Electron Impact Excitation Research Articles

Electron-impact excitation data for W2+ in support of tungsten spectroscopy and re-deposition measurements for magnetically-confined plasmas

Abstract To better understand plasma wall interactions involving tungsten, accurate atomic structure and electron-impact driven collisional processes for near-neutral ion stages of tungsten are required. Complementing existing work on neutral and singly ionised tungsten, atomic structure and collisional calculations for W2+ electron-impact excitation have been completed. These excitation calculations are an important component of S/XB coefficients for near-neutral charge states, which may be used to spectroscopically infer re-deposition of tungsten at the plasma-solid boundary of fusion relevant devices. With W2+ in particular having emission lines that can be observed at ultraviolet (UV) wavelengths, while higher charge states of tungsten are unlikely to have lines possible to observe outside of the vacuum UV range. The atomic structure was generated using the General-purpose Relativistic Atomic Structure Package (GRASP0), implementing the Multi-configuration Dirac Fock approach. This structure was the basis for a subsequent Dirac R-matrix electron-impact excitation calculation to provide Maxwellian averaged rate coefficients. A synthetic spectrum was generated from this data using a collisional-radiative model to predict the strongest W III spectral lines and these lines were compared to emission from the Compact Toroidal Hybrid (CTH) plasma device. Several of the strongest W III lines are observed in CTH and agree well with the modelled line wavelengths and intensities, a table of these lines is provided that could be observed in other devices.

MHz sampling rate measurements of N2(A3Σu+) population in a Ns pulse discharge in a heated plasma flow reactor

Abstract Absolute, time-resolved population of a metastable electronic state of molecular nitrogen, N2( A 3 Σ u + , v = 0 ), is measured in a heated plasma flow reactor excited by a ns pulse discharge burst, by tunable diode laser absorption spectroscopy using a distributed feedback laser. Nitrogen or NO–N2 gas mixture in the reactor are heated by a tube furnace maintained at T = 800–1000 K, at pressures of P = 50–300 Torr. A diffuse plasma in the flow channel made of quartz is generated using a repetitively pulsed, double dielectric barrier, ns discharge in a plane-to-plane geometry. N2( A 3 Σ u + ) molecules in the plasma are generated by electron impact excitation of N2 ( B 3 Π g ) and N2 ( C 3 Π u ) states, followed by their cascade quenching. The laser is tuned across an absorption line near 1028 nm in a N2 B 3 Π g , v ′ = 0 ← A 3 Σ u + , v ′ ′ = 0 band at 100 kHz–1 MHz. The laser output wavelength and the absorption signal are measured by an etalon and two high bandwidth detectors. At all operating conditions, the absorption signal is fully resolved in time. The data points are taken every 500 ns–5 μs, with the temporal uncertainty of 50–500 ns, respectively. The data are used to infer the line pressure broadening coefficient and its temperature dependence. This study demonstrates the feasibility of this approach for the time-resolved N2( A 3 Σ u + ) measurements in pulsed hypersonic flow facilities, behind strong shock waves and in hypervelocity expansion flows.

Electron impact excitation of bismuth

Abstract The present study investigates the electron impact excitation of bismuth from the ground state 6p3 4S3/2 to the excited state 6p27s 4P1/2. Motivated by the latest measurements by Marinković et al [J. Phys. B, 49 23 520 (2016)], relativistic distorted wave calculations are performed to obtain the differential and integrated cross sections for incident electron energies at 10, 20, 40, 60, 80, and 100 eVs. These results are compared with the available experimental data and a good agreement is observed. Our results represent the first theoretical work to provide such a comparison. Additionally, we report the generalized oscillator strengths derived from our calculated differential cross sections.

Laboratory Benchmark of n ≥ 4 Dielectronic Recombination Satellites of Fe xvii

We calculated cross sections for the dielectronic recombination (DR) satellite lines of Fe xvii and benchmarked our predictions with experimental cross sections of Fe xvii resonances that were monoenergetically excited in an electron-beam ion trap. We extend the benchmark to all resolved DR and direct electron-impact excitation (DE) channels in the experimental data set, specifically the n ≥ 4 DR resonances of Fe xvii, complementing earlier investigations of n = 3 channels. Our predictions for the DR and DE absolute cross sections for the higher n complexes disagree considerably with experimental results when using the same methods as in previous works. However, we achieve agreement within ∼10% of the experimental results by an approach whereby we doubly convolve the predicted cross sections with both the spread of the electron-beam energy and the photon energy resolution of our experiment. We then calculated rate coefficients from the experimental and theoretical cross sections, finding general agreement within 2σ with the rates found in the OPEN-ADAS atomic database.

