Flexible Atomic Code Research Articles

Collision strengths and effective collision strengths for Ne-like Ge

We have carried out a calculation of 241 levels for Ne-like Ge (Z = 36) to calculate electron impact collision strengths and effective collision strengths belonging to 1s22s22p5nl, 1s22s12p6nl (n = 3, 4, 5, 6; l = s, p, d, f, g, and h) configurations, which have been calculated by the fully relativistic flexible atomic code (FAC). Our calculations, based on the distorted-wave method with large configuration interactions, are included. Collision strengths have been generated over an electron energy range of (10–20 000 eV) and they have been listed at seven representative energies of 65.33, 1714.98, 2944.1, 4868.3, 7564.6, 11 040, and 15 221 eV in this work, and effective collision strengths data have been calculated from these at electron plasma temperatures 650, 850, 1050, 1250, 1450, 1650, and 1850 eV. Our results are compared with those available in the literature. It is found that the resonance effects are important in calculating the effective collision strengths.

Fully relativistic atomic structure calculations for W XLIV for determination of plasma diagnostic terms

We report accurate calculations of W XLIV through application of multi-configuration Dirac–Fock wave functions. We have calculated the energies for the lowest 100 fine structure levels, transition wavelengths, radiative rates, oscillator strengths, and line strengths for electric (E1) and magnetic dipole (M1) transitions with the extended average level multi-configurational Dirac–Fock method in the General-Purpose Relativistic Atomic Structure Package (GRASP). We have taken into account the electron correlations, quantum electrodynamics (QED) and Breit corrections in our calculations. We have also performed parallel calculations with the flexible atomic code (FAC) to assess the accuracy of our calculations. This is a fully relativistic code that provides a variety of atomic parameters, and (generally) yields results for energy levels and radiative rates comparable to GRASP. Our calculated results match well with experimentally observed results that are obtained in ASDEX upgrade Tokamak. Additionally, we have also provided the line intensity ratios and electron density for W XLIV, which is useful and important in plasma diagnostics and modeling in future International Thermonuclear Experimental Reactor (ITER) experiments. We believe that our results would be beneficial in the areas of fusion plasma research and astrophysical investigations and applications.

Observation of an extremely-long-lived metastable level in a Ti-like system via an L -shell dielectronic recombination measurement in highly charged 3dn ions of tungsten

In this paper we report the L-shell dielectronic recombination measurement in highly charged $3{d}^{n}$ ions of tungsten by employing a fast electron beam-energy scanning technique at Shanghai EBIT. The studies of the LMM DR resonance strengths of Ar-like up to Mn-like tungsten were implemented through the experiment as well as a fully relativistic configuration interaction method in the flexible atomic code. In the analysis of DR spectrum, an isolated resonant peak was discovered coming from the DR processes via an extremely-long-lived metastable level in a Ti-like system. This work indicated the population of this Ti-like metastable level in the present EBIT plasma condition was as large as 45%.

Theoretical investigation on the soft X-ray spectrum of the highly-charged W54+ ions

A detailed level collisional-radiative model of the E1 transition spectrum of Ca-like W54+ ion has been constructed. All the necessary atomic data has been calculated by relativistic configuration interaction (RCI) method with the implementation of Flexible Atomic Code (FAC). The results are in reasonable agreement with the available experimental and previous theoretical data. The synthetic spectrum has explained the EBIT spectrum in 29.5–32.5 Å , while several new strong transitions has been predicted to be observed in 18.5–19.6 Å for the future EBIT experiment with electron density ne = 1012 cm−3 and electron beam energy Ee = 18.2 keV.

Analysis of spectra of 3s-3p and 3p-3d transitions of highly-charged copper ions

Beam-foil excited spectra in the range of 160–360 Å from highly charged copper ions were identified with the aid of the National Institute of Standards and Technology Atomic Spectra Database and theoretical calculations with Cowan and Flexible Atomic Code (FAC) calculations. Spectra arising from 3s-3p and 3p-3d transitions of Cu13+–Cu22+ ions were considered. The ion fraction at an ion beam energy of 110 MeV was estimated from the equilibrium charge distribution of the fast ion beams after passing through the solid. The corresponding simulated spectra were in good agreement with the experimental result. Our Cowan and FAC calculation results should be useful for further spectral identification and lifetime measurements of highly charged copper ions.

