Effective Ionization Rate Coefficients Research Articles

The Influence of Hot Electrons on the Calculation of Ionization Rates

Electron-Impact Ionization (EII) is considered one of the most important ionization methods in dynamic systems, in which elements and ions are suddenly exposed to energetic electrons. In many plasma types, it has been observed that some electrons (hot) are governed by a non-Maxwellian energy distribution. This study illustrates the effects of a non-Maxwellian distribution on beryllium and Be+2 emission lines and their effective ionization rate coefficients. The focus on beryllium as an impacted material by electron flux aimed to evaluate the EII rates for Be and generate the corresponding datasets needed for Be+2 data analysis. An interaction cross-section was generated using the Flexible Atomic Code (FAC) and used in the estimation of the EII distribution energy functions to estimate the ionization rates for a non-Maxwellian distribution. The use of non-Maxwellian energy distributions for different fractions of hot electrons showed the sensitivity of these rates to the fraction of hot electrons and the forms of the electron energy distribution. The results were in good agreement with those found in the literature.

Pulsed Townsend measurement of electron swarm parameters in C4F7N–CO2 and C4F7N–N2 mixtures as eco-friendly insulation gas

Recently, C4F7N mixtures have attracted attention as a promising SF6 alternative due to their low global warming potential and excellent electrical performance. In this study, we introduce a newly built experimental setup for pulsed Townsend measurements as well as the physical model for the acquisition of electron swarm parameters. The effective ionization rate coefficients, electron drift velocity, and density-normalized longitudinal diffusion coefficients in C4F7N and its mixtures with CO2 and N2 were obtained. The reduced critical electric field for pure C4F7N at 100 Pa is determined to be 1002 Td, while it decreases with increasing pressure because of the effect of ion kinetics during the discharge process. C4F7N shows good synergism with CO2 and N2. To have a dielectric strength equivalent to that of SF6, the mixing ratio of C4F7N in its mixtures with CO2 and N2 should be 18% and 12%, respectively. The results provide fundamental data for modeling discharges in C4F7N and its mixtures.

The role of excited-state ionization on the effective ionization of neutral neon using non-perturbative atomic data

With the aim of providing accurate atomic data for plasma edge temperature and density modeling with neutral neon, new non-perturbative R-Matrix with Pseudostates (RMPS) calculations are performed for both the electron-impact excitation and ionization of neutral neon. The new calculations agree well with past measurements and calculations for both electron-impact excitation and ionization. For ionization, the addition of pseudostates from to allows us to extract new cross sections and rate coefficients for all of the excited states through 2p5 5p. The new RMPS ionization calculation gives a 20% increase in the cross section for the ionization compared with previous non-perturbative calculations and shows classically-expected n4-scaled convergence for the np and nd valence shells. Ionization from these excited states contributes significantly to the effective ionization rate coefficient: a factor of three more than the ground-state ionization rate coefficient at an electron temperature of 25 eV and density of 1014 cm−3. An accurate, non-perturbative set of atomic rates, both LS- and LSJ-resolved, for neutral neon across a wide range of temperatures and densities is compiled.

Measurements of the electron swarm parameters of R1225ye(Z) (C3HF5) and its mixtures with N2 and CO2

The electron swarm parameters of R1225ye(Z) (cis--pentafluoroprop-1-ene) and its mixtures with the buffer gases N2 and CO2 (content of R1225ye(Z) from 1% to 50%) are experimentally investigated using a pulsed Townsend experiment. The analysis of the electron avalanche displacement current yields the effective ionization rate coefficient, the electron drift velocity and the longitudinal electron diffusion coefficient mainly around the density-reduced critical electric field , which is of interest for application in medium or high voltage insulation. In pure R1225ye(Z), increases with increasing pressure from around 280 Td at 2 kPa to 300 Td at 14 kPa. We assume that this is due to a three-body attachment rate coefficient of approximately . Mixtures of R1225ye(Z) with N2 and CO2 are discussed and a comparison to the structurally similar gases HFO1234ze(E) and l-C3F6 is given, which also exhibit three-body attachment.

