An R -matrix with pseudo-states calculation of electron-impact excitation in C 2 +

We have performed an R-matrix with pseudo-states (RMPS) calculation of electron-impact excitation in C2+.Collision strengths and effective collision strengths were determined for excitation between the lowest 24 terms, including all those arising from the 2s3l and 2s4l configurations. In the RMPS calculation, 238 terms (90 spectroscopic and 148 pseudo-state) were employed in the close-coupling (CC) expansion of the target. In order to investigate the significance of coupling to the target continuum and highly excited bound states, we compare the RMPS results with those from an R-matrix calculation that incorporated all 238 terms in the configuration- interaction expansion, but only the lowest 44 spectroscopic terms in the CC expansion. We also compare our effective collision strengths with those from an earlier 12-state R-matrix calculation (Berrington et al 1989 J. Phys. B: At.Mol. Opt. Phys. 22 665). The RMPS calculation was extremely large, involving (N +1)-electron Hamiltonian matrices of dimension up to 36 085, and required the use of our recently completed suite of parallel R-matrix programs. The full set of effective collision strengths fromourRMPS calculation is available at theOakRidgeNationalLaboratoryControlledFusion Atomic Data Center web site. 1.

Vibrational excitation of the N2+ first negative (0,0), (1,0) and (2,0) bands by electron impact: a theoretical study using the R-matrix approach

Ab initio cross section calculations for vibronic excitation using the R -matrix approach have been performed on the N 2 + molecular ion complex. A three-state close-coupling expansion is used where the electronic target states; X 2 g + , A 2 u and B 2 u + of the molecular cation are represented by a valence configuration-interaction approximation. A non-adiabatic approximation is invoked to study vibronic excitation for the first three negative bands, (0,0), (1,0) and (2,0) of the X-B transition (B 2 u + v ´ X 2 g + v ´´ ) of N 2 + . Fixed-nuclei and non-adiabatic cross section results are compared with the available experimental data for the (0,0) band and the breakdown of the adiabatic fixed-nuclei approximation is clearly evident for the vibronic excitation of the (1,0) and (2,0) bands in this molecular ion complex.

Electron-impact single ionization of Mg and Al+

Theory and experiment are compared for the electron-impact single ionization of Mg and Al+. Nonpertur- bative R matrix with pseudostates RMPS and time-dependent close-coupling TDCC calculations have been carried out that exhibit large reductions from perturbative distorted-wave results of 38% for Mg and 20% for Al+. Experimental single-ionization data available for Mg and Al+ are in reasonable accord with distorted-wave data and lie substantially above the new theoretical results. Rate coefficients, necessary for the collisional- radiative modeling of Mg and Al plasmas were generated from the RMPS ionization cross sections. In the collisional-ionization region near the ionization threshold, the resulting rates were found to be up to two times lower for Mg and three times lower for Al+ than the rates generated from experimental data.

The 2p interloper resonances in collisions

Ab initio electron scattering calculations using the R -matrix approach have been performed for within a three-state valence configuration-interaction model (VCI). The lowest three electronic target states ( , and the ) of this molecular nitrogen cation are included in the close-coupling method, with each state being represented by a valence CI approximation. From a detailed analysis of the resonance structure found in our work for the symmetries we find four prominent Rydberg series of the type , , , and a interloper resonance. This interloper molecular resonance associated with the B state of is seen to cause distortions of the resulting resonance spectra. A comparison of our total cross sections for the X - B transition shows excellent agreement with the available experimental data.

Dielectronic recombination of W 35 +

Accurate data for dielectronic recombination (DR) of the ions of tungsten are of significant interest in the modelling of tungsten impurity transport and radiative power loss in current tokamaks and in ITER. However, the complexity of the atomic structure for many of these ions makes level-resolved DR calculations untenable on currently available computers, especially for open d- and f-subshell ions. The majority of DR data presently available for ITER modelling are based on an average-atom approximation. To improve upon these baseline calculations, we investigate the use of the configuration-average distorted-wave (CADW) method to calculate DR rate coefficients for complex open d-shell systems. The aim is to produce rate coefficients that are sufficiently accurate in terms of modelling, yet greatly reduced in term of computational complexity compared to level-resolved calculations. In this paper, we consider the DR of W 35 + . Initially, we carry out several large-scale level-resolved calculations for the DR associated with the 4d → 4f and 4p → 4d excitations in this ion, using both the level-resolved distorted-wave and Dirac R -matrix methods. These calculations allow us to test the validity of the CADW approach on these same excitations by comparing cross sections and rate coefficients. These comparisons demonstrate that the CADW method is relatively accurate in relation to these level-resolved methods for the temperature range for which W 35 + should exist in a collisionally ionized plasma. We then present results for CADW rate coefficients for both Δ n = 0 and Δ n = 1 excitations for this ion. This study indicates that it is now feasible to generate a much improved comprehensive set of DR data for the entire tungsten isonuclear sequence.