High ionization states observed in soft x-ray spectra from plasmas of second row transition elements produced by femtosecond laser pulses

The soft x-ray emission spectra of femtosecond-laser-produced plasmas from 2nd row transition elements from yttrium (Z = 39) to palladium (Z = 46), with the exception of technetium (Z = 43), were measured in the 1–5 nm region. Plasmas were produced by shining pulses from a titanium–sapphire laser with 65 fs pulse duration and an energy per pulse of 4.5 mJ focused to an intensity of 3 × 1015 W cm−2 onto bulk targets. While the emission spectra from yttrium to molybdenum (Z = 42) contain only the unresolved transition arrays (UTA) already observed in nanosecond and picosecond laser-target interactions described in our previous paper (Lokasani et al 2015 J. Phys. B: At. Mol. Opt. Phys. 48 245009), transitions from higher ionization states are clearly demonstrated in the spectra emitted from ruthenium (Z = 44), rhodium (Z = 45) and palladium targets heated by the femtosecond laser. These UTAs are interpreted by comparing the experimental spectra to calculated results, obtained using the Cowan suite of codes, the flexible atomic code as well as previous predictions of isoelectronic trends. The 3d–4f transitions arrays emitted from Ru XXI-XXIII, Rh XXI-XXIII and Pd XXI-XXIII ions are clearly seen in the observed spectra. To our knowledge, such high ionization states are demonstrated for the first time at such moderate laser energies.

Modeling of soft N, M and L X-ray lines from tungsten relevant to plasma parameters in the WEST tokamak

Soft X-ray diagnostics on tokamak fusion reactors such as ITER and the Tungsten (W) Environment in Steady-state Tokamak (WEST) intend to provide valuable information on the plasma, in particular on the tungsten impurities that appear in the central plasma following plasma-wall interaction. Various highly charged tungsten ions occur depending on the plasma’s electron temperature, all with complex N, M and L X-ray spectra structures that can be properly understood only after comprehensive theoretical research. For a nominal density and electron temperatures relevant to WEST, this paper presents the results of tungsten N, M and L X-ray lines modeling, in the region from 0.1keV to 20keV, performed within the Collisional-Radiative model using the Flexible Atomic Code package.

Individual contributions of M X-ray line from Cu- and Co-like tungsten ions and L X-ray line from Ne-like molybdenum ions – Benchmarks for new approach to determine the high-temperature tokamak plasma parameters

We propose a new advanced approach to determine the parameters for plasma generated in tokamaks. It is based on a detailed interpretation of the high-resolution X-ray spectra structure for tungsten from Zn-like to Co-like and molybdenum Ne-like ions that can, and have, be registered by the KX1 crystal spectrometer on the JET tokamak with an ITER-like wall. An earlier paper found that high-resolution M X-ray spectra structures of tungsten ions can be properly interpreted only by including separately all the individual contributions from the 4s1, 4p1, 4d1 and 4f1 subshell states for the 4d→3p transitions in the case of Cu-like (W45+) ions, and also separately both 4s→3p and 4d→3p transitions for the Co-like (W47+) ions. Here a similarly detailed analysis is done for the M X-ray line structures coming from Cu-like and Co-like tungsten ions and L X-ray line from Ne-like molybdenum ions in different high-temperature plasmas. The predictions are obtained within the Collisional-Radiative approach by the Flexible Atomic Code package, for plasma electron temperatures from 2.0keV to 6.0keV and a single electron density, 3×1019m−3, that is relevant to JET. The obtained shapes of spectra for Cu- and Co-like tungsten and Ne-like molybdenum ions (benchmarks) are important part of prepared reference base, which is crucial for applications of proposed approach. These results should be also useful for ITER, and for tokamaks such as WEST and ASDEX Upgrade, where tungsten plasma-facing components are implemented and kept track of with a high-resolution X-ray diagnostic similar to those based on the KX1 spectrometer.