Identification of the discharge kinetics in the perfluoro-nitrile C4F7N with swarm and breakdown experiments

We follow up on our previous publication on C4F7N and investigate the ion kinetics influencing C4F7N discharges with a pulsed Townsend experiment. The measured current signals at pressures between 0.06 and 6.9 kPa, in the range of density-reduced electric fields E/N from 500 to 1050 Td, show evidence of three anions: one long-lived anion with a detachment rate coefficient in the order of , a presumably non-detaching anion, and a short-lived anion with a detachment rate coefficient in the order of . We obtain the corresponding rate coefficients for ionization, attachment and detachment in C4F7N. Using these results, we calculate a corrected value of the effective ionization rate coefficient , taking into account detachment from negative ions. It results in a corrected value of the density-reduced critical electric field strength Td, much lower than the previously obtained value of Td, which is valid only when electron detachment is negligible, i.e. for low pressure and small geometric distance. To find which value is most relevant for electrical insulation, we perform breakdown voltage measurements in homogeneous electric fields in C4F7N at 5–65 kPa. We compare the measured density-reduced breakdown field strength to that calculated using the streamer criterion with the presently obtained rate coefficients, including electron detachment. We find excellent agreement between the measured and calculated .

Detailed precision and accuracy analysis of swarm parameters from a pulsed Townsend experiment.

A newly built pulsed Townsend experimental setup which allows one to measure both electron and ion currents is presented. The principle of pulsed Townsend measurements itself is well established to obtain swarm parameters such as the effective ionization rate coefficient, the density-reduced mobility, and the density-normalized longitudinal diffusion coefficient. The main novelty of the present contribution is a detailed and comprehensive analysis of the entire measurement and evaluation chain with respect to accuracy, precision, and reproducibility. The influence of the input parameters (gap distance, applied voltage, measured pressure, and temperature) is analyzed in detail. An overall accuracy of ±0.5% in the density reduced electric field (E/N) is achieved, which is close to the theoretically possible limit using the chosen components. The precision of the experimental results is higher than the accuracy. Through an extensive measurement campaign, the repeatability of our measurements proved to be high and similar to the precision. The reproducibility of results at identical (E/N) is similar to the precision for different distances but decreases for varying pressures. For benchmark purposes, measurements for Ar, CO2, and N2 are presented and compared with our previous experimental setup, simulations, and other experimental references.

Measurement of the electron attachment properties of SF5CF3 and comparison to SF6

The electron attachment properties of are experimentally investigated using a pulsed Townsend setup. Different / and / mixtures, with mole fractions ranging from to 1, are characterized. The effective ionization rate coefficient, electron drift velocity and reduced longitudinal electron diffusion coefficient in these mixtures are obtained. For low mole fractions of , the effective ionization rate coefficient is compared to calculations from available electron scattering cross sections, and is also used for estimating the electron attachment cross section of . For pure , the present data is compared to early data from a steady-state Townsend experiment. The presentation of the measurement results is followed by a discussion on the properties of and and their significance for gaseous electrical insulation.

Electron attachment properties of c-C4F8O in different environments

The electron attachment properties of octafluorotetrahydrofuran (c-C4F8O) are investigated using two complementary experimental setups. The attachment and ionization cross sections of c-C4F8O are measured using an electron beam experiment. The effective ionization rate coefficient, electron drift velocity and electron diffusion coefficient in c-C4F8O diluted to concentrations lower than 0.6% in the buffer gases N2, CO2 and Ar, are measured using a pulsed Townsend experiment. A kinetic model is proposed, which combines the results of the two experiments.

Photon Trapping Effects in DEMO Divertor Plasma

AbstractIn the DEMO divertor, the neutral density becomes high to produce the full detachment and therefore the photon trapping can become important. In this paper, effects of the photon trapping on the DEMO divertor plasma has been studied. The pre‐evaluation of the photon trapping effects on the fixed background plasma profile was carried out by using an iterative self‐consistent collisional radiative model. The recombining plasma near the inner target and the private region changed to the ionizing plasma by the photon‐excitation. Based on the preevaluation result, the database of the effective ionization rate coefficient including the photon transport inside a 2 mm sphere. Advantage of the 2 mm sphere approximation is that the extra calculation cost is not necessary. Iterative calculation of the SONIC including the photon trapping effects was carried out. While the electron density increased and the neutral density decreased in the wide region, the electron density decreases close to the inner strike point. This may be due to decrease in the ionization rate by decrease in the neutral density. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electron swarm parameters of the hydrofluoroolefine HFO1234ze

In this contribution, the electron swarm parameters of the hydrofluoroolefine HFO1234ze (systematic name trans-1,3,3,3-tetrafluoro-1-propene) are experimentally investigated. The analysis of the electron avalanche current measured in a pulsed Townsend experiment yields the effective ionization rate coefficient, the electron drift velocity and the longitudinal electron diffusion coefficient. The subsequent ion current is analyzed as well, to obtain separately the ionization and attachment rate coefficients. Measurements in pure HFO1234ze at different pressures show that the effective ionization rate is strongly influenced by three-body attachment and the three-body attachment rate coefficient is derived.

