Total Dielectronic Recombination Rate Research Articles

Dielectronic recombination in non-LTE plasmas

Novel phenomena and methods related to dielectronic capture and dielectronic recombination are studied for non-local thermodynamic equilibrium (LTE) plasmas and for applications to non-LTE ionization balance. It is demonstrated that multichannel autoionization and radiative decay strongly suppress higher-order contributions to the total dielectronic recombination rates, which are overestimated by standard approaches by orders of magnitude. Excited-state coupling of dielectronic capture is shown to be much more important than ground-state contributions, and electron collisional excitation is also identified as a mechanism driving effective dielectronic recombination. A theoretical description of the effect of angular-momentum-changing collisions on dielectronic recombination is developed from an atomic kinetic point of view and is visualized with a simple analytical model. The perturbation of the autoionizing states due to electric fields is discussed with respect to ionization potential depression and perturbation of symmetry properties of autoionization matrix elements. The first steps in the development of statistical methods are presented and are realized in the framework of a local plasma frequency approach. Finally, the impact of collisional–radiative processes and atomic population kinetics on dielectronic recombination is critically discussed, and simple analytical formulas are presented.

Ab initio dielectronic recombination rate coefficients for highly-charged Ar-like ions

Employing the independent-processes isolated-resonance distorted-wave approximation, we have made a comprehensive study on dielectronic recombination (DR) for 19 highly-charged Ar-like ions with nuclear charge number Z=23–30, 36, 42, 50, 54, 60, 64, 70, 74, 79, 85 and 92. For the convenience of usage, the ab initio level-by-level total rate coefficients for DR initially from both the ground state 3s23p6 1S0 and the metastable state 3s23p53d 3P0 are presented in a simple compact fitting form. We include the 3 → 3 (Δn=0), 2 → 3 and 3 → 4 (Δn=1), and 3 → 5 (Δn=2) core-excitations resonances as well as the decays from the resonances toward low-lying autoionizing levels followed possibly by radiative cascade effects in our ab initio DR results. The detailed configuration interaction analysis and comparisons with both theoretical and experimental results show that present total DR rate coefficients are reliable at both low (with a typical uncertainty of a factor of 2 in the photoionized plasma zone) and high (with an uncertainty of about 20% in the collisional plasma zone) temperature. To our knowledge, these are the first ab initio DR results for most of ions with Z > 30.

Suppression of Dielectronic Recombination Due to Finite Density Effects. II. Analytical Refinement and Application to Density-dependent Ionization Balances and AGN Broad-line Emission

We present improved fits to our treatment of suppression of dielectronic recombination at intermediate densities. At low densities, most recombined excited states eventually decay to the ground state, and therefore the total dielectronic recombination rate to all levels is preserved. At intermediate densities, on the other hand, collisions can lead to ionization of higher-lying excited states, thereby suppressing the dielectronic recombination rate. The improved suppression factors presented here, although highly approximate, allow summed recombination rate coefficients to be used to intermediate densities. There have been several technical improvements to our previously presented fits. For H- through B-like ions the activation log densities have been adjusted to better reproduce existing data. For B-, C-, Al-, and Si-like ions secondary autoionization is now included. The treatment of density discontinuity in electron excitations out of ground state H-, He-, and Ne-like ions has been improved. These refined dielectronic recombination suppression factors are used in the most recent version of the plasma simulation code Cloudy. We show how the ionization and emission spectrum change when this physics is included. Although these suppression factors improve the treatment of intermediate densities, they are highly approximate and are not a substitution for a complete collisional-radiative model of the ionization balance.

Dielectronic recombination data for dynamic finite-density plasmas

Context.We aim to present a comprehensive theoretical investigation of dielectronic recombination (DR) of the silicon-like isoelectronic sequence and provide DR and radiative recombination (RR) data that can be used within a generalized collisional-radiative modelling framework.Aims.Total and final-state level-resolved DR and RR rate coefficients for the ground and metastable initial levels of 16 ions between P+and Zn16+are determined.Methods.We carried out multi-configurational Breit-Pauli DR calculations for silicon-like ions in the independent processes, isolated resonance, distorted wave approximation. Both Δnc= 0 and Δnc= 1 core excitations are included usingLSand intermediate coupling schemes.Results.Results are presented for a selected number of ions and compared to all other existing theoretical and experimental data. The total dielectronic and radiative recombination rate coefficients for the ground state are presented in tabulated form for easy implementation into spectral modelling codes. These data can also be accessed from the Atomic Data and Analysis Structure (ADAS) OPEN-ADAS database. This work is a part of an assembly of a dielectronic recombination database for the modelling of dynamic finite-density plasmas.