Analysis of magnetic-dipole transitions in tungsten plasmas using detailed and configuration-average descriptions

This paper is devoted to the analysis of transition arrays of magnetic-dipole (M1) type in highly charged ions. Such transitions play a significant role in highly ionized plasmas, for instance in the tungsten plasma present in tokamak devices. Using formulas recently published and their implementation in the Flexible Atomic Code for M1-transition array shifts and widths, absorption and emission spectra arising from transitions inside the 3*n complex of highly-charged tungsten ions are analyzed. A comparison of magnetic-dipole transitions with electric-dipole (E1) transitions shows that, while the latter are better described by transition array formulas, M1 absorption and emission structures reveal some insufficiency of these formulas. It is demonstrated that the detailed spectra account for significantly richer structures than those predicted by the transition array formalism. This is due to the fact that M1 transitions may occur between levels inside the same relativistic configuration, while such inner configuration transitions are not accounted for by the currently available averaging expression. In addition, because of configuration interaction, transition processes involving more than one electron jump, such as 3p1/23d5/2 → 3p3/23d3/2, are possible but not accounted for in the transition array formulas. These missing transitions are collected in pseudo-arrays using a post-processing method described in this paper. The relative influence of inner- and inter-configuration transitions is carefully analyzed in cases of tungsten ions with net charge around 50. The need for an additional theoretical development is emphasized.

Theoretical study of the dielectronic recombination process of Li-like Xe51+ ions

The dielectronic recombination of Li-like Xe51+ (2s) ions was studied using the flexible atomic code based on the relativistic configuration interaction method. The resonance energies, radiative and autoionization rates, and resonance strengths were calculated systematically for the doubly excited states (2p 1/2 n l j ) J (n = 18−32) and (2p 3/2 n′l j ) J (n′ = 9−27) of Be-like Xe50+ ions. For the higher Rydberg resonance states with n ≥ 33 and n′ ≥ 28, the resonance energies and strengths were obtained by extrapolation based on quantum defect theory. The theoretical rate coefficients, covering the center-of-mass energy range 0–505 eV, are in a better agreement with the experimental results measured at the heavy-ion storage ring ESR than the Multi-Configuration Dirac-Fock calculations, especially at the resonance energy range close to the series limits.

K-shell X-ray transition energies of multi-electron ions of silicon and sulfur

Prompted by the detection of K-shell absorption or emission features in the spectra of plasma surrounding high mass X-ray binaries and black holes, recent measurements using the Livermore electron beam ion trap have focused on the energies of the n=2 to n=1 K-shell transitions in the L-shell ions of lithiumlike through fluorinelike silicon and sulfur. In parallel, we have made calculations of these transitions using the Flexible Atomic Code and the multi-reference Møller-Plesset (MRMP) atomic physics code. Using this code we have attempted to produce sets of theoretical atomic data with spectroscopic accuracy for all the L-shell ions of silicon and sulfur. We present results of our calculations for oxygenlike and fluorinelike silicon and compare them to the recent electron beam ion trap measurements as well as previous calculations.

Responsivity calibration of the extreme ultraviolet spectrometer in the range of 175-435 Å

We reported the relative responsivity calibration of the grazing-incidence flat-field EUV spectrometer between 175 and 435 Å by means of two methods. The first method is implemented by measuring the diffraction efficiency of the grating with synchrotron radiation light source. Considering the transmission efficiency and quantum efficiency of the other optical components in the spectrometer, the total responsivity was then obtained. The second one was carried out by measuring line emissions from C3+, N4+ and O3+ ions at Shanghai high temperature super conductor electron beam ion trap (SH-HtscEBIT). The EUV spectra were also simulated theoretically via a collisional radiative model. In the calculation, the second-order relativistic many-body perturbation theory approach based on the flexible atomic code was used to calculate the energy levels and transition rates; the close-coupling R-matrix approach and relativistic distorted wave method were utilized to calculate the collision strength of electron impact excitation. In comparison with the spectroscopic measurements at EBIT device, the differences between the measured and simulated relative line intensities were obtained. The responsivity calibration for the spectrometer was then achieved by a 3rd degree polynomial function fitting. Our measurement shows that the responsivity between 175 and 435 Å varies by factor of ∼ 46. The two results of calibration demonstrated a consistency within an average deviation of 24%. In addition, an evaluation of our calculations on C iv, N v and O iv line emissions in this wavelength region was given.