Electron-impact ionization of atomic ions: Theoretical results

A brief overview is given of theoretical results for electron-impact ionization of atoms and ions. A description is given of the main theoretical methods, along with the databases where the data are archived. It is shown that for light species, ground and metastable ionization cross sections are in reasonable agreement with experiment when non-perturbative data are used for the near neutrals and distorted wave data are used for ions greater than a few times ionized. Some discrepancies between theory and experiment still remain for systems with open d and open p subshells. The sensitivity of ionization rate coefficients to the near threshold part of the ionization cross section is shown. The role of excited states in effective ionization rate coefficients is demonstrated and recent excited state ionization cross section results for H, He, He+, B2+ and Ne are presented.

The role of excited state ionization data on H and He generalized collisional–radiative coefficients

We present results of collisional–radiative modelling of H, He and He+ for use in plasma transport studies. Generalized collisional–radiative (GCR) coefficients are generated for each ion using the most recent atomic data available. The data generated cover electron densities up to 1 × 1015 cm−3 and electron temperatures up to about 200 eV. These data are archived online for use by modelling codes. We then present a study on the role of excited state ionization data on GCR coefficients. For most ions, excited state ionization cross sections are not well known. We use the high quality data that are available for H, He and He+ to test two commonly used methods for excited state ionization data, namely, semi-classical methods or perturbative methods. It is found that for neutral H and He, the exchange classical impact parameter (ECIP) method provides accurate data for derived GCR coefficients, while the perturbative distorted-wave methods lead to significant overestimates of the effective ionization rate coefficient. For He+, using perturbative distorted-wave data for the excited state ionization processes gives reasonably accurate results for the GCR coefficients, while the ECIP results significantly underestimate the effective ionization rate coefficient. Thus, for neutral H and He the semi-classical method is to be preferred over the distorted-wave method, and the situation is reversed for He+.

Iterative numerical method for the inclusion of radiation trapping into a collisional-radiative model

The effect of radiation trapping is included in the standard collisional-radiative model for atomic hydrogen under a typical condition of divertor plasmas The population of the first excited level of the ionizing plasma component is strongly enhanced by the absorption of resonance line photons produced by the recombining plasma component, and the effective ionization rate coefficient is also strongly enhanced.

Generalised collisional-radiative model for light elements. A: Data for the Li isonuclear sequence

A first stage collision database is assembled which contains electron-impact effective collision strengths, and ionization and recombination rate coefficients for Li, Li+, and Li2+. The first stage database is constructed using the R-matrix with pseudo-states, time-dependent close-coupling, converged close-coupling, and perturbative distorted-wave methods. A second stage collision database is then assembled which contains generalized collisional-radiative and radiated power loss coefficients. The second stage database is constructed by solution of collisional-radiative equations in the quasi-static equilibrium approximation using the first stage database. Both collision database stages reside in electronic form at the ORNL Controlled Fusion Atomic Data Center and in the ADAS database, and are easily accessed over the worldwide internet.

Effect of excited states on the ionization balance in plasmas via the enhancement of ionization and recombination rate coefficients.

The effect of excited states on the effective ionization and recombination rate coefficients for the ground states was investigated analytically and by computer simulation. The calculation was done for carbon ions. The results using carbon ions show (1) the contribution from excited states to ionization rate coefficients becomes significant even at an electron density as low as 10(15) cm(-3) and saturated from around N(e) approximately 10(20) cm(-3); (2) the lower the electron temperature, the larger the contribution; (3) in the case of recombination rate coefficients, there is still a non-negligible contribution from excited states even at a very low electron density of 10(10) cm(-3), where the contribution has been considered negligible; (4) this contribution to the recombination rate coefficients increases linearly with the electron density; (5) the enhancements of the ionization and recombination rate coefficients increase as N(e) increases and are saturated to the same value at higher densities; (6) there exists a region of temperature and density where the recombination is effectively hindered. Some of the behaviors of the ionization and recombination rate coefficients in the extreme regions of a very low and high electron density were analytically understood. The calculated ionization and recombination rate coefficients for carbon ions, including the effect of excited states, were used in a one-dimensional magnetohydrodynamic code for the calculation of the ionization balance of carbon ions in a Z-pinch carbon plasma and the gain of C VI H(alpha) (18.2 nm) line. The significant change in the evolution of the ionization balance was observed. The rapid depletion of C VII ions by the increased recombination rate reduces the gain significantly by a factor of approximately 3 compared to the case where the contribution from excited states was neglected. Such calculations can be done for other ions. The characteristics found for carbon ions are generic and applicable to other ions.