Dielectronic recombination of lowly charged tungsten ions W[formula omitted

Dielectronic recombination (DR) rate coefficients for the ground levels of low ionization state Wq+ (q=5−10) ions have been obtained by an ab-inito level-by-level calculation using the flexible atomic code (FAC) based on relativistic jj coupling scheme and independent process, isolated resonance, distorted wave approximation. The radiative transition calculation in the original FAC has been adapted into parallel programming for time effective dealing with so many resonance levels of the complex open 4f, 5p, or 5d-shell structure ion. Core excitations Δnc=0,1 of 4f, 5p, and 5d (W5+), Δnc=2 of 4f, and Δnc=0 of 4d (W7+), and 5s (W8+) are included to the total DR rate coefficient. The core excitations Δnc=0, 5p → 5l and Δnc=1, 4f → 5l mainly contribute to the total DR rate coefficients. The strong resonances involved in the DR are analyzed and the total DR rate coefficients are compared with available previous ab-initio predictions and with ADAS data by a simple semiempirical formula.

Partial and total dielectronic recombination rate coefficients for W55+ to W38+

Dielectronic recombination (DR) is the dominant mode of recombination in magnetically confined fusion plasmas for intermediate to low-charged ions of W. Complete, final-state resolved partial isonuclear W DR rate coefficient data is required for detailed collisional-radiative modelling for such plasmas in preparation for the upcoming fusion experiment ITER. To realise this requirement, we continue The Tungsten Project by presenting our calculations for tungsten ions to . As per our prior calculations for to , we use the collision package autostructure to calculate partial and total DR rate coefficients for all relevant core-excitations in intermediate coupling (IC) and configuration average (CA) using κ-averaged relativistic wavefunctions. Radiative recombination rate coefficients are also calculated for the purpose of evaluating ionisation fractions. Comparison of our DR rate coefficients for with other authors yields agreement to within 7%–19% at peak abundance verifying the reliability of our method. Comparison of partial DR rate coefficients calculated in IC and CA yield differences of a factor at peak abundance temperature, highlighting the importance of relativistic configuration mixing. Large differences are observed between ionisation fractions calculated using our recombination rate coefficient data and that of Pütterich et al (2008 Plasma Phys. Control. Fusion 50 085016). These differences are attributed to deficiencies in the average-atom method used by the former to calculate their data.

Statistical Model of Dielectronic Recombination of Heavy Ions in Plasmas

AbstractCalculation of the total dielectronic recombination (DR) rates was done in the frame of a statistical model of atoms. The model is based on the idea of collective excitations of atomic electrons with the local plasma frequency, which depends on atomic electrons density distribution. The electron density is described in a frame of the Thomas‐Fermi model of atoms. Simple scaling laws for temperature Te and nuclear charge Z dependences follow from the statistical model of DR. Results of the statistical model were compared with other numerical data following detailed level‐by‐level computations for different multielectron ions. The specific attention is paid to Ni‐like ion sequences of different chemical elements in order to check the Z ‐dependence of DR rates. A comparison with numerical data of Flexible Atomic Code (FAC) is presented for tungsten ions. The reasonable correspondence between the statistical model and the detailed numerical data is demonstrated. The application of the statistical model provides very simple and fast calculations of the DR rates useful in modern plasma modelling. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Partial and total dielectronic recombination rate coefficients forW73+toW56+