Contribution of satellite lines to temperature diagnostics with He-like triplet lines in photoionized plasma

In the present paper, the Heα triplet line ratios (resonance, intercombination, and forbidden lines) are computed for photoionized plasmas, when the contributions of nearby satellite lines are taken into account. The computations have been carried out with our radiative-collisional code, RCF, which is based on the flexible atomic code. The calculations of these line ratios have been done for three materials, namely, silicon, magnesium, and neon. Our calculations are used to derive the plasma temperatures for several astronomical objects, where the spectra are emitted from photoionizing plasmas. It is shown that the incorporation of the satellite lines from doubly excited Li-like ions into the Heα triplet lines is necessary to obtain reliable temperature diagnostics for these astrophysical objects.

Analysis of soft x-ray emission spectra of laser-produced dysprosium, erbium and thulium plasmas

Soft x-ray emission spectra of dysprosium, erbium and thulium ions created in laser-produced plasmas were recorded with a flat-field grazing-incidence spectrometer in the 2.5–8 nm spectral range. The ions were produced using an Nd:YAG laser of 7 ns pulse duration and the spectra were recorded at various power densities. The experimental spectra were interpreted with the aid of the Cowan suite of atomic structure codes and the flexible atomic code. At wavelengths above 5.5 nm the spectra are dominated by overlapping n = 4 − n = 4 unresolved transition arrays from adjacent ion stages. Below 6 nm, n = 4 − n = 5 transitions also give rise to a series of interesting overlapping spectral features.

Collision strength and effective collision strength for Ba XLVIII

Collision strengths for the lowest 52 fine-structure levels of Ba XLVIII have been computed using Dirac atomic R-matrix code (DARC). Resonances in the threshold region have been completely resolved and the contributions of these resonances to allowed and forbidden transitions have been presented. Effective collision strengths have also been determined within a temperature range from the ground state. Collision strengths from ground state have also been computed with the relativistic distorted wave method, the flexible atomic code (FAC) was used for checking the accuracy of our results. The present work represents a new and significant work with improvement in the field. We believe that our presented data of collision and effective collision strengths may be useful in the future for benchmark calculations and for plasma diagnostics.

2000 eV X-ray laser transparent mechanism of neon atom

X-ray transparency occurs during the interaction of X-ray free electron laser with matter. The study of the mechanism of X-ray transparency is of great value for understanding the interaction between X-ray free electron laser and matter. In this paper, the main ionization modes from neutral neon atom till bare nucleus at different flux densities are determined based on the 2000 eV photoionization cross sections and the Auger decay rates of various neon atoms (ions), calculated by the Flexible Atomic Code program. By establishing and solving the rate equations, the formulas of the proportions of various electronic configurations of neon in the main ionization mode are obtained. The proportions of electron configurations in the main ionization modes and the atomic average photoionization cross sections at flux densities of 2000 and 10000 -2fs-1 are calculated by using the formulas. The ratios of the number of hollow atoms to that of complete valence electrons at any time under different flux density laser irradiations are calculated. It is found that both the bare nuclei and the hollow atoms cause X-ray transparency, and a relatively high ratio of the number of hollow atoms to that of complete valence electrons can be achieved by choosing appropriate flux density and pulse duration.

Analysis of unresolved transition arrays in XUV spectral region from highly charged lead ions produced by subnanosecond laser pulse

Soft x-ray and extreme ultraviolet (XUV) spectra from lead (Pb, Z=82) laser-produced plasmas (LPPs) were measured in the 1.0–7.0nm wavelength region employing a 150-ps, 1064-nm Nd:YAG laser with focused power densities in the range from 3.1×1013W/cm2 to 1.4×1014W/cm2. The flexible atomic code (FAC) and the Cowan's suite of atomic structure codes were applied to compute and explain the radiation properties of the lead spectra observed. The most prominent structure in the spectra is a broad double peak, which is produced by Δn=0, n=4–4 and Δn=1, n=4–5 transition arrays emitted from highly charged lead ions. The emission characteristics of Δn=1, n=4–5 transitions were investigated by the use of the unresolved transition arrays (UTAs) model. Numerous new spectral features generated by Δn=1, n=4–5 transitions in ions from Pb21+ to Pb45+ are discerned with the aid of the results from present computations as well as consideration of previous theoretical predictions and experimental data.

