FLYCHK: Generