lower energy region, the density-reduced ionization coefficient α/N and density-reduced effective ionization coefficient (α-η)/N decreases, whereas density-reduced attachment coefficient η/N, density-reduced critical electric field strength increases, (E/N)crt and critical electric field Ecrt increases. It is found that dielectric field strength depends on pressure and temperature. To confirm the validity of the two term solution of Boltzmann equation analysis, a set of elastic and inelastic cross-sections for each gas He and H2 are used to calculate the electron swarm parameters and dielectric field strength. Compared with previous experimental and theoretical literatures, the values obtained are generally in good agreement.

Investigation of the Langdon effect on the nonlinear evolution of SRS from the early-stage inflation to the late-stage development of secondary instabilities

In a laser-irradiated plasma, the Langdon effect can result in a super-Gaussian electron energy distribution function (EEDF), imposing significant influences on stimulated backward Raman scattering (SRS). In this work, the influence of a super-Gaussian EEDF on the nonlinear evolution of SRS is investigated by the three wave coupling model simulation and Vlasov–Maxwell simulation for plasma parameters covering a wide range of kλ De from 0.19 to 0.48 at both high and low intensity laser drives. In the early stage of SRS evolution, it is found that besides the kinetic effects due to electron trapping (2018 Phys. Plasmas 25 100702), the Langdon effect can also significantly widen the parameter range for the absolute growth of SRS, and the time for the absolute SRS to reach saturation is greatly shortened by the Langdon effect within certain parameter regions. In the late stage of SRS, when secondary instabilities such as decay of the electron plasma wave to beam acoustic modes, rescattering, and Langmuir decay instability become important, the Langdon effect can influence the reflectivity of SRS by affecting secondary instabilities. The comprehension of the Langdon effect on nonlinear evolution and saturation of SRS would contribute to a better understanding and prediction of SRS in inertial confinement fusion.

Electron energy distribution and swarm parameters in DC Argon, Chlorine discharge and their mixtures

A study of electron energy distribution function and some swarm parameters in a DC discharge of pure Argon and chlorine is presented using Boltzmann transport equation. Moreover, the electron swarm parameters namely are: drift velocity and ionization coefficient.Reported electron cross-section data have been used in the calculation. The calculated distribution function are found to be remarked non-Maxwillian that have energy variations which reflect the import electron-molecule energy exchange processes It is notes that a small quantity of Cl2 affects the electron energy distribution function.

Properties of Electron Swarm Parameters in Tetrahydrofuran

Reported electron collision cross sections data in the energy range ~ 0 to 300 eV from gaseous biomolecule Tetrahydrofuran (THF) have been used to calculate the electron energy distribution function (EEDF) and swarm parameters for electrically excited of THF, using a two-term solution of the Boltzmann equation. The electron swarm parameters namely (mean energy, drift velocity, diffusion coefficient, electron mobility, characteristic energy, attachment and ionization coefficient), at room temperature and atmospheric pressure are presented over a wide range of applied electric field strength E/N (E is the electric field and N is the gas number density) varying from 0.1 Td to 1000 Td (1Td = 10-17 Vcm2). The EEDF found to be non-Maxwellian. The electron swarm parameters are compared with those calculated using multi term kinetic theory and experimentally using the pulsed Townsend technique. The influence of inelastic cross section on the calculated transport parameters is also explained.

(Invited) Role of Trace Impurities in Microwave-Excited Atmospheric Pressure Plasmas: Application to 3D Nano-Printing

Because rare gases like helium, neon or argon have first-excited levels at high energy (respectively 19.8, 16,62 and 11.5 eV), impurities with much lower energy levels are more easily excited. Thus, if their concentrations are high enough (hundreds of ppm or more), these impurities drive the behavior of the discharge, leading for instance to emission spectra where no lines of rare gas are visible.Modelling these discharges is a challenge because of the complexity of the chemical behavior of these trace elements. In microwave discharges, several problems arise among which one finds the role of electron-electron collisions, super-elastic collisions and the possible non-local heating of the electron energy distribution function. Based on a collisional–radiative model proposed to describe the behavior of a helium plasma sustained in a resonant cavity at atmospheric pressure, we will discussed these different aspects. The role of impurities will be described next. The level of dry air used as impurity typically varies from 0 to 1500 ppm, which corresponds to the most commonly encountered range in atmospheric pressure discharge experiments. Results clearly show that the plasma chemistry and consequently the discharge evolution is highly affected by the concentration level of impurities (from tens of thousands of ppm) in the mixture.Next, the use of these plasmas for 3D-nanoprinting will be detailed. This technology, named DISCRIBE, might be used for drawing electrical contacts, building pillars as part of metasurfaces or even creating 3D parts of clocks in watchmaking industry. A plasma-assisted printer, operated at atmospheric pressure, was developed to write patterns with sub-micrometric resolution. A reactive gas is injected through a needle within an atmospheric argon microwave plasma. Forming sub-micrometric needles (down to 100 nm in diameter) by pulling glass capillaries heated locally by laser is simple as this technology is readily available in the medical field. By plasma-enhanced chemical vapor deposition, a coating is formed on a substrate (conveniently a silicon wafer, but any other substrate can be used) with a spot size that almost corresponds to the needle aperture. Then, when the substrate moves, a pattern is formed accordingly. The writing speed is dependent on the dynamic deposition rate, which can be as high as 2 nm·m·s-1.In the specific case of acetylene used as precursor, the shape of the hydrogenated-carbon spot is strongly dependent on the amount of oxygen-containing impurities present in the microwave argon plasma. The influence of the plasma composition and the local hydrodynamic flow pattern are essential to control the deposition conditions and these aspects will be discussed. In particular, the distance between the needle exit and the substrate turns out to be a key parameter in the deposition process. DISCRIBE offers the advantage of all PECVD processes: it allows deposition at atmospheric pressure and reduced temperature of multi-materials (semiconductors, metals, ceramics, plasma polymers) ony any kind of substrate.

Simulation of Electron Swarm Parameters in CO2, Xe and their mixtures using Boltzmann Equation

The Boltzmann transport equation is used to calculate the electron energy distribution function (EEDF) and the transport parameters in pure CO2, Xe and their mixtures. Moreover, the electron swarm parameters are evaluated in the rang( 1 x 10-18 < E < 2 X 10-15 ) V.cm2 . These parameters, namely are drift velocity and ionization coefficient. Reported electron cross-section data have been used in the calculation. The calculated distribution function are found to be remarkably non- Maxwillian that have energy variations which reflect the import electron-molecule energy exchange processes the importance of the results obtained from molecular gas discharge lasers is also discussed.

Effect of electron energy distributions on the electron density in nitrogen inductively coupled plasmas

The effect of the electron energy distribution function (EEDF) on the behavior of the electron density (n e) is investigated under various gas pressures of nitrogen (N2) in inductively coupled plasma (ICP) operated at low and high input powers. A Langmuir probe is used to measure the EEDFs and electron densities, and the antenna coil current is measured to obtain the absorbed power in the plasma (P abs). At gas pressures above 2.67 Pa (20 mTorr) and 2500 W, P abs increases continually with increasing the gas pressure, but the electron density slightly decreases. In this case, the EEDF has a Maxwellian distribution with a high-energy tail. On the other hand, at 300 W, P abs decreases slightly with increasing gas pressure, but the electron density dramatically decreases, and the EEDF evolves from a bi-Maxwellian to a non-Maxwellian distribution with substantially highly depleted high-energetic part (high-energy tail). To analyze the difference in the behavior of the decrease rate in electron density, the total energy loss per electron–ion pair lost (ε T) is measured through the probe diagnostics, and the measured electron density is compared with the calculated electron density from the global model. An additional experiment is performed in Ar plasma under the same discharge conditions as N2 plasma to compare the EEDF effect. This study provides experimental evidence that the EEDF has a decisive effect on the behavior of the electron density in plasmas.

