An R-matrix approach for plasma modelling and the interpretation of astrophysical observation

Over the last decade an Auburn-Rollins-Strathclyde consortium has developed several suites of parallel R-matrix codes [1, 2, 3] that can meet the fundamental data needs required for the interpretation of astrophysical observation and/or plasma experiments. Traditionally our collisional work on light fusion-related atoms has been focused towards spectroscopy and impurity transport for magnetically confined fusion devices. Our approach has been to provide a comprehensive data set for the excitation/ionization for every ion stage of a particular element. As we progress towards a burning fusion plasma, there is a demand for the collisional processes involving tungsten, which has required a revitalization of the relativistic R-matrix approach. The implementation of these codes on massively parallel supercomputers has facilitated the progression to models involving thousands of levels in the close-coupling expansion required by the open d and f sub-shell systems of mid Z tungsten. This work also complements the electron-impact excitation of Fe-Peak elements required by astrophysics, in particular the near neutral species, which offer similar atomic structure challenges. Although electron-impact excitation work is our primary focus in terms of fusion application, the single photon photoionisation codes are also being developed in tandem, and benefit greatly from this ongoing work.

Non-equilibrium modeling of the FE XVII 3C/3D Line Ratio in an Intense X-ray Free-electron Laser Excited Plasma

Recent measurements using an X-ray Free Electron Laser (XFEL) and an Electron Beam Ion Trap at the Linac Coherent Light Source facility highlighted large discrepancies between the observed and theoretical values for the Fe XVII 3C/3D line intensity ratio. This result raised the question of whether the theoretical oscillator strengths may be significantly in error, due to insufficiencies in the atomic structure calculations. We present time-dependent spectral modeling of this experiment and show that non-equilibrium effects can dramatically reduce the predicted 3C/3D line intensity ratio, compared with that obtained by simply taking the ratio of oscillator strengths. Once these non-equilibrium effects are accounted for, the measured line intensity ratio can be used to determine a revised value for the 3C/3D oscillator strength ratio, giving a range from 3.0 to 3.5. We also provide a framework to narrow this range further, if more precise information about the pulse parameters can be determined. We discuss the implications of the new results for the use of Fe XVII spectral features as astrophysical diagnostics and investigate the importance of time-dependent effects in interpreting XFEL-excited plasmas.

Electron-impact excitation of Li to high principal quantum numbers

The time-dependent close-coupling method is used to calculate electron-impact excitation cross sections for the Li(2s)--{\textgreater}Li(nl) and Li(2p)--{\textgreater}Li(nl) transitions at incident energies just above the ionization threshold. The implementation of the time-dependent close-coupling method on a nonuniform lattice allows the study of continuum-coupling effects in excitations to high principal quantum number, i.e., n{\textless}=10. Good agreement is found with R-matrix with pseudostates calculations, which also include continuum-coupling effects, for excitations to low principal quantum number, i.e., n{\textless}=4. Poor agreement is found with standard distorted-wave calculations for excitations to all principal quantum numbers, with differences still at the 50% level for n=10. We are able to give guidance as to the accuracy expected in the n3 extrapolation of nonperturbative close-coupling calculations of low n cross sections and rate coefficients.

Electron-impact ionization of Al2+

We report on a nonperturbative R-matrix with PseudoStates (RMPS) calculation for the electron-impact ionization cross section of the ground state of Al2+. We include both the direct ionization of the 3s and 2p subshells and the indirect ionization from the 2p subshell. This calculation, thus, includes extra decay channels for the indirect-ionization process not included in previous RMPS calculations. This lowers the total-ionization cross section, resulting in closer agreement with the most recent experimental measurements. This calculation also shows better agreement with the position and height of the resonant-excitation double autoionization features seen in the experiment.

Line ratio diagnostics in helium and helium seeded argon plasmas

We investigate the potential use of line ratio diagnostics to evaluate electron temperature in either helium or helium seeded argon plasmas. Plasmas are produced in a helicon plasma source. A rf compensated Langmuir probe is used to measure both the electron temperature and plasma density while a spectrometer is used to measure He I line intensities from the plasma. For all plasma densities where the electron temperature remains at 5 ± 1 eV, three He line ratios are measured. Each experimental ratio is compared with the prediction of three different collisional radiative models. One of these models makes uses of recent R-matrix with pseudo-states calculations for collisional rate coefficients. A discussion related to the different observations and model predictions is presented.

Electron-impact ionization of Al

Perturbative distorted-wave and non-perturbative close-coupling methods are used to calculate electron-impact ionization cross sections for the ground state of the neutral Al atom. Configuration-average distorted-wave calculations are made for both direct ionization and excitation-autoionization contributions. The total perturbative results are found to be almost a factor of 2 higher than experiment over a wide energy range. On the other hand, the R-matrix with pseudo-states results for total ionization are found to be in good agreement with experiment. Comparison of time-dependent close-coupling calculations for the direct ionization with the R-matrix with pseudo-state calculations for total ionization reveals that both the direct ionization and excitation-autoionization contributions are strongly affected by correlation effects.

PAMOP: Petascale atomic, molecular and optical collision calculations

Petaflop architectures are currently being utilized efficiently to perform large scale computations in Atomic, Molecular and Optical Collisions. We solve the Schr\"odinger or Dirac equation for the appropriate collision problem using the R-matrix or R-matrix with pseudo-states approach. We briefly outline the parallel methodology used and implemented for the current suite of Breit-Pauli and DARC codes. In this report, various examples are shown from our theoretical results compared with experimental results obtained from Synchrotron Radiation facilities where the Cray architecture at HLRS is playing an integral part in our computational projects.

Dirac R -matrix calculations of electron-impact excitation of neon-like krypton

We have employed the Dirac R -matrix method to determine electron-impact excitation cross sections and effective collision strengths in Ne-like Kr 26+ . Both the configuration-interaction expansion of the target and the close-coupling expansion employed in the scattering calculation included 139 levels up through n = 5. Many of the cross sections are found to exhibit very strong resonances, yet the effects of radiation damping on the resonance contributions are relatively small. Using these collisional data along with multi-configuration Dirac–Fock radiative rates, we have performed collisional-radiative modeling calculations to determine line-intensity ratios for various radiative transitions that have been employed for diagnostics of other Ne-like ions.

Electron-impact excitation of Ar+: an improved determination of Ar impurity influx in tokamaks

Electron-impact scattering data for argon and its ions continue to be of interest in studies of magnetically confined plasmas. In an earlier paper, Griffin et al (1997 J. Phys. B: At. Mol. Opt. Phys. 30 3543) employed the results of 28-term and 40-term R-matrix calculations of electron-impact excitation in Ar+ to carry out a collisional-radiative modelling study of the impurity influx of argon in tokamaks. We have now completed a 452-term R-matrix with pseudo-states (RMPS) calculation of electron-impact excitation for Ar+ in order to provide more accurate excitation data; using these improved data, we have repeated the modelling studies presented in the earlier paper. We compare our excitation data, as well as the results of the collisional radiative calculations, with those arising from the 40-term R-matrix calculation and find significant differences.

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.

Photoionization cross-sections for Fe II

The LS R-matrix method was used to compute new photoionization cross sections for Fe II. Results are compared with available experimental data and with previous calculations of the cross section. We also present the first fine-structure photoionization data for this ion obtained with the fully-relativistic DARC codes.

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.