Electron Impact Excitation Rates Research Articles

Simple electron-impact excitation cross-sections including plasma density effects

The modeling of non-local-thermodynamic-equilibrium plasmas is crucial for many aspects of high-energy-density physics. It often requires collisional–radiative models coupled with radiative-hydrodynamics simulations. Therefore, there is a strong need for fast and as accurate as possible calculations of the cross-sections and rates of the different collisional and radiative processes. We present an analytical approach for the computation of the electron-impact excitation (EIE) cross-sections in the Plane Wave Born (PWB) approximation. The formalism relies on the screened hydrogenic model. The EIE cross-section is expressed in terms of integrals, involving spherical Bessel functions, which can be calculated analytically. In order to remedy the fact that the PWB approximation is not correct at low energy (near threshold), we consider different correcting factors (Elwert–Sommerfeld, Cowan–Robb, Kilcrease–Brookes). We also investigate the role of plasma density effects such as Coulomb screening and quantum degeneracy on the EIE rate. This requires to integrate the collision strength multiplied by the Fermi–Dirac distribution and the Pauli blocking factor. We show that, using an analytical fit often used in collisional–radiative models, the EIE rate can be calculated accurately without any numerical integration, and compare our expression with a correction factor presented in a recent work.

Electron-impact recombination and excitation rates for charge-state-selected highly charged Si ions

Charge-state selective recombination rate coefficients were measured by time of flight (TOF) analyzed highly charged Si ions extracted from an electron-beam ion trap. Additionally, the combination of simultaneous TOF and x-ray measurements and a separation of the dielectronic recombination contribution in the x-ray spectra is used for extracting electron-impact excitation rate coefficients for several overlaying charge states. Experimentally derived dielectronic recombination spectra for XIII and XIV Si are compared and found in excellent agreement with the results of relativistic many-body perturbation theory calculations.

Vibrationally resolved electron impact electronic excitation of BeH

Beryllium is being adopted for plasma facing walls in fusion reactors. This has led to the observation of emissions from the A 2Π state of beryllium hydride. Use of these emissions to monitor Be erosion requires electron impact excitation rates. Cross sections for electron impact vibrational excitation within the X 2Σ+ state and vibrationally resolved electronic excitation to the A 2Π state are reported for BeH, BeD and BeT. Electron collisions are studied at a range of internuclear separations using the UK molecular R-matrix (UKRmol+) codes. Electronic excitation is studied both within the Franck–Condon approximation and by explicit averaging of the T-matrix elements. It is found that (a) inclusion of the effect of higher partial waves using the Born approximation leads to significant increases in the cross sections and (b) the Franck–Condon approximation underestimates the importance of collisions for which the vibrational state changes during electronic excitation.

Two-temperature Collisional-radiative Modeling of Partially Ionized O2-Ar Mixtures over 8000-10,000 K Behind Reflected Shock Waves.

The collisional excitation kinetics of atomic oxygen was studied behind reflected shock waves using tunable diode laser absorption spectroscopy. A test gas mixture of 1% O2/Ar was shock-heated to temperatures between 8000 and 10,000 K and pressures between 0.15 and 1 atm. The time evolution of the atomic oxygen population in the 3 s 5S0 state was monitored by laser absorption at 777.2 nm. The measured O(3 s 5S0) population revealed multistage behavior that was not observed in previous measurements over a temperature range of 5300-7200 K. To interpret the multistage behavior, a three-level collisional-radiative model for atomic oxygen excitation kinetics was developed. The model utilized two independent temperatures, that is, heavy particle translational temperature Ttr and electron translational temperature Te, to describe the fundamental rate constants of atomic oxygen excitation because of collisions with heavy particles and electrons, respectively. The heavy particle excitation rate was inferred from the early stage of the measurement to be k(3P →5S0) = 3.4 × 10-27 (T/K)0.5(1.061 × 105 + 2 (T/K)) exp(-1.061 × 105 K/T) ± 50% m3 s-1. The electron impact excitation rate constant of oxygen, electron impact, and heavy particle impact ionization rate constants of Argon were modified in the model to match the experimental population time histories. The modified rate parameters are also reported for the temperature range explored in the current study.

Energy levels, transition rates and electron impact excitation rates for B-like Kr XXXII

Energy levels and transition rates for electric-dipole, electric-quadrupole, electric-octupole, magnetic-dipole, and magnetic-quadrupole transitions among the levels arising from the n≤ 5 configurations in B-like Kr XXXII are calculated by using two state-of-the-art methods, namely, the multi-configuration Dirac–Hartree–Fock (MCDHF) approach and the second-order many-body perturbation theory (RMBPT). Our results are compared with several available experimental and other theoretical values. Electron-impact excitation (EIE) collision strengths are calculated via the independent process and isolated resonance approximation using distorted-wave (denoted by IPIRDW). Radiation damping effects on the resonance excitation contributions are included. Effective collision strengths are calculated as a function of electron temperature by assuming a Maxwellian electron velocity distribution. Spectral line intensities are modelled by using collision radiative model, and several line pairs pointed out might be useful for density diagnostics.

Stagnation-point heating of Fire II with a non-Boltzmann radiation model

The present work analyzes the stagnation-point radiative heating in the Fire II flight experiment by devising a collisional-radiative model with non-local absorption. In the stagnation-line flow-field calculations, a viscous shock layer method with a thermochemical nonequilibrium model is utilized. In the radiation calculations, a line-by-line method with the non-Boltzmann electronic populations is employed by adopting the quasi-steady state approach of the electronic master equation calculations. In constructing the electronic master equation, the best set of the electron and heavy-particle impact excitation rates is proposed to achieve better agreement with the measured radiative heating flight data. In the flow-radiation coupling procedure, the effect of the non-local absorption is modeled by devising an iterative process between the quasi-steady state electronic master equation and the radiative transfer equation calculations. Escape factors of the strongest atomic lines and the diatomic nitrogen vacuum ultraviolet systems with the non-local absorption effect are also proposed to more efficiently consider the non-local nature of the radiative transition. When compared with the experimental data from the Fire II trajectories, it is found that the present collisional-radiative model with the non-local absorption improves the ability to predict non-Boltzmann radiative heating.

Calculations of Dielectronic Recombination and Electron-impact Excitation Rate Coefficients of Highly Charged Sulfur Ions

Abstract Connected to the experiment performed at the Stockholm electron beam ion trap, a systematic relativistic configuration-interaction calculation is carried out to compare with the experimental spectra. In particular, separate rate coefficients are calculated for dominant recombination and excitation processes in the range of the impact electron energy determined by the experiment. By means of the relevant experimental parameters, the presently calculated dielectronic recombination rate coefficients for and S14+ ions and electron-impact excitation ones for S15+, S14+, and S13+ ions are employed further to synthesize overall theoretical spectra for comparison with the experimentally measured spectra. Overall, very good agreements with the experimental results are found except for one missing excitation peak around the impact electron energy 2.52 keV, which cannot be explained by the present calculations and thus remains open.

Helium metastable species generation in atmospheric pressure RF plasma jets driven by tailored voltage waveforms in mixtures of He and N2

Spatially resolved tunable diode-laser absorption measurements of the absolute densities of He-I (23S1) metastables in a micro atmospheric pressure plasma jet operated in He/N2 and driven by ‘peaks’- and ‘valleys’-type tailored voltage waveforms are presented. The measurements are performed at different nitrogen admixture concentrations and peak-to-peak voltages with waveforms that consist of up to four consecutive harmonics of the fundamental frequency of 13.56 MHz. Comparisons of the measured metastable densities with those obtained from particle-in-cell/Monte Carlo collision simulations show a good quantitative agreement. The density of helium metastables is found to be significantly enhanced by increasing the number of consecutive driving harmonics. Their generation can be further optimized by tuning the peak-to-peak voltage amplitude and the concentration of the reactive gas admixture. These findings are understood based on detailed fundamental insights into the spatio-temporal electron dynamics gained from the simulations, which show that voltage waveform tailoring allows to control the electron energy distribution function to optimize the metastable generation. A high degree of correlation between the metastable creation rate and the electron impact excitation rate from the helium ground state into the He-I ((3s)3S1) level is observed for some conditions which may facilitate an estimation of the metastable densities based on phase resolved optical emission spectroscopy measurements of the 706.5 nm He-I line originating from the above level and metastable density values at proper reference conditions.

Resonance contribution to electron-impact excitation rate coefficients of helium-like S14+ ions

SynopsisElectron-impact excitation rate coefficients of S14+ ions have been studied by using a relativistic flexible atomic code that can account systematically for configuration interactions. Moreover, we also considered the resonance excitation contributions to the rate coefficients. It is found that the contributions of resonance excitation on rate coefficients is very important.

Measurement of Radiative Nonequilibrium for Air Shocks Between 7 and

This paper describes a characterization of thermochemical nonequilibrium radiance for shock speeds between 7 and in the NASA Ames Electric Arc Shock Tube. Data are spectrally resolved from 190 to 1450 nm and spatially resolved behind the shock front on the order of 10 cm. The data are analyzed in terms of a spectral nonequilibrium metric, defined as the average radiance within of the peak radiance and presented in a format that may be used to test predictive nonequilibrium radiation tools. The data collected in two shock tubes of differing diameter (10 and 60 cm) at the same nominal shock condition agree within 30%. The spectra are compared with simulations using the DPLR/NEQAIR software tools using a combination of different modeling options (reaction rates, energy mode accounting, and electron impact excitation rates). The results show mixed agreement, with no one modeling option being a clear preference. This suggests that the data may be used to help to identify improvements to methodologies for modeling nonequilibrium air radiation.

Energy levels, oscillator strengths, radiative transition probabilities, level lifetimes and electron-impact excitation rate coefficients for Ne-like Mo XXXIII

The energy levels, oscillator strengths, radiative decay rates, lifetimes, collision strengths, direct and resonance electron-impact excitation rate coefficients have been computed for the 257 fine-structure levels arising from 1s22s22p5nl and 1s22s2p6n′l′ configurations belonging to the Mo32+ ion with n≤7, l≤4 and n′≤5, l′≤4. The model-potential approach is used for the target ion structure calculations. Additionally, we employ the multiconfiguration Dirac–Hartree–Fock method to further assess the energy levels and transition probabilities. The collision strengths for the electron-impact direct excitation are computed within the relativistic distorted-wave approximation at 34, 135, 680, 1700, 5436, and 12,740 eV scattered electron energy values. We also perform collision calculations at 85, 175, and 450 keV electron energies using the plane-wave approximation and interpolate the reduced cross section within Fano plots, thus accounting for relativistic effects at asymptotic energies. This assures the convergence of Maxwellian integration for effective collision strengths calculation at electron temperatures up to 80 keV. The resonance contribution to the excitation rates is accounted for within the independent process isolated resonance approximation by including Na-like Mo31+ doubly excited autoionization states arising from the 1s227nln′l′ configurations with n≤7,l≤4,n′≤20,l′≤8. Contributions from high n′≥21 Rydberg states to the excitation rate coefficients are included by employing the n′−3 extrapolation law for radiative and autoionization decay rates. Radiative decay of resonances to lower autoionization states followed by autoionization cascade as well as radiative damping via core transitions are included in our model. The highest rate coefficients corresponding to ground state excitations are the 2p–3d allowed and 2p–3p electric monopole transitions, respectively. Intercombination and generally higher-order electric multipole transitions amount to lower excitation rate coefficients but are not to be neglected. Magnetic transitions are only relevant for low electron temperatures since both their direct and resonance contributions to excitation significantly decrease with increasing electron energy. Present results compare well with existing data from literature. The resonance contributions play an important role in the accuracy of rate coefficients, especially for weak forbidden transitions at low electron temperatures. These results may be useful in fusion related plasmas, astrophysics and fundamental physics.

Striations in dual-frequency capacitively coupled CF4 plasmas: the role of the high-frequency voltage amplitude

Striations in dual-frequency (DF, 8/40 MHz) capacitively coupled CF4 plasmas have been investigated by phase resolved optical emission spectroscopy and via Particle-in-Cell/Monte Carlo collision simulations. The properties of striated structures of various plasma parameters in a DF discharge and the effect of the high-frequency voltage amplitude, ϕH, on the striated structures and charged species densities were studied at a gas pressure of 100 Pa. The measured spatiotemporal electronic excitation rates at different ϕH are in good agreement with the simulation results. It was found that the excitation/ionization patterns are modulated not only in space, but also in time by two frequencies. As ϕH increases, the width of a single ion density peak, dpeak, generally increases, leading to a decrease of the number of striations and finally to the disappearance of striations at higher ϕH. dpeak is believed to be determined by a local balance between the generation (via electron-impact ionization and dissociative attachment) and losses (primarily via recombination of the positive and negative ions, and detachment) of ions. We observed a hysteresis of the axial profiles of the measured plasma emission intensity and the simulated electron-impact excitation rate induced by increasing and decreasing ϕH semi-continuously. The dependence of dpeak on ϕH was found to play a key role in the appearance of the hysteresis.

Enhancement of surface discharge in catalyst pores in dielectric barrier discharges

The generation of high-density plasmas on the surface of porous catalysts is very important for plasma catalysis, as it determines the active surface of the catalyst that is available for the reaction. In this work, we investigate the mechanism of surface and volume plasma streamer formation and propagation near micro-sized pores in dielectric barrier discharges operating in air at atmospheric pressure. A two-dimensional particle-in-cell/Monte Carlo collision model is used to model the individual kinetic behavior of plasma species. Our calculations indicate that the surface discharge is enhanced on the surface of the catalyst pores compared with the microdischarge inside the catalyst pores. The reason is that the surface ionization wave induces surface charging along the catalyst pore sidewalls, leading to a strong electric field along the pore sidewalls, which in turn further enhances the surface discharge. Therefore, highly concentrated reactive species occur on the surfaces of the catalyst pores, indicating high-density plasmas on the surface of porous catalysts. Indeed, the maximum electron impact excitation and ionization rates occur on the pore surface, indicating the more pronounced production of excited state and electron-ion pairs on the pore surface than inside the pore, which may profoundly affect the plasma catalytic process.

Experimental investigation of the electron impact excitation behavior in pulse-modulated radio frequency Ar/O2 inductively coupled plasma

In inductively coupled plasmas (ICPs), mode transition between capacitive coupling (E mode) and inductive coupling (H mode) is a key issue. Using an intensified charge-coupled device camera, the mode transition-related behaviors of the electron impact excitation of Ar(2p1) are investigated under different discharge conditions in pulse-modulated radio-frequency (rf) Ar/O2 ICPs. The initiation time of the E-H mode transition at the initial stage of a pulse period is examined under nanosecond time-resolution for the first time. It is found that the initiation time increases with increasing the applied power (300-600 W), while it decreases with raising the duty cycle (50%-80%) or gas pressure (20-80 mTorr). Besides, we also examined the spatial-temporal electron impact excitation rate over the whole pulse period (microsecond time-resolution), especially in the H mode when the discharge is operated at the steady state. We found that as the O2 content/pressure increases, the electron impact excitation axially concentrates closer to the quartz window, and the bimodal structure becomes more prominent in the H mode. However, the excitation gets farther away from the window at higher power. In addition, the maximum value of the excitation rate appears earlier at the initial stage of a pulse period at higher pressure/O2 content.

Energy Levels, Transition Rates and Electron Impact Excitation Rates for the B-like Isoelectronic Sequence with Z = 24–30

Abstract We report calculations of spectroscopic accuracy for 513 states in the B-like ions with Z = 24–30. The energy levels and transition rates are calculated using the second-order many-body perturbation theory, while multiconfiguration Dirac–Hartree–Fock calculations are performed to support the former results. The present two sets of results agree excellently with each other, and can be used as benchmarks in the future. The electron-impact excitation (EIE) collision strengths are calculated based on independent processes and isolated resonances approximation using the distorted wave method. Based on the present atomic data, the spectral lines of these ions are simulated using a collisional radiative model. The amount of energy, transition data, and EIE collision strengths of high accuracy are significantly increased for several B-like ions of astrophysical interest, where experimental data are still very scarce. The results can be used in line identification, plasma modeling, and diagnostics of astrophysical plasmas.

Spatio-temporal plasma heating mechanisms in a radio frequency electrothermal microthruster

Low-power micro-propulsion sources are currently being developed for a variety of space missions. Electrothermal plasma thrusters are of specific interest since they enable spatial control of the power deposition to the propellant gas. Understanding the mechanisms whereby electrical power is coupled to the propellant will allow for optimization of the heating and fuel efficiencies of electrothermal sources. Previous studies of radio frequency (RF) plasmas have shown a dependence of the gas and electron heating mechanisms on the local collisionality. This is of particular importance to thrusters due to the large pressure gradients that exist between the inlet and outlet when expanding into vacuum. In this work, phase-resolved optical emission spectroscopy and numerical simulations were employed to study plasma heating in an asymmetric RF (13.56 MHz) electrothermal microthruster operating in argon between 186–226 Pa (1.4–1.7 Torr) plenum pressure, and between 130–450 V (0.2–5 W). Three distinct peaks in the phase-resolved Ar(2p1) electron impact excitation rate were observed, arising from sheath collapse heating, sheath expansion heating, and heating via secondary electron collisions. These experimental findings were corroborated with the results of two-dimensional fluid/Monte Carlo simulations performed using the Hybrid Plasma Equipment Model (HPEM). The influence of each mechanism with respect to the position within the plasma source during an α-γ mode transition, where plasma heating is driven via bulk and sheath heating, respectively, was investigated. Sheath dynamics were found to dictate the electron heating at the inlet and outlet, this is distinct from the center of the thruster where interactions of secondary electrons were found to be the dominant electron heating mechanism. Optimization of the heating mechanisms that contribute to the effective exhaust temperature will directly benefit electrothermal thrusters used on miniaturized satellite platforms.