Dielectronic recombination (DR) is a key atomic process which affects the spectroscopic diagnostic modelling of tungsten, most of whose ionization stages will be found somewhere in the ITER fusion reactor: in the edge, divertor, or core plasma. Accurate DR data is sparse while complete DR coverage is unsophisticated (e.g. average-atom or Burgess General Formula) as illustrated by the large uncertainties which currently exist in the tungsten ionization balance. To this end, we present a series of partial final state-resolved and total DR rate coefficients for W73+ to W56+ Tungsten ions. This is part of a wider effort within The Tungsten Project to calculate accurate dielectronic recombination rate coefficients for the tungsten isonuclear sequence for use in collisional-radiative modelling of finite-density tokamak plasmas. The recombination rate coefficients have been calculated with autostructure using kappa-averaged relativistic wavefunctions in level resolution (intermediate coupling) and configuration resolution (configuration average). The results are available from OPEN-ADAS according to the adf09 and adf48 standard formats. Comparison with previous calculations of total DR rate coefficients for W63+ and W56+ yield agreement to within 20% and 10%, respectively, at peak temperature. It is also seen that the Juttner correction to the Maxwell distribution has a significant effect on the ionization balance of tungsten at the highest charge states, changing both the peak abundance temperatures and the ionization fractions of several ions.

Dielectronic recombination of Ni-, Cu-, and Zn-like tungsten ions

Dielectronic recombination (DR) for Ni- and Zn-like Wq+ (q=46, 44) has been investigated extending the previous theoretical methodology (Kwon and Lee, 2016 [6]) applied for Cu-like W45+ which treats configuration mixing (CM) between resonances, non-resonant stabilization to non-closed inner-shells and decays to autoionizing levels possibly followed by cascades. For W46+ DR via 3[s,p,d]174lnl′ and 3[s,p,d]175lnl′ resonances (Δnc=1, 2) are included to the total Maxwellian rate coefficient. CM between 3p63d94lnl′ and 3p53d104lnl′ resonances largely changes low energy DR near the threshold. For W45+ radiative decay channels 3d104l′n′l′′ (4<n′<n) of DR via 3d104lnl′ resonances (Δnc=0) which were missed in our previous calculation (Kwon and Lee, 2016 [6]) are included and the rate coefficient is revised. For W44+ CM involving double electron core excitation is taken into account. All non-negligible core excitations Δnc=0 of 4s, Δnc=1 of 4s, 3d, and 3p, and Δnc=2 of 4s, 3d, and 3p are included to the total DR rate coefficient for W44+. Our total DR rate coefficients for Wq+ (q=46−44) are compared with available previous ab initio predictions by other level-to-level calculations and by a configuration-averaged level group calculation, and with ADAS data by semiempirical formula in detail.

Theoretical studies of dielectronic recombination for Au34+ ions

Dielectronic recombination (DR) rate coefficients of complex structure ions are very important for spectral simulation in some application researches, such as nuclear fusion and extreme ultraviolet lithography. Theoretical calculations are made for dielectronic recombination rate coefficients of Au34+ ions by using a flexible relativistic atomic code. Influences of excitation and radiation channels, configuration interactions, and decays to autoionizing levels possibly followed by radiative cascades (DAC) on DR rate coefficient are analyzed. The contribution of DAC is evident. The total DR rate coefficient is greater than either the radiation recombination coefficient or three-body recombination coefficient for electron temperature greater than 1 eV. In order to facilitate simple applications, the total DR rate coefficients for the ground state and the first excited state are fitted to an empirical formula. These results should be useful for further analyzing the DR process of complex structures ions.

Dielectronic recombination of Cu-like W45+

We have investigated dielectronic recombination (DR) for Cu-like W45+ forming Zn-like W44+ by theoretical calculation using the flexible atomic code based on an independent process, isolated resonance, and distorted wave approximation. We have focused on the effect of configuration mixing involving double electron core excitation as well as single electron core excitation on the DR via 3d94l4l′4l″ and 3p53d104l4l′4l″ resonances by inner-shell core excitation Δnc=1. About 20% and over 100% changes in Maxwellian rate coefficient are shown at high energies over 200eV and at low energies near the threshold, respectively, by the configuration mixing. Non-resonant stabilizations (NRS) and decays to autoionizing levels possibly followed by cascades (DAC) to non-closed inner-shells 3d94l4l′4l″ are also considered. The NRS and DAC effect on the DR Maxwellian rate coefficient is relatively smaller than the configuration mixing effect and is less than ~20%. Particular attention has been paid to the DR via 3d104lnl′ resonances by valence-shell core excitation Δnc=0 which was not considered in the previous work (Behar et al., 1997 [4]). The 3d104lnl′ resonances very dominate the DR at low energies below ~100eV. Δnc=2 core excitations are small but not negligible (~10%) relatively at high energy range around 10keV. Our total DR rate coefficient shows the difference with the recombination coefficient on the ADAS database obtained by using a simple semiempirical formula over order of magnitude at low energies and about 30–50% at 2–7keV energy range where W45+ is abundant.

