Total Dielectronic Recombination Rate Coefficients Research Articles

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.

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.

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.

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).

Theoretical investigation of dielectronic recombination of Sn12+ions

Theoretical calculations have been made for the dielectronic recombination (DR) rate coefficients of Sn${}^{12+}$ ion using a relativistic flexible atomic code with configuration interaction. Comparison of the rate coefficients for $4s$, $4p$, and $4d$ subshell excitation shows that while the $4p$ subshell excitation dominates over the whole temperature region, $4d$ subshell excitation at low temperature and $4s$ subshell excitation at high temperature cannot be neglected. In order to facilitate simple applications, the calculated DR rate coefficients are fitted to an empirical formula. The total DR rate coefficient is greater than either the radiative recombination or three-body recombination coefficients for electron temperatures greater than 1 eV. Therefore, DR can strongly influence the ionization balance of laser-produced tin plasmas.

Dielectronic recombination of heavy species: the tin 4p64dq − 4p64d(q − 1)4f + 4p54d(q + 1) transition arrays for q = 1–10

We report on detailed calculations of dielectronic recombination (DR) rate coefficients for Sn4 +–Sn13 + using three approaches of differing degrees of complexity. These are configuration-mixed Breit–Pauli using the autostructure code, bundled-nl using the Burgess–Bethe general program (BBGP) and configuration average (CA) using the DRACULA code. We find that target Δn = 0 dipole promotions dominate the total DR rate coefficients; configuration-mixing effects are small for the totals; results for the totals are highly dependent on the initial levels averaged over—the results for averaging over all levels of the ground configuration being typically nearly a factor of 2 smaller than for using only the ground level. On comparing the total DR rate coefficients obtained using the three methods we find that the BBGP results are systematically lower than those obtained from autostructure—in some cases they are significantly lower (by a factor of 2)—while the CA results are systematically and significantly higher (by up to 80%) in general. These findings need to be borne in mind for the finite-density modelling of tin plasma sources for microlithography and tin markers for magnetic fusion plasmas especially when using simple descriptions of DR. They apply also to heavy species in general such as tungsten ions which are of great importance for magnetic fusion plasmas.

EFFECTS OF CONFIGURATION INTERACTION FOR DIELECTRONIC RECOMBINATION OF Na-LIKE IONS FORMING Mg-LIKE IONS

Theoretical dielectronic recombination (DR) rate coefficient calculations can be sensitive to configuration interaction (CI) between resonances with different captured electron principle quantum numbers n. Here we explore the importance of this multi-n CI process for DR via 2l → 3l' core excitations and its effect on the total DR rate coefficient. Results are presented for selected Na-like ions from Ca9 + to Zn19 +. We find that including this multi-n CI can reduce the DR rate coefficient by up to ~10% at temperatures where an ion is predicted to form in collisional ionization equilibrium and up to ~15% at higher temperatures. To a first approximation, this will translate into a corresponding increase in the ion abundance. Charge state distributions calculation seeking to be accurate to better than 10% will thus need to take this effect into account. We also present simple fits to the calculated rate coefficients for ease of incorporation into plasma models.

Dielectronic recombination and satellite line spectra of highly charged tungsten ions1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

We present our recent progress on theoretical studies that involve auto-ionizing states of highly charged tungsten ions. Such auto-ionizing states have two channels for decay, which requires that both radiative and auto-ionization atomic data be calculated and combined in a detailed study of the dielectronic recombination (DR). Three atomic codes are used to produce relativistic atomic data (energy levels, radiative transition probabilities, and auto-ionization rates). These are the relativistic many-body perturbation theory (RMBPT) code, the multiconfiguration relativistic Hebrew University Lawrence Livermore atomic code (HULLAC), and the Hartree–Fock relativistic (Cowan) code. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and DR rate coefficients are determined for the excited states. The total DR rate coefficient is derived as a function of electron temperature, and it is shown that the contribution of the highly excited states is very important for the calculation of the total DR rates. Synthetic dielectronic satellite spectra are constructed, and the atomic properties specific to the relevant tungsten ions are highlighted. First, we will consider the results for Na-like tungsten (W63+) and Mg-like tungsten (W62+) using all three codes. Then, we move to even higher ionization states and present the results in Li-like W (W71+). For this we use the RMBPT code as well as the quasi-relativistic many-body perturbation theory (MZ) code. The inclusion of the DR process is essential for correct identification of the lines in impurity spectra and for understanding the main contributions to the total radiation losses.

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

Energy levels, radiative transition probabilities and autoionization rates for [Kr]4d94fnl (n = 4–9), [Kr]4d95l′nl (n = 5–9) and [Kr]4d96l′nl (n = 6–7) states in Ag-like tungsten (W27 +) are calculated using the relativistic many-body perturbation theory method, the multiconfiguration relativistic Hebrew University Lawrence Livermore Atomic Code and the Hartree–Fock-relativistic method. 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 singly excited [Kr]4d10nl (n = 4–9) states. The total DR rate coefficient is derived as a function of electron temperature. These atomic data are important in the modelling of N-shell radiation spectra of heavy ions generated in various collision as well as plasma experiments. The tungsten data are particularly important for fusion application.