Influence of air and water vapor on EEDF, plasma parameters, and the main RONS in atmospheric pressure low temperature helium plasmas: Global model approach

A zero-dimensional global model is developed with an aim to study the influence of air and water vapor on an electron energy distribution function, electron density, and temperature as well as on the chemical composition of atmospheric pressure helium plasmas, with special focus on the main reactive oxygen and nitrogen species important for applications of low temperature plasmas. The main channels for the production and consumption of electrons and electron energy gain and loss are examined by a global model based on a parametric study with variations of the mole fractions of air and water vapor. The calculations are done for 100, 1000, and 10 000 ppm of air in plasma, and for each of these values, the content of water vapor is taken to be 100, 1000, 2000, …, to 10 000 ppm. The variations of the most important production and consumption processes for reactive oxygen and nitrogen species are analyzed in detail. According to the results presented in this paper, water vapor highly contributes to electronegativity of the plasma through pronounced attachment of electrons, which then leads to an increase in electron temperature. For high water vapor content, vibrational excitations of water molecules are one of the main electron energy loss processes, leading to a further effect on the plasma composition. Water decreases concentrations of atomic oxygen, nitrogen, and ozone, while there is an increase in nitrogen oxide, OH, H2O2, and HO2 concentrations. Cross-sectional data for electron scattering on ground and excited state neutrals are mainly taken from the Quantemol-DB database.

Non-equilibrium plasma kinetics of CO2 in glow discharges: a comparison with existing modeling and experimental results

We report results obtained by our 0D, time-dependent self-consistent model for the description of the CO2 plasma kinetics in glow discharge conditions, comparing our results with the simulation and experimental results reported by Grofulovic et al (2018 Plasma Sources Sci. Technol. 27 115009; 2019 PhD Thesis) and Klarenaar et al (2017 Plasma Sources Sci. Technol. 26 115008). Our model is based on the simultaneous solution of the kinetic equations describing the vibrational, the electronic excited states and the plasma chemistry and of the electron Boltzmann equation for the calculation of the electron energy distribution function (eedf). The results for the vibrational level densities of CO2 show a satisfactory agreement with the Grofulovic’s model results, despite the differences in the vibrational energy level scheme and in the kinetic processes included with the correspondent rate coefficients, with a good match also with the corresponding experimental results. Moreover, conditions characterized by higher power density (5–50 W cm−3) have been investigated to understand the behavior of the CO2 plasma discharge when a higher vibrational excitation is present. Large deviations of the vibrational distributions of CO2 and CO from equilibrium ones are predicted both in discharge and post discharge conditions. In particular, the CO2 vibrational distribution presents a behavior similar to a Treanor distribution for v < 15 while a deactivation of the plateau in the vibrational distribution function after v > 15 appears as a consequence of the dissociation induced by vibrational excitation mechanism, i.e. pure vibrational mechanism, becoming important at higher power densities. Finally, the results dependence on the selection of the CO2 electron molecule dissociation cross section, i.e. Phelps (1973 J. Appl. Phys. 44 4464 or Cosby (1993 Report No. AD-A266 464 WL-TR-93-2004 (Dayton, OH: Wright-Patterson Airforce Base)), has been investigated, showing that its more opportune choice is still a problem to be discussed for the description of conditions in which the electron impact dissociation dominates the kinetics, while once vibrational excitation is activated, CO2 dissociation is essentially driven by vibrational-induced dissociation, depending to a minor extent from that choice.

Comparison of Langmuir probe and optical emission spectroscopy on a volume-cusp filament ion source using helium.

D-Pace has a Penning ion source that runs with helium for studies of α-particle production. We want to study its plasma properties as a function of varying operational parameters, which results in varied output ion beam characteristics. In order to diagnose the ion source plasma, a collisional-radiative code for helium to be used with optical emission spectroscopy measurements is developed. This has the advantage of being non-invasive, which allows for measurements using the emitted light from the plasma. This collisional-radiative code is shown to compare well with the Yacora on the Web model developed at IPP-Garching, and improves upon it with the addition of radiation trapping. Furthermore, the sensitivity of this model to the inclusion of additional excited state populations and non-Maxwellian electron energy distribution functions is investigated. It is shown that non-Maxwellian distributions can significantly affect spectroscopy measurements. This diagnostic is benchmarked to Langmuir probe measurements on the TRIUMF-licensed volume-cusp ion source to determine whether it can replicate the measured electron density and electron temperature as a function of varied operational parameters. The operational parameters are helium gas flow (10-40 SCCM), arc voltage (100-200V), and arc current (1-5A). The measured plasma properties, while different in absolute value, have similar trends for each operational parameter except when varying arc voltage. It is shown that this mismatch as a function of arc voltage is likely due to high energy non-Maxwellian electrons from the cathode sheath, which are not included within the collisional-radiative model.