Dielectronic recombination of Zn-likeW44+from Cu-likeW45+

Energy levels, radiative transition probabilities, and autoionization rates for $\text{[Ar]}3{d}^{10}4{l}^{\ensuremath{'}}nl (n=4--12, l\ensuremath{\le}n\ensuremath{-}1), \text{[Ar]}3{d}^{10}5{l}^{\ensuremath{'}}nl (n=5--8, l\ensuremath{\le}n\ensuremath{-}1)$, and $\text{[Ar]}3{d}^{9}4{l}^{\ensuremath{'}}4{l}^{\ensuremath{'}\ensuremath{'}}nl (n=4--5, l\ensuremath{\le}n\ensuremath{-}1$) states in Zn-like tungsten (${\mathrm{W}}^{44+}$) are calculated using the relativistic Hartree-Fock method (cowan code), the multiconfiiguration relativistic Hebrew University Lawrence Livermore Atomic Code (hullac code), and the relativistic many-body perturbation theory method (rmbpt code). Autoionizing levels above the thresholds $\text{[Ar]}3{d}^{10}4s$ are considered. It is found that configuration mixing $[4sns+4pnp+4dnd+4fnf], [4snp+4pns+4pnd+4dnp+4fns+4fnd]$ plays an important role for all atomic characteristics. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the first excited odd- and even-parity states. It is shown that the contribution of the highly excited states is very important for the calculation of total DR rates. Contributions to DR rate coefficients from the excited $\text{[Ar]}3{d}^{10}4{l}^{\ensuremath{'}}nl$ states with $ng12$ and $\text{[Ar]}3{d}^{10}5{l}^{\ensuremath{'}}nl$ states with $ng8$, and additionally from core-excited $\text{[Ar]}3{d}^{9}4{l}^{\ensuremath{'}}4{l}^{\ensuremath{'}\ensuremath{'}}nl$ states with $ng5$, are estimated by extrapolation of all atomic parameters. The orbital angular momentum quantum number $l$ distribution of the rate coefficients shows two peaks at $l=2$ and $l=5$. The total DR rate coefficient is derived as a function of electron temperature. The dielectronic satellite spectra of ${\mathrm{W}}^{44+}$ are important for $M$-shell diagnostic of very high-temperature laboratory plasmas such as those found in future tokamaks.

Dielectronic recombination rate coefficients of initially rubidium-like tungsten

Ab initio calculations of dielectronic recombination (DR) rate coefficients of initially rubidium-like W37+ ions have been performed for the electron temperatures from 1 eV to 5 × 104 eV, by using the Flexible Atomic Code based on the relativistic configuration-interaction method. Special attention has been paid to the partial contributions to total DR rate coefficients as associated with the excitation of individual subshells. A detailed comparison of the calculations shows that the excitation from 4p subshell dominates total DR rate coefficients followed by the excitations from 4s and 4d subshells, while the contribution of excitations from 3l(l = s, p, d) subshells becomes important only at high temperatures. Besides, it is found that the electron excitations associated with △n = 0,1 dominate at low-temperature plasmas, however, the excitations associated with △n ≥ 2 become non-negligible at high-temperature ones.