Ionization and recombination rates of atomic oxygen in high-temperature air plasma flows

A nonlinear time-dependent collisional-radiative model for atomic oxygen is presented. Effective ionization and three-body recombination rate coefficients are calculated for either optically thin or thick plasmas where ${10}^{18}{\mathrm{m}}^{\mathrm{\ensuremath{-}}3}<~{n}_{e}<~{10}^{21}{\mathrm{m}}^{\mathrm{\ensuremath{-}}3}$ and $8000\mathrm{K}<~{T}_{e}<~20000\mathrm{K}.$ In order to implement these coefficients easily in plasma flow codes, simple analytical expressions are proposed. Significant discrepancies with existing literature values are pointed out and discussed. The time-dependent approach confirms the importance of a quasi-steady-state condition to derive meaningful rate coefficients. Therefore the relaxation time necessary for the system to reach a quasi-steady-state limits the validity of the rate coefficients determined in this study. In optically thick cases, this relaxation time in either recombining or ionizing plasmas depends weakly on the electron temperature but strongly increases as the electron number density decreases. In optically thin cases, it is more difficult to derive general results since the relaxation time depends on the electron temperature, on densities, but also on the initial distribution on atomic levels.

Time-dependent H-like and He-like al lines produced by ultra-short pulse laser

We perform numerical modeling of time-resolved x-ray spectra from thin foil targets heated by the LLNL Ultra-short pulse (USP) laser. The targets were aluminum foils of thickness ranging from 250 to 1250 A, heated with 120 fsec pulses of 400 nm light from the USP laser. The laser energy was approximately 0.2 J focused to a 3 μm spot size for a peak intensity near 2 × 10 19 W/cm 2. Lyoe and Heα lines were recorded using a 900 fsec x-ray streak camera. We calculate the effective ionization, recombination and emission rate coefficients including density effects for H-like and He-like aluminum ions using a collisional-radiative model. We calculate time-dependent ion abundances using these effective ionization and recombination rate coefficients. The time-dependent electron temperature and density used in the calculation are based on an analytical model for the hydrodynamic expansion of the target foils. During the laser pulse the target is ionized. After the laser heating stops, the plasma begins to recombine. Using the calculated time-dependent ion abundances and the effective emission rate coefficients, we calculate the time-dependent Lyα and Heα lines. The calculations reproduce the main qualitative features of the experimental spectra. We also calculate the He-like spectra including satellite lines.

Effective ionization and emission rate coefficients of the helium atom in a plasma

Effective rate coefficients for ionization, line emission and line radiation power of the helium atom in an ionizing plasma are defined, with a collisional radiative model including new recommended excitation rate coefficients, which can be applied for divertor plasmas. Line intensity ratios for electron temperature and density measurements in this model are compared with results by Schweer et al. (J. Nucl. Mater. 196–198 (1992) 174–178) and the differences between the atomic data and the model are discussed.

Effective ionization and dissociation rate coefficients of molecular hydrogen in plasma

A simplified collisional-radiative model has been constructed for the system of the ground state, electronically excited stable states, and the ionic state of molecular hydrogen in plasma. Effective rate coefficients have been calculated for production of electrons, molecular ions, protons, and hydrogen atoms from molecular hydrogen. The ratio of the effective ionization rate of molecular hydrogen to the Balmer α photon emission rate and the effective rate coefficients for radiation and energy losses are also presented.

Line emissions from carbon atoms in the divertor plasma

We have investigated line emission from carbon atoms in an ionizing plasma for the purpose of diagnosing a divertor plasma in which the electron temperature is high compared to the carbon ionization temperature. We study the temperature and density dependence of the population densities by including the population dynamics of the excited states. The effective line emission and ionization rate coefficients of atomic carbon are computed. The effective ionization rate coefficient increases with density, especially at low temperatures. The radiation power from atomic carbon increases proportionally to the electron density at low densities but saturates for n e > 10 14cm −3. The opacity for the line emission of carbon atoms is estimated.