Experimental investigation of standing wave effect in dual-frequency capacitively coupled argon discharges: role of a low-frequency source

It is well known that the plasma non-uniformity caused by the standing wave effect has brought about great challenges for plasma material processing. To improve the plasma uniformity, a low-frequency (LF) power source is introduced into a 100 MHz very-high-frequency (VHF) capacitively coupled argon plasma reactor. The effect of the LF parameters (LF voltage amplitude ϕL and LF source fL) on the radial profile of plasma density has been investigated by utilizing a hairpin probe. The result at a low pressure (1 Pa) is compared to the one obtained by a 2D fluid-analytical capacitively coupled plasma model, showing good agreement in the plasma density radial profile. The experimental results show that the plasma density profile exhibits different dependences on ϕL and fL at different gas pressures/electrode driven types (i.e., the two rf sources are applied on one electrode (case I) and separate electrodes (case II)). At low pressures (e.g., 8 Pa), the pronounced standing wave effect revealed in a VHF discharge can be suppressed at a relatively high ϕL or a low fL in case I, because the HF sheath heating is largely weakened due to strong modulation by the LF source. By contrast, ϕL and fL play insignificant roles in suppressing the standing wave effect in case II. At high pressures (e.g., 20 Pa), the opposite is true. The plasma density radial profile is more sensitive to ϕL and fL in case II than in case I. In case II, the standing wave effect is surprisingly enhanced with increasing ϕL at higher pressures; however, the center-high density profile caused by the standing wave effect can be compensated by increasing fL due to the enhanced electrostatic edge effect dominated by the LF source. In contrast, the density radial profile shows a much weaker dependence on ϕL and fL in case I at higher pressures. To understand the different roles of ϕL and fL, the electron excitation dynamics in each case are analyzed based on the measured spatio-temporal distributions of the electron-impact excitation rate by phase resolved optical emission spectroscopy.

Discrepancies in Atomic Data and Suggestions for Their Resolutions

The analysis and modelling of a range of plasmas (for example, astrophysical, laser- produced and fusion) require atomic data for a number of parameters, such as energy levels, radiative rates and electron impact excitation rates, or equivalently, the effective collision strengths. Such data are desired for a wide range of elements and their many ions, although all elements are not useful for all types of plasmas. Since measurements of atomic data are mostly confined to only a few energy levels of some ions, calculations for all parameters are highly important. However, often, there are large discrepancies among different calculations for almost all parameters, which makes it difficult to apply the data with confidence. Many such discrepancies (and the possible remedies) were discussed earlier (Fusion Sci. Technol. 2013, 63, 363). Since then, many more anomalies for almost all of these atomic parameters have been noticed. Therefore, this paper is a revisit of various atomic parameters to highlight the large discrepancies, their possible sources and some suggestions to avoid these, so that comparatively more accurate and reliable atomic data may be available in the future.

Development of electron impact excitation and ionization in noble gases and liquids in strong electric fields

This paper reports on establishing the electron energy distribution function and electron impact excitation and ionization rates in noble gases and liquids in strong electric fields. The method of the unsteady electron kinetic Boltzmann equation is used allowing for all the dense effects typical of the electron scattering at spatially correlated heavy particles. Account is also taken of the influence of the electron number density growth on the relaxation process. Some special features of the excitation and ionization processes in noble media are revealed. The respective electron impact rates have been calculated and the delay times for each the process determined. A paradoxical conclusion has been drawn about the electron multiplication rates in the media with extremely sharp increase in the momentum transfer frequency.

Excitation of Electronic States of N2 in Radio-Frequency Electric Field by Electron Impact

Electron impact excitation rate coefficients for singlet and triplet electronic states of the carbon monoxide molecule have been calculated under non-equilibrium conditions in the presence of radio-frequency electric field. A Monte Carlo simulation of electron transport has been performed in order to determine non-equilibrium electron energy distribution functions within one period of applied electric field. By using these distribution functions and corresponding cross sections, the excitation rate coefficients have been calculated for all electronic states of CO in the frequency range from 13.56 up to 500 MHz, at reduced root mean square electric field values ranging from 200 to 700 Td. We expect these rates to be valuable for modeling radio-frequency CO plasmas since excited neutrals exhibit greater chemical reactivity than neutrals in ground electronic state, hence altering many properties of plasma.