The effect of ionization on the populations of excited levels of C IV and C V in tokamak edge plasmas

The main populating and depopulating mechanisms of the excited energy levels of ions in plasmas with densities <10²³-10²⁴ m^-3 are electron collisional excitation from the ion's ground state and radiative decay, respectively, with the majority of the electron population being in the ground state of the ionization stage. Electron collisional ionization is predominately expected to take place from one ground state to that of the next higher ionization stage. However, the question arises as to whether, in some cases, ionization can also affect the excited level populations. This would apply particularly to those cases involving transient events such as impurity influxes in a laboratory plasma. An analysis of the importance of ionization in populating the excited levels of ions in plasmas typical of those found in the edge of tokamaks is undertaken for the C IV and C V ionization stages. The emphasis is on those energy levels giving rise to transitions of most use for diagnostic purposes (n ≤ 5). Carbon is chosen since it is an important contaminant of JET plasmas; it was the dominant low Z impurity before the installation of the ITER-like wall and is still present in the plasma after its installation. Direct electron collisional ionization both from and to excited levels is considered. Distorted-wave flexible atomic code calculations are performed to generate the required ionization cross sections, due to a lack of atomic data in the literature. Employing these data, ionization from excited level populations is not found to be significant in comparison with radiative decay. However, for some energy levels, ionization terminating in the excited level has an effect in the steady-state of the order of the measurement errors (±10%). During transient events, ionization to excited levels will be of more importance and must be taken into account in the calculation of excited level populations. More accurate atomic data, including possible resonance contributions to the cross sections, would tend to increase further the importance of these effects. 

Energy levels, radiative rates and electron impact excitation rates for transitions in Be-like Ti XIX

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in Be-like Ti XIX. The general-purpose relativistic atomic structure package is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 98 levels of the n≤ 4 configurations. Additionally, theoretical lifetimes are listed for all 98 levels. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 10 ^7.7K. Comparisons are made with similar data obtained from the flexible atomic code (fac) to highlight the importance of resonances, included in calculations with darc, in the determination of effective collision strengths. Discrepancies between the collision strengths from darc and fac, particularly for forbidden transitions, are also discussed. 

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Kr XXXV

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Kr XXXV. The grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac Atomic R-matrix Code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels. Additionally, theoretical lifetimes are listed for all 49 levels. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 10 ^8.1K. Comparisons are made with similar data obtained with the Flexible Atomic Code (fac) to assess the accuracy of the results and to highlight the importance of resonances, included in calculations with darc, in the determination of effective collision strengths. Differences between the collision strengths from darc and fac, particularly for forbidden transitions, are also discussed. Finally, discrepancies between the present results of effective collision strengths from the darc code and earlier semi-relativistic R-matrix data are noted over a wide range of electron temperatures for many transitions of KrXXXV. 

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Ti XXI, v XXII, Cr XXIII and Mn XXIV

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Ti XXI, V XXII, Cr XXIII and Mn XXIV. grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels of each ion. Additionally, theoretical lifetimes are listed for all the 49 levels of the above four ions. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 10 ^7.5K. Comparisons are made with similar data obtained using the flexible atomic code (fac) to highlight the importance of resonances, included in calculations with darc, in the determination of effective collision strengths. Discrepancies between the collision strengths from darc and fac, in particular for forbidden transitions, are also discussed. Finally, discrepancies between the present results for effective collision strengths with the darc code and earlier semi-relativistic R-matrix data are noted over a wide range of electron temperatures for many transitions in all ions. 

Double ionization in R-matrix theory using a two-electron outer region

We have developed a two-electron outer region for use within R-matrix theory to describe double ionisation processes. The capability of this method is demonstrated for single-photon double ionisation of He in the photon energy region between 80 eV to 180 eV. The cross sections are in agreement with established data. The extended RMT method also provides information on higher-order processes, as demonstrated by the identification of signatures for sequential double ionisation processes involving an intermediate He⁺ state with n=2.

Optimising element choice for nanoparticle radiosensitisers

There is considerable interest in the use of heavy atom nanoparticles as theranostic contrast agents due to their high radiation cross-section compared to soft tissue. However, published studies have primarily focused on applications of gold nanoparticles. This study applies Monte Carlo radiation transport modelling using Geant4 to evaluate the macro- and micro-scale radiation dose enhancement following X-ray irradiation with both imaging and therapeutic energies on nanoparticles consisting of stable elements heavier than silicon. An approach based on the Local Effect Model was also used to assess potential biological impacts. While macroscopic dose enhancement is well predicted by simple absorption cross-sections, nanoscale dose deposition has a much more complex dependency on atomic number, with local maxima around germanium (Z = 32) and gadolinium (Z = 64), driven by variations in secondary Auger electron spectra, which translate into significant variations in biological effectiveness. These differences may provide a valuable tool for predicting and elucidating fundamental mechanisms of these agents as they move towards clinical application.

Electron-impact ionization of diatomic molecules using a configuration-average distorted-wave method

Electron-impact ionization cross sections for diatomic molecules are calculated in a configuration-average distorted-wave method. Core bound orbitals for the molecular ion are calculated using a single-configuration self-consistent-field method based on a linear combination of Slater-type orbitals. The core bound orbitals are then transformed onto a two-dimensional (r,θ) numerical lattice from which a Hartree potential with local exchange is constructed. The single-particle Schrödinger equation is then solved for the valence bound orbital and continuum distorted-wave orbitals with S-matrix boundary conditions. Total cross section results for H2 and N2 are compared with those from semiempirical calculations and experimental measurements.

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 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.

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 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 of beryllium and its ions

Inelastic electron scattering from light atomic species is of fundamental importance and has significant applications in fusion-plasma modeling. Therefore, it is of interest to apply advanced nonperturbative, close-coupling methods to the determination of electron-impact excitation for these atoms. Here we present the results of R matrix with pseudostate (RMPS) calculations of electron-impact excitation cross sections through the n=4 terms in Be, Be+, Be2+, and Be3+. In order to determine the effects of coupling of the bound states to the target continuum in these species, we compare the RMPS results with those from standard R-matrix calculations. In addition, we have performed time-dependent close-coupling calculations for excitation from the ground and the metastable terms of Be+ and the metastable term of Be3+. In general, these results are found to agree with those from our RMPS calculations. The full set of data resulting from this work is now available on the Oak Ridge National Laboratory Controlled Fusion Atomic Data Center web site, and will be employed for collisional-radiative modeling of Be in magnetically confined plasmas.

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.