Measurements and interpretation of EEDF in a discharge with a hollow cathode in helium: effect of the measuring probe and the anode on the form of the distribution function

Experimental and theoretical studies of the electron energy distribution function in hollow cathode discharge plasma have been carried out. The discharge was ignited in helium at a pressure of 0.75 Torr, and the distance between the rectangular hollow cathode and anode was 3 cm. The measurements were performed using the probe method at various distances from the anode. The obtained distribution functions turned out to be strongly depleted in low-energy electrons. As applied to the experimental conditions, the role of two effects that can lead to such depletion was analyzed: instrumental distortions of the distribution function due to the electron sink on the probe and the absorption of electrons by the anode. According to the calculations, under the considered conditions, the main contribution to the depletion of the measured distribution functions by the slow electrons comes from the second effect.

State enhanced actinometry in the COST microplasma jet

A new actinometry approach, helium state enhanced actinometry (SEA), is presented. This diagnostic uses the emission of the atomic states O(3p3P) (λ = 844.6 nm), Ar(2p1) (λ = 750.4 nm) and He(33S) (λ = 706.5 nm) and allows the atomic oxygen density and the mean electron energy to be determined simultaneously from the spectral line intensity ratios. Here, the atomic states are selected in a way that they cover a wide range of the electron energy distribution function (EEDF). The method is compared to the classical actinometry approach and energy resolved actinometry (ERA) based on measurements on the COST microplasma jet. In addition, a benchmark against two-photon absorption laser induced fluorescence measurements is performed. Both atomic oxygen densities and mean electron energies are in good agreement with the literature. Furthermore, SEA offers a number of advantages over known approaches. Firstly, the experimental complexity is significantly reduced by using time-integrated spectra instead of phase-resolved measurements, as used in the original ERA approach. Secondly, the precision of the electron energy measurement can be significantly improved by the use of the helium state. In addition, known uncertainties e.g. due to excitation of oxygen excited levels via metastable oxygen states can be reduced.

The LisbOn KInetics Monte Carlo solver

The LisbOn KInetics Monte Carlo (LoKI-MC) is an open-source simulation tool that solves the electron kinetics for low-temperature plasmas excited by uniform DC electric fields from different gas mixtures, using Monte Carlo techniques. Following the strategy and data organization of the LisbOn KInetics Boltzmann (LoKI-B) solver, the program easily addresses any complex mixture of atomic/molecular species, describing electron collisions with any target state (electronic, vibrational and rotational), characterized by any user-prescribed population. LoKI-MC is written in C++, benefiting from a highly-efficient object-oriented structure. On input, the code requires the working conditions, the gas-mixture composition, the distributions of populations for the levels of the atomic/molecular gases considered, and the relevant sets of electron-scattering cross sections obtained from the open-access website LXCat. On output, it yields the electron energy and velocity distribution functions, the electron swarm parameters, the collision rate-coefficients, and the electron power absorbed from the electric field and transferred to the different collisional channels. This paper presents LoKI-MC and gives examples of results obtained for different model and real gases, verifying and benchmarking the simulation tool against analytical solutions and other available codes, and assesses its computational performance. Moreover, the effects of the gas temperature, anisotropic ionization scattering (induced by momentum conservation) and superelastic collisions are analyzed in real gases. Program summaryProgram title: LoKI-MCCPC Library link to program files:https://doi.org/10.17632/n7t6ctp2st.1Developer's repository link:https://github.com/IST-Lisbon/LoKI-MCLicensing provisions: GPLv3Programming language: C++17Nature of problem: Simulation of the electron kinetics in non-equilibrium low-temperature plasmas, excited from arbitrarily complex gas-mixtures, under static and uniform electric fields.Solution method: Monte Carlo sampling techniques.