Modelling of the soft X-ray tungsten spectra expected to be registered by GEM detection system for WEST

Abstract In the future International Thermonuclear Experimental Reactor (ITER), the interaction between the plasma and the tungsten chosen as the plasma-facing wall material imposes that the hot central plasma loses energy by X-ray emission from tungsten ions. On the other hand, the registered X-ray spectra provide alternative diagnostics of the plasma itself. Highly ionized tungsten emits extremely complex X-ray spectra that can be understood only after exhaustive theoretical studies. The detailed analyses will be useful for proper interpretation of soft X-ray plasma radiation expected to be registered on ITER-like machines, that is, Tungsten (W) Environment in Steady-state Tokamak (WEST). The simulations of the soft X-ray spectra structures for tungsten ions have been performed using the flexible atomic code (FAC) package within the framework of collisional-radiative (CR) model approach for electron temperatures and densities relevant to WEST tokamak.

Atomic data and line intensities for the S V ion

The energy levels, oscillator strengths, spontaneous radiative decay rates, lifetimes and electron impact collision strengths have been obtained for the [Ne]3snl, [Ne]3pnl, [Ne]3dnl configurations belonging to S V ion, with n≤7 and l≤4, resulting in 567 fine-structure levels. The calculations have been performed within the fully relativistic Flexible Atomic Code (FAC, Gu, 2008) framework and the distorted wave approximation. To attain the desired accuracy for the levels energy, the valence–valence and valence–core correlations have been taken care of by including 96 configuration state functions (CSFs) in the model, reaching a total of 3147 fine-structure levels. Two separate calculations have been performed with the local central potential computed for two different average configurations. A third calculation is also performed without the addition of the core-excited states in the atomic model for completeness. The effects of slightly different mean configurations and valence–core correlations on the energy levels and decay rates are investigated. The collision data have been computed employing the relativistic distorted-wave method along with the atomic model containing the 96 CSFs and corresponding to the ground state mean configuration. The collision strengths corresponding to excitation from the first four fine-structure levels are given for five energy values of the scattered electron 2.65, 6.18, 11.02, 17.36, 25.43 Rydberg, plus an additional variable small energy value near the threshold. A collisional-radiative model has been employed to solve the rate equations for the populations of the 567 fine-structure levels, for a temperature of LogTE(K)=5.2 corresponding to the maximum abundance of S V, and at densities 106–1016cm−3, assuming a Maxwellian electron energy distribution function and black body radiation of temperature 6000 K and dilution factor 0.35 for the photon distribution function. The main processes responsible for the level population variations are the electron-impact collisional excitation and the radiative decay along with their inverse processes. As a result, the level populations along with the spectral high-line intensity ratios are provided.

LABORATORY MEASUREMENTS OF THE K-SHELL TRANSITION ENERGIES IN L-SHELL IONS OF SI AND S

ABSTRACT We have measured the energies of the strongest 1s–2 transitions in He- through Ne-like silicon and sulfur ions to an accuracy of using the Lawrence Livermore National Laboratory’s electron beam ion traps, EBIT-I and SuperEBIT, and the NASA/GSFC EBIT Calorimeter Spectrometer (ECS). We identify and measure the energies of 18 and 21 X-ray features from silicon and sulfur, respectively. The results are compared to new Flexible Atomic Code calculations and to semi-relativistic Hartree–Fock calculations by Palmeri et al. (2008). These results will be especially useful for wind diagnostics in high-mass X-ray binaries, such as Vela X-1 and Cygnus X-1, where high-resolution spectral measurements using Chandra's high-energy transmission grating has made it possible to measure Doppler shifts of . The accuracy of our measurements is consistent with that needed to analyze Chandra observations, exceeding Chandra's limit. Hence, the results presented here not only provide benchmarks for theory, but also accurate rest energies that can be used to determine the bulk motion of material in astrophysical sources. We show the usefulness of our results by applying them to redetermine Doppler shifts from Chandra observations of Vela X-1.