Dielectronic Recombination of Br-Like Tungsten Ions

Accurate data for dielectronic recombination of tungsten ions are essential in the modeling of tungsten impurity transport and radiative power loss in International Thermonuclear Experimental Reactor (ITER). Theoretical calculations have been made for dielectronic recombination (DR) rate coefficients of Br-like tungsten ions using a flexible relativistic atomic code (FAC) from 1 eV to 50 keV. Level-by-level calculations are carried out for evaluating the contributions to DR through all the relevant Kr-like tungsten ions autoionizing inner-shell excited configuration complexes: (3s23p63d10)−14s24p5nln′l′ (n = 4–5, n′ = 4–100, l′ = 0–8), (4s24p5)−1 nln′l′ (n = 4–6, n′ = 4–100, l′ = 0–12). Comparison of the rate coefficients for 3s, 3p, 3d, 4s and 4p subshell excitations shows that the 4p subshell excitation dominates over the whole temperature region, 4s subshell excitation at low temperature and 3p, 3d subshell excitations at high temperature can not be neglected. In order to facilitate simple applications, the total DR rate coefficient, Δn = 0, 1 and 2 core excitations DR rate coefficients are fitted to an empirical formula.

SUPPRESSION OF DIELECTRONIC RECOMBINATION DUE TO FINITE DENSITY EFFECTS

We have developed a general model for determining density-dependent effective dielectronic recombination (DR) rate coefficients in order to explore finite-density effects on the ionization balance of plasmas. Our model consists of multiplying by a suppression factor those highly-accurate total zero-density DR rate coefficients which have been produced from state-of-the-art theoretical calculations and which have been benchmarked by experiment. The suppression factor is based-upon earlier detailed collision-radiative calculations which were made for a wide range of ions at various densities and temperatures, but used a simplified treatment of DR. A general suppression formula is then developed as a function of isoelectronic sequence, charge, density, and temperature. These density-dependent effective DR rate coefficients are then used in the plasma simulation code Cloudy to compute ionization balance curves for both collisionally ionized and photoionized plasmas at very low (ne = 1 cm^-3) and finite (ne=10^10 cm^-3) densities. We find that the denser case is significantly more ionized due to suppression of DR, warranting further studies of density effects on DR by detailed collisional-radiative calculations which utilize state-of-the-art partial DR rate coefficients. This is expected to impact the predictions of the ionization balance in denser cosmic gases such as those found in nova and supernova shells, accretion disks, and the broad emission line regions in active galactic nuclei.

Effects of configuration interaction for dielectronic recombination of Na-like ions forming Mg-like ions

Dielectronic recombination (DR) of Na-like ions forming Mg-like ions via excitation of a 2l core electron has been investigated for selected ions from Ca9+ to Zn19+. We find that configuration interaction (CI) between DR resonances with different captured electron principal quantum numbers n can lead to a significant reduction in resonance strengths for n ≳ 5. We also explored the effect of this multi-n CI for the total DR rate coefficient. DR rate coefficients can be reduced by up to ∼ 10% at temperatures where an ion is predicted to form in collisional ionization equilibrium and up to ∼ 15% at higher temperatures.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines, and dielectronic recombination rates for excited states of Yb-like W

Energy levels, radiative transition probabilities and autoionization rates for [Cd]4f145p65l′nl, [Cd]4f145p66l″nl, [Cd]4f145p55d2nl, [Cd]4f145p55d6l″nl, [Cd]4f135p65d2nl and [Cd]4f135p65d6l″nl (l′ = d, f, g, l″ = s, p, d, l = s, p, d, f, g and n = 5–7) states of Yb-like tungsten (W4 +) are calculated using the relativistic many-body perturbation theory method (RMBPT code), the multiconfiguration relativistic Hebrew University–Lawrence Livermore Atomic Code (HULLAC code) and the Hartree–Fock relativistic method (COWAN code). Branching ratios relative to the [Cd]4f145p65d, [Cd]4f145p66s and [Cd]4f145p66p thresholds in Tm-like tungsten and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the singly excited, as well as non-autoionizing core-excited states in Yb-like tungsten. Contributions from the autoionizing doubly excited states [Cd]4f145p65fnl, [Cd]4f145p66l″nl and core-excited [Cd]4f145p55d2nl, [Cd]4f145p55d6l″nl, [Cd]4f135p65d2nl, [Cd]4f135p65d6l″nl states (with n up to 100), which are particulary important for calculating the total DR rates, are estimated. Synthetic dielectronic satellite spectra from Yb-like W are simulated in a broad spectral range from 200 to 1400 Å. These calculations provide recommended values critically evaluated for their accuracy for a number of W4 + properties useful for a variety of applications including for fusion applications.

Dielectronic recombination of Pd-like gadolinium

As research and development of extreme ultraviolet lithography (EUVL) sources at 6.7 nm (which will be based on emission from ionized gadolinium) has already begun, reliable atomic data are required in order to determine the optimum plasma conditions. However, the complexity of the atomic structure means that ab initio level-resolved dielectronic recombination (DR) calculations are currently unavailable for the ions of interest. Here we report the first detailed calculation of the DR rate coefficients for the ground state and first excited states of Pd-like gadolinium. Energy levels, radiative transition probabilities, and autoionization rates of Ag-like gadolinium for [Kr]4${d}^{9}$4$fnl$, [Kr]4${p}^{5}$4${d}^{10}$4$fnl$, [Kr]4${d}^{9}$5$l$\ensuremath{'}$nl$, and [Kr]4${d}^{9}$6$l$\ensuremath{'}$nl$ ($n$ \ensuremath{\leqslant} 18) complexes were calculated using the flexible atomic code (FAC). It was found that inclusion of 4${p}^{5}$4${d}^{10}$4$fnl$ configurations has significant influence on the total DR rate coefficient. The DR rate coefficients obtained here are compared with radiative recombination and three-body recombination coeffcients. The results show that the DR rate coefficient is almost an order of magnitude higher than the coefficients for the other two recombination processes combined at plasma electron temperatures around 110 eV, which suggests that the DR process should be included in theoretical modeling for Pd-like gadolinium in EUVL source plasmas.

Dielectronic recombination data for dynamic finite-density plasmas

Context. A comprehensive study of dielectronic recombination (DR) for the aluminum-like isoelectronic sequence has been completed. Aims. Total and final-state resolved DR rate coefficients for the ground and metastable initial levels of 17 ions between Si ii and Zn xviii are presented. Methods. Within an isolated-resonance, distorted-wave (IPIRDW) approximation, multiconfiguration Breit-Pauli (MCBP) calculations are carried out for the total and partial DR rate coefficients of Al-like ions. Both Δnc = 0 and Δnc = 1 core-excitations are included, using LS-coupled and intermediate-coupling (IC) schemes. Results. The inaccuracies of earlier empirical data and/or LS-coupling calculations, particularly at lower temperatures characteristic of photoionized plasmas, is demonstrated by comparison with present, state-of-the-art IC DR rate coefficients. Fine-structure effects are found to increase the DR rate coefficient at low temperatures and decrease it at high temperatures, rendering earlier LS calculations incomplete. Good agreement is found between present IC results and experimental measurements.

The study of dielectronic recombination (DR) rate coefficient for ground state of Ne-like isoelectronic sequence ions

The dielectronic recombination (DR) rate coefficients for Ne-like isoelectronic sequence ions in the ground state 2s22p6 are calculated by using relativistic configuration interaction (RCI) method over a wide temperature ranging from 0.1EI to 10EI where EI is the ionization energy of corresponding Na-like ion. The (2s2p)73ln'l', (2s2p)74l4l' and (2s2p)74l5l' complexes are considered as autoionizing doubly excited states of Ne-like ions in the calculation. The contribution of (2s2p)73ln'l' complex with l' &gt;8 is found to be negligible. The contribution of high Rydberg states of (2s2p)73ln'l' complex obeys the complex-complex n'-3 extrapolation, and the larger the nuclear charge, the smaller the value of n' is. On the basis of the detailed level-by-level results, a general analytic formula for the total DR rate coefficient for all the ions along the Ne-like isoelectronic sequence is constructed. This formula can generally reproduce the calculated DR rate coefficients within 2% for electron temperature between 0.1EI and 10EI. Burgess-Merts semiempirical formula is found to be inadequate for predicting the DR rates of Ne-like ions at low electron temperatures (kTeEI) and may be used for high electron temperatures (kTe &gt; 2EI).