Electron-impact excitation and ionization of W 3+ for the determination of tungsten influx in a fusion plasma

Tungsten will be employed as a plasma facing material in the ITER fusion reactor under construction in Cadarache, France; therefore, there is a significant need for accurate electron-impact excitation and ionization data for the ions of tungsten. We report on the results of extensive calculations of ionization and excitation for W 3+ that are intended to provide the atomic data needed for the determination of impurity influx diagnostics of tungsten in several existing tokamak reactors. The electron-impact excitation rate coefficients for this study were determined using the relativistic R -matrix method. The contribution to direct electron-impact ionization was determined using the distorted-wave approximation, the accuracy of which was verified by an R -matrix with pseudo states calculation. Contributions to total ionization from excitation autoionization were also generated from the relativistic R -matrix method. These results were then employed to calculate values of ionization per emitted photon, or SXB ratios, for four carefully selected spectral lines; these data will allow the determination of impurity influx from tungsten facing surfaces. For the range of densities of importance in the edge region of a tokamak reactor, these SXB ratios are found to be nearly independent of electron density but vary significantly with electron temperature.

Electron-impact ionization of Xe 24 +

Configuration-average distorted-wave calculations are carried out for the electron-impact single ionization of Xe 24 + . Contributions are included from direct ionization of the 3s, 3p, 3d and 4s subshells and from indirect ionization via 3s → nl , 3p → nl and 3d → nl excitations followed by autoionization. Branching ratios are found for single versus double ionization of the 3s and 3p subshells and for autoionization versus radiative decay of all 3 l → nl excitations. Additional distorted-wave and R -matrix calculations find resonant-capture double-autoionization contributions to be quite small. The total ionization cross section for Xe 24 + is found to be dominated by indirect excitation–autoionization contributions, especially near the single-ionization threshold. An approximate 15% reduction in the total ionization cross section is found due to the radiative decays included in the branching ratios.

Collisional-radiative calculations of He line emission in low-temperature plasmas

We present spectral modeling results for neutral helium. Our underlying atomic data contains radiative transition rates that are generated from atomic structure calculations and electron-impact excitation rates, that are determined from both the standard R-matrix method and the R-matrix with pseudostates RMPS method. In this paper, we focus on transitions of particular importance to diagnostic line ratios. For example, our calculated rate coefficient for the electron-impact transition 1s3s 1S→1s3p 1P, which has a pronounced effect on the 728.1 nm diagnostic spectral line, is found to be in good agreement with previous experimental mea- surements. We also consider transitions from the 1s2 1S ground and 1s2s 3S terms to terms of the n=4 shell. They are found to be affected significantly by coupling of the bound states to the target continuum continuum coupling, which is included in our RMPS calculation, but not in our standard R-matrix calculation. We perform collisional-radiative calculations to determine spectral line intensity ratios for three ratios of particular interest, namely the 504.8 nm/471.3 nm, 492.2 nm/471.3 nm, and 492.2 nm/504.8 nm line ratios. Comparing our results determined from the RMPS excitation rates with those from the standard R-matrix excitation rates, we find that continuum coupling affects the rate coefficients significantly, leading to different values for all three line ratios. We also compare our modeling results with spectral measurements taken recently on the Auburn Helicon plasma device, finding that the ground and metastable populations are not in equilibrium, and that the experimental measurements are more consistent with the 1s2s 3S metastable term populations being short lived in the plasma.

Electron-impact ionization of the C atom

Time-dependent close-coupling (TDCC), R-matrix-with-pseudostates (RMPS), and time-independent distorted-wave (TIDW) methods are used to calculate electron-impact ionization cross sections for the carbon atom. The TDCC and RMPS results for the 1s22s22p2 ground configuration are in reasonable agreement with the available experimental measurements, while the TIDW results are 30% higher. Ionization of the 1s22s2p3 excited configuration is performed using the TDCC, RMPS, and TIDW methods. Ionization of the 1s22s22p3l (l=0–2) excited configurations is performed using the TDCC and TIDW methods. The ionization cross sections for the excited configurations are much larger than for the ground state. For example, the peak cross section for the 1s22s22p3p excited configuration is an order of magnitude larger than the peak cross section for the 1s22s22p2 ground configuration. The TDCC results are again found to be substantially lower than the TIDW results. The ionization cross-section results will permit the generation of more accurate, generalized collisional-radiative ionization coefficients needed for modeling moderately dense carbon plasmas.

Electron-impact ionization of the metastable excited states of Li +

Electron-impact ionization cross sections for the 1s2s 1S and 1s2s 3S metastable states of Li+ are calculated using both perturbative distorted-wave and non-perturbative close-coupling methods. Term-resolved distorted-wave calculations are found to be approximately 15% above term-resolved R-matrix with pseudostates calculations. On the other hand, configuration-average time-dependent close-coupling calculations are found to be in excellent agreement with the configuration-average R-matrix with pseudostates calculations. The non-perturbative R-matrix and close-coupling calculations provide a benchmark for experimental studies of electron-impact ionization of metastable states along the He isoelectronic sequence.

The effects of radiative cascades on the x-ray diagnostic lines of Fe16+

We present complete collisional-radiative modelling results for the soft x-ray emission lines of Fe16+ in the 15 Å–17 Å range. These lines have been the subject of much controversy in the astrophysical and laboratory plasma community. Radiative transition rates are generated from fully relativistic atomic structure calculations. Electron-impact excitation cross sections are determined using a fully relativistic R-matrix method employing 139 coupled atomic levels through n = 5. We find that, in all cases, using a simple ratio of the collisional rate coefficient times a radiative branching factor is not sufficient to model the widely used diagnostic line ratios. One has to include the effects of collisional-radiative cascades in a population model to achieve accurate line ratios. Our line ratio results agree well with several previous calculations and reasonably well with tokamak experimental measurements, assuming a Maxwellian electron-energy distribution. Our modelling results for four EBIT line ratios, assuming a narrow Gaussian electron-energy distribution, are in generally poor agreement with all four NIST measurements but are in better agreement with the two LLNL measurements. These results suggest the need for an investigation of the theoretical polarization calculations that are required to interpret the EBIT line ratio measurements.

Electron-impact ionization of argon using the R-matrix with a pseudo-states method

Electron-impact ionization cross sections for argon are calculated using both non-perturbative R-matrix with pseudo-states (RMPS) and perturbative distorted-wave methods. At twice the ionization potential, the 3p(61)S ground-term cross section from a distorted-wave calculation is found to be a factor of 4 above crossed-beams experimental measurements, while with the inclusion of term-dependent continuum effects in the distorted-wave method, the perturbative cross section still remains almost a factor of 2 above experiment. In the case of ionization from the metastable 3p(5)4s(3)P term, the distorted-wave ionization cross section is also higher than the experimental cross section. On the other hand, the ground-term cross section determined from a nonperturbative RMPS calculation that includes 27 LS spectroscopic terms and another 282 LS pseudo-state terms to represent the high Rydberg states, and the target continuum is found to be in excellent agreement with experimental measurements, while the RMPS result is below the experimental cross section for ionization from the metastable term. We conclude that both continuum term dependence and interchannel coupling effects, which are included in the RMPS method, are important for ionization from the ground term, and interchannel coupling is also significant for ionization from the metastable term

Electron-impact ionization of the boron atom

Accurate knowledge of the electron-impact ionization of the B atom is urgently needed in current fusion plasma experiments to help design ITER wall components. Since no atomic measurements exist, nonperturba- tive time-dependent close-coupling (TDCC) calculations are carried out to accurately determine the direct ionization cross sections of the outer two subshells of B. Perturbative distorted-wave and semiempirical binary encounter calculations are found to yield cross sections from 26% lower to an order of magnitude higher than the current TDCC results. Unlike almost all neutral atoms, large excitation-autoionization contributions are found for the B atom. Nonperturbative R matrix with pseudostates (RMPS) calculations are also carried out to accurately determine the total ionization cross section of B. Previous 60 LS-term RMPS calculations are found to yield cross sections up to 40% higher than the current more extensive 476 LS-term RMPS results

Electron-impact ionization and recombination of M -shell atomic ions in the argon isonuclear sequence

Electron-impact ionization and recombination cross sections and rate coefficients are calculated for M-shell Ar atomic ions using a configuration-average distorted-wave method. The electron-impact ionization calcula- tions are for all atomic ions in the Ar isonuclear sequence. Ionization contributions include both direct ioniza- tion and excitation-autoionization processes. Good agreement is found between theory and experimental crossed-beam measurements for moderately charged ion stages. Comparisons are made with previous theoret- ical calculations where possible.We also generate rate coefficients for neutral argon ionization, based on recent R-matrix with pseudostates calculations. Electron-impact dielectronic recombination is calculated for all M-shell ions of argon. For Ar6+ and Ar7+ the current theoretical results agree well with previous level-resolved distorted-wave calculations. In order to compare with published ionization balance results our dielectronic recombination data are combined with literature values for the higher ion stages and with recent radiative recombination data for all the ion stages. We find significant differences in our equilibrium fractional abun- dances for the M-shell ions, compared with literature values. We relate these differences to the underlying atomic data.

Dielectronic recombination of W20 + (4d104f8): Addressing the half-open f shell

A recent measurement of the dielectronic recombination (DR) of W20+ [Schippers et al., Phys.Rev.A 83, 012711 (2011)] found an exceptionally large contribution from near-threshold resonances (1 eV). This still affected the Maxwellian rate coefficient at much higher temperatures. The experimental result was found to be higher by a factor of 4 or more than that currently in use in the 100- to 300-eV range, which is of relevance for modeling magnetic fusion plasmas. We have carried out DR calculations with AUTOSTRUCTURE which include all significant single-electron promotions. Our intermediate-coupling (IC) results are more than a factor of 4 larger than our LS-coupling ones at 1 eV but still lie a factor of 3 below experiment here. If we assume complete (chaotic)mixing of near-threshold autoionizing states, then our results come into agreement (to within 20%)with experiment below 2 eV. Our total IC Maxwellian rate coefficients are 50%–30% smaller than those based on experiment over 100–300 eV.