C P Ballance

The time-dependent close-coupling method for atomic and molecular collision processes

We review the development of the time-dependent close-coupling method to study atomic and molecular few body dynamics. Applications include electron and photon collisions with atoms, molecules, and their ions.

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 A–17 A 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.

A radiation-damped R -matrix approach to the electron-impact excitation of helium-like ions for diagnostic application to fusion and astrophysical plasmas

Electron-impact excitation collision strengths for transitions between all singly excited levels up to the n = 4 shell of helium-like argon and the n = 4 and 5 shells of helium-like iron have been calculated using a radiation-damped R-matrix approach. The theoretical collision strengths have been examined and associated with their infinite-energy limit values to allow the preparation of Maxwell-averaged effective collision strengths. These are conservatively considered to be accurate to within 20% at all temperatures, 3×105-3×108 K for Ar16+ and 106-109 K for Fe24+. They have been compared with the results of previous studies, where possible, and we find a broad accord. The corresponding rate coefficients are required for use in the calculation of derived, collisional-radiative, effective emission coefficients for helium-like lines for diagnostic application to fusion and astrophysical plasmas. The uncertainties in the fundamental collision data have been used to provide a critical assessment of the expected resultant uncertainties in such derived data, including redistributive and cascade collisional-radiative effects. The consequential uncertainties in the parts of the effective emission coefficients driven by excitation from the ground levels for the key w, x, y and z lines vary between 5% and 10%. Our results remove an uncertainty in the reaction rates of a key class of atomic processes governing the spectral emission of helium-like ions in plasmas.

Relativistic radiatively damped R-matrix calculation of the electron-impact excitation of W46+

The current design plans for the International Thermonuclear Experimental Reactor (ITER) call for tungsten to be employed for certain plasma facing components in the divertor region. Thus, accurate atomic collision data are needed for emission modelling of tungsten. Electron-impact excitation and radiative rates are of particular importance for Ni-like W, since this ion emits some of the most intense spectral lines of all ionization stages. We report on a fully relativistic 115-level R-matrix calculations of W46+, which includes the effects of radiation damping. Although radiation damping is very important in most highly ionized species, its effects are reduced in this case because of the closed-shell Ni-like ground state. The rates from these relativistic atomic calculations will be employed for collisional-radiative modelling of this ion.

Dielectronic recombination of W35

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 W35 +. 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 W35 + should exist in a collisionally ionized plasma. We then present results for CADW rate coefficients for both Δn = 0 and Δn = 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 of neon: a pseudo-state convergence study

A number of convergent close-coupling and R-matrix with pseudo-state (RMPS) calculations for H-like, He-like, Li-like and Be-like ions have demonstrated that coupling to the target continuum can have large effects on the electron-impact excitation cross sections of neutral and low-charge species. However, no one has yet attempted such advanced calculations on a system as complex as neutral neon. We report on a series of RMPS calculations of electron-impact excitation of Ne using recently developed parallel Breit-Pauli R-matrix programs. Our largest calculation included 235 spectroscopic and pseudo-state levels in the close-coupling expansion of the target. Although the results clearly reveal the importance of coupling to the target continuum in this atom, the pseudo-state expansion is not yet sufficiently complete to provide reliable cross sections for energies above the ionization limit. However, this is the largest intermediate-coupling calculation that can be performed with present computer resources. Thus, we have also carried out a series of RMPS calculations in LS coupling with different pseudo-state expansions. Comparisons of these results have allowed us to determine the approximate size of the pseudo-state expansion required to achieve convergence in future intermediate-coupling calculations for neon.

Atomic data for modelling fusion and astrophysical plasmas

Trends and focii of interest in atomic modelling and data are identified in connection with recent observations and experiments in fusion and astrophysics. In the fusion domain, spectral observations are included of core, beam penetrated and divertor plasma. The helium beam experiments at JET and the studies with very heavy species at ASDEX and JET are noted. In the astrophysics domain, illustrations are given from the SOHO and CHANDRA spacecraft which span from the solar upper atmosphere, through soft x-rays from comets to supernovae remnants. It is shown that non-Maxwellian, dynamic and possibly optically thick regimes must be considered. The generalized collisional-radiative model properly describes the collisional regime of most astrophysical and laboratory fusion plasmas and yields self-consistent derived data for spectral emission, power balance and ionization state studies. The tuning of this method to routine analysis of the spectral observations is described. A forward look is taken as to how such atomic modelling, and the atomic data which underpin it, ought to evolve to deal with the extended conditions and novel environments of the illustrations. It is noted that atomic physics influences most aspects of fusion and astrophysical plasma behaviour but the effectiveness of analysis depends on the quality of the bi-directional pathway from fundamental data production through atomic/plasma model development to the confrontation with experiment. The principal atomic data capability at JET, and other fusion and astrophysical laboratories, is supplied via the Atomic Data and Analysis Structure (ADAS) Project. The close ties between the various experiments and ADAS have helped in this path of communication.

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 from our RMPS calculation is available at the Oak Ridge National Laboratory Controlled Fusion Atomic Data Center web site.

Hybrid time dependent/independent solution for the He I line ratio temperature and density diagnostic for a thermal helium beam with applications in the scrape-off layer-edge regions in tokamaks

Spectroscopic studies of line emission intensities and ratios offer an attractive option in the development of non-invasive plasma diagnostics. Evaluating ratios of selected He I line emission profiles from the singlet and triplet neutral helium spin systems allows for simultaneous measurement of electron density (ne) and temperature (Te) profiles. Typically, this powerful diagnostic tool is limited by the relatively long relaxation times of the 3S metastable term of helium that populates the triplet spin system, and on which electron temperature sensitive lines are based. By developing a time dependent analytical solution, we model the time evolution of the two spin systems. We present a hybrid time dependent/independent line ratio solution that improves the range of application of this diagnostic technique in the scrape-off layer (SOL) and edge plasma regions when comparing it against the current equilibrium line ratio helium model used at TEXTOR.

A pseudo-state sensitivity study on hydrogenic ions

An electron-impact excitation study of light hydrogenic ions has been carried out to quantify the effects of coupling to high bound/continuum states utilizing the R-matrix with pseudo-states method. As the ionization stage increases, the neglect of loss of flux into high-lying excitation/ionization channels impacts less upon excitation between the bound terms explicitly included within our close coupling expansion. C5+ is used as our benchmark study. The differences in Maxwell averaged collision strengths between a standard R-matrix calculation and those of a similar pseudo-state model across a range of temperatures shall be our criteria for judging differences. We carried out calculations for He+, Li2+, Be3+, B4+, C5+, O7+ and Ne9+ so as to provide excitation data amongst terms up to n = 5. Pseudo-state calculations were carried out for the first five ions, following a similar model to earlier neutral hydrogen work, whilst non-pseudo-state calculations sufficed for the remaining two ions. The results of these seven calculations will enhance existing excitation data sets for use in the modelling of controlled nuclear fusion plasma experiments.