Impurity transport study based on measurement of visible wavelength high-n charge exchange transitions at W7-X

A recently installed high-speed charge exchange diagnostic at the W7-X stellarator has been used to identify several high-n Rydberg emission lines near 500 nm following impurity injections. The wavelengths of observed high-n Rydberg transitions are independent of the impurity species and originate from ions with ionization states ranging from 14+ to 45+ suggesting that this approach can be applied to a variety of heavy impurities. Moreover, little to no passive signal is observed since the high-n energy levels are unlikely to be populated by electron impact excitation. The combination of the newly developed diagnostic and the observation of high-n Rydberg states provides spatially resolved, high-speed measurements of multiple charge states which are analyzed in a Bayesian inference framework to determine both impurity diffusion and convection profiles. Measurements from the 2023 experimental campaign conclusively show high diffusion and an inward pinch in the core, well above predictions by neoclassical theory.

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.

Atomic structure, electron-impact excitation and collisional-radiative modelling for Ar II

The spectra from singly ionized argon Ar II has significant diagnostic capability in the characterization and modelling of both magnetically-confined fusion and astrophysical plasmas. The literature has several pre-existing data sets for Ar+ but this paper presents the results from 3 new atomic structure and electron-impact scattering models in order to better constrain the differences in atomic data and how they impact well-known plasma diagnostics. Several independent atomic structure methodologies are employed to calculate the energy levels and transition probabilities for each model. The first approach employs a relativistic Dirac–Coulomb Hamiltonian model, the second approach uses a semi-relativistic Breit–Pauli Hamiltonian with the mass-velocity, Darwin and spin–orbit corrections, and in a third case an ICFT approach. Three atomic structure models provide a foundation for Dirac R-matrix, a semi-relativistic ICFT (Intermediate Coupling Frame Transformation) and a Breit–Pauli R-Matrix with Pseudostates (BPRMPS) calculation. Synthetic spectra utilizing these three data sets are compared against measurements taken at the Compact Toroidal Hybrid (CTH) stellarator, and the total radiative power loss is also benchmarked against previous calculations.

Evaluating plasma fluctuation by collisional-radiative model using Malliavin derivative

Abstract Non-equilibrium plasma has garnered significant attention due to its involvement in short-term phenomena. One example is plasma fluctuation, encompassing variations in electron temperature or density. This phenomenon is explored not only in nuclear fusion but also in semiconductor etching and thin film deposition. This study introduces an evaluation method employing Malliavin derivatives to predict plasma fluctuations based on a collisional-radiative model. This model delineates the chemical kinetics of excited states within the plasma. Given that electron impact excitation and atomic collisional processes are stochastic, they exhibit characteristics similar to a Wiener process. Furthermore, the properties of fractional Brownian motion are applied to the Malliavin derivative. The revised Wiener process is utilized to analyze the changes in excited-level populations within short durations. This approach assesses electron or atomic density fluctuations by considering the contributions of electron collisions and those of ground-state atoms.

Effect of a negative DC bias on a capacitively coupled Ar plasma operated at different radiofrequency voltages and gas pressures

The effect of a negative DC bias, |V dc|, on the electrical parameters and discharge mode is investigated experimentally in a radiofrequency (RF) capacitively coupled Ar plasma operated at different RF voltage amplitudes and gas pressures. The electron density is measured using a hairpin probe and the spatio-temporal distribution of the electron-impact excitation rate is determined by phase-resolved optical emission spectroscopy. The electrical parameters are obtained based on the waveforms of the electrode voltage and plasma current measured by a voltage probe and a current probe. It was found that at a low |V dc|, i.e. in α-mode, the electron density and RF current decline with increasing |V dc|; meanwhile, the plasma impedance becomes more capacitive due to a widened sheath. Therefore, RF power deposition is suppressed. When |V dc| exceeds a certain value, the plasma changes to α–γ hybrid mode (or the discharge becomes dominated by the γ-mode), manifesting a drastically growing electron density and a moderately increasing RF current. Meanwhile, the plasma impedance becomes more resistive, so RF power deposition is enhanced with |V dc|. We also found that the electrical parameters show similar dependence on |V dc| at different RF voltages, and α–γ mode transition occurs at a lower |V dc| at a higher RF voltage. By increasing the pressure, plasma impedance becomes more resistive, so RF power deposition and electron density are enhanced. In particular, the α–γ mode transition tends to occur at a lower |V dc| with increase in pressure.

Performance assessment of spectroscopic measurements of hydrogen and beryllium influxes and ionization fronts in ITER divertor plasmas using the divertor impurity monitor

Characteristics of Hα and Be II emissions in ITER divertor plasmas have been evaluated, and the applicability of a spectroscopic evaluation method of influxes and ionization front positions by using the divertor impurity monitor (DIM) has been systematically verified for the first time based on plasma profile datasets with parameter scans. In addition, practical values of the ionization/photon factor (S/XB) for DIM to evaluate influxes have been determined. In attached divertor plasmas and the onset of plasma detachment, H influx integrated over the entire area of the divertor can be evaluated within ±30 % accuracy using Hα intensities measured by the DIM and S/XB value of 32, which is higher than the S/XB in most divertor plasmas in previous devices owing to high electron density. The ionization front position can also be evaluated to within a few mm by using peak channel position. However, when electron temperature further decreases from the detachment onset, the ionizing plasma component (caused by electron impact excitation) in the total Hα emission decreases and the spatial profiles of emission and ionization diverge, making spectroscopic evaluation difficult. In all conditions, Hα intensities could be measured with a more than sufficient number of photons at the required time resolution using the current DIM design. For Be influx integrated over the entire divertor area, it has been found that Be I is not suitable for the DIM since its intensity is similar to the background continuous spectra. Replacing Be I with Be II solves this problem. Even in detached divertor plasmas, it is possible to evaluate Be1+ ionization flux within ±30 % accuracy using Be II intensities and S/XB, the value of which depends on the DIM’s fields of view. However, the evaluated Be1+ ionization flux is lower than Be influx by more than 80 %, meaning that the evaluation of Be influx using Be II would be an underestimate. But, Be II can be measured with a more than sufficient number of photons.

Relativistic calculations of energy levels, lifetimes, transition parameters, and electron impact excitation cross sections for Kr XIX

In this study, we present a detailed analysis of atomic properties for Kr XIX, specifically focusing on the lowest 128 fine-structure levels originating from the 3s23p6, 3s23p53d, 3s3p63d and 3s23p43d2 configurations. We report energy levels, lifetimes, wavelengths, weighted oscillator strengths, and transition probabilities for multipole transition types (E1, E2, M1, and M2). To achieve this, we employed the GRASP2018 code, which implements the fully relativistic multiconfigurational Dirac–Hartree–Fock method and accounts for Breit interaction and quantum electrodynamic effects. We performed another set of calculations using the many-body perturbation theory implemented in the flexible atomic code (FAC). By comparing the results obtained from GRASP2018 and FAC, we established the accuracy and consistency of our calculations. Furthermore, using the relativistic distorted wave theory, we studied electron impact excitation of all transitions to upper levels from the ground and metastable levels and reported excitation cross sections for incident electron energies up to 5 keV. To enhance the practical utility of our findings, we also provided analytical fittings of these cross sections and excitation rate coefficients for their applications in plasma modeling. This work contributes to the atomic properties and excitation cross sections of Kr XIX, addressing a marked gap in the available atomic data.

Excitation and recombination studies with silicon and sulphur ions at an EBIT

Measurements of electron-impact excitation and recombination rate coefficients of highly charged Si and S ions at the Stockholm electron beam ion trap are reported. The experimental method was a combination of photon detection from the trapped ions during probing and subsequently extraction and time-of-flight (TOF) charge analysis of these ions. The TOF technique allows to measure recombination rate coefficients separately for every charge state, and together with the photon spectra of these ions also the excitation rate coefficients. In this paper, we present more details of the experimental procedure and summarize the experimental results in comparison with two different state-of-the-art calculations of recombination and excitation rates for Si10+–Si13+ and S12+–S15+ ions. One of these uses a relativistic configuration interaction approach (flexible atomic code) and the other is a relativistic many-body perturbation theory. A good to excellent agreement with both of them is found in energy and resonance strength for the investigated ions.

Nonadiabatic Molecular Dynamics of Water Cluster Dissociation by Vacuum Ultraviolet Absorption or Electron Impact Excitation.

After five decades of investigation since the 1970s, the nature of photon-induced or electron-induced water dissociation is still largely studied only in the gas phase, with a notable absence of dynamics studies of water clusters and bulk water. We study the problem with density functional theory and the nonadiabatic fewest switches surface hopping technique considering both singlet and triplet excited states to study the dissociation of water clusters leading mainly to OH + H. For clusters of 40 water molecules, the mean dissociation time was found to be <10 fs, and the threshold energy was ∼6 eV. Dissociation is almost exclusively associated with the cluster surface due to the lower energy of surface water excited states relative to the bulk. Recombination plays a major role in vacuum ultraviolet dissociation. O + H2 is found as a minor product in the dissociation and is mostly produced in "roaming" trajectories.

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.

Theoretical study of valence excitations in fluoromethanes by high energy electron impact

We report a theoretical study of the electron-impact electronic excitation of fluoromethanes. Generalized oscillator strengths (GOSs) are calculated for the molecules at the equation-of-motion coupled-cluster singles and doubles level. To clarify the influence of nuclear dynamics on the electronic excitations, the effects of internal molecular vibrations are included in the calculation. Comparison with experimental data resolves some inconsistencies in the assignment of the transition bands. Furthermore, it is shown that the lengthening of the CH bond enhances the excitation from the highest occupied orbital to the 3s Rydberg orbital for CHF3, CH2F2, and CH3F, and that the CH stretching vibrations thus have a significant influence, especially at small momentum transfer where electric dipole transitions are dominant. Since the 2 1A1 state of CHF3 dissociates into CF3 + H, the result indicates that the CH stretching vibration causes an increase in the production of CF3 by electron collision and by photoabsorption.

Effect of the configuration mixing on the polarization and angular distribution of x-ray line emissions following electron-impact excitation of Ne-like ions.

We present a systematic theoretical study on the angular distribution and linear polarization of x-ray line emissions of neon-like ions following the electron-impact excitation from the ground state to the excited levels [(2p5)1/23d3/2]J=1, [(2p5)3/23d5/2]J=1, [(2p5)3/23d3/2]J=1, and [(2p5)1/23s]J=1. The cross sections are calculated by using the flexible atomic code under configuration-interaction plus many-body perturbation theory method. The angular distribution and linear polarization are obtained based on density matrix theory. Emphasis has been placed on the effect of the configuration mixing on the angular distribution and polarization. It has been proved that the strong mixing of configuration [(2p5)3/23d3/2]J=1 with configuration [(2p5)1/23s]J=1 can result in the abrupt change of Z-dependence of angular distribution and polarization. It indicates that angular distribution and polarization can be expected to serve as a tool for investigation of configuration mixing effect.

Nitrogen admixture-driven electron cooling and plasma bullet dynamics in atmospheric-pressure dc nanosecond-pulsed argon jet plasmas

We present experimental measurements of the electron temperature and density profiles and analyze the dynamics of a plasma bullet at volumetric concentrations of nitrogen admixture, 0%–3%, in an atmospheric-pressure nanosecond-pulsed argon jet plasma. Time-resolved Thomson scattering measurements taken 2.5 mm from the exit plane reveal that the temporal maximum of electron temperature and density reduced by as much as 55% and 29%, respectively, when mixing only 3% nitrogen to pure argon. These trends were consistent across axial locations from 2.5 to 14 mm from the exit plane for both electron temperature and density at nitrogen admixture plasmas. Moreover, the propagation velocity and length of the plasma bullet decreased by 13% while the radius by 23% at 3%-nitrogen admixture when compared to the pure argon jet case. The analysis suggests that the nitrogen admixture causes electron cooling due to inelastic energy losses, which results in a reduced electron density and propagation velocity due to a decrease in the electron-impact ionization rate. It is therefore inferred that the electron cooling mechanism and reduced density at nitrogen admixture will significantly impact the electron-impact excitation rate coefficient of nitrogen as well as the concentration of the precursor species such as N2(A3Σu+).

Fine structure resolved excitation cross sections of singly ionized Ga for the modeling and diagnostics of Ga plasmas

Calculation of electron impact excitation cross sections for singly charged Ga ions plays a crucial role in plasma modeling, facilitating the comprehension of plasma behavior, characteristics, and dynamics in diverse domains, such as astrophysics, fusion research, the semiconductor industry, etc. In the available literature, there is a notable scarcity of, or even a complete absence of, these cross sections. Hence, in the present work, electron impact excitation cross sections are calculated for the transitions from the fine structure resolved energy levels of the configurations 4s2 and 4s4p to the fine structure resolved energy levels of the configurations 4s4p , 4s5s , 4p2 and 4s4d of the singly charged Ga ion (Ga+) using the relativistic distorted wave approximation theory with the target states represented by multi configurational Dirac Fock wavefunctions. The cross sections are calculated for projectile electron energy varying from threshold to 500 eV. Furthermore, the electron impact excitation rate coefficients for all the transitions under investigation are also calculated for electron temperatures ranging from 0.5 to 5 eV. In addition, analytic fitting of the rate coefficients is also performed, providing a practical resource for directly utilizing in plasma modeling applications.

Frequency-dependent electron power absorption mode transitions in capacitively coupled argon-oxygen plasmas

Phase Resolved Optical Emission Spectroscopy (PROES) measurements combined with 1d3v Particle-in-Cell/Monte Carlo Collisions simulations are performed to investigate the excitation dynamics in low-pressure capacitively coupled plasmas (CCPs) in argon-oxygen mixtures. The system used for this study is a geometrically symmetric CCP reactor operated in a 70% Ar-30% O2 mixture at 120 Pa, applying a peak-to-peak voltage of 350 V, with a wide range of driving RF frequencies (2 MHz ⩽f⩽ 15 MHz). The measured and calculated spatio-temporal distributions of the electron impact excitation rates from the Ar ground state to the Ar 2p1 level show good qualitative agreement. The distributions show significant frequency dependence, which is generally considered to be predictive of transitions in the dominant discharge operating mode. Three frequency ranges can be distinguished, showing distinctly different excitation characteristics: (i) in the low frequency range ( f⩽ 3 MHz), excitation is strong at the sheaths and weak in the bulk region; (ii) at intermediate frequencies (3.5 MHz ⩽f⩽ 5 MHz), the excitation rate in the bulk region is enhanced and shows striation formation; (iii) above 6 MHz, excitation in the bulk gradually decreases with increasing frequency. Boltzmann term analysis was performed to quantify the frequency-dependent contributions of the Ohmic and ambipolar terms to the electron power absorption.

An experimental and computational study on the ignition process of a pulse modulated dual-RF capacitively coupled plasma operated at various low-frequency voltage amplitudes

The ignition process of a pulse modulated capacitively coupled argon discharge driven simultaneously by two radio frequency voltages [12.5 MHz (high frequency) and 2.5 MHz (low frequency, LF)] is investigated by multifold experimental diagnostics and particle in cell / Monte Carlo collision simulations. In particular, (i) the effects of the LF voltage amplitude measured at the end of the pulse-on period, VL,end , on the spatiotemporal distribution of the electron impact excitation rate determined by phase resolved optical emission spectroscopy, and (ii) the electrical parameters acquired by analyzing the measured waveforms of the plasma current and voltage, are studied. Computed electrical parameters and spatio-temporal excitation maps show a good qualitative agreement with the experimental results. Especially, various breakdown mechanisms are found at different VL,end . At low values of VL,end , the ‘RF-avalanche’ mode (volume process) dominates the electron multiplication process. By increasing VL,end , the ionization caused by the volume electrons is suppressed and the electron loss at the electrodes is enhanced, leading to a delayed ignition. At higher values of VL,end , the avalanche ionization is significantly enhanced by ion-induced secondary electron emission at the electrodes, so that the ignition is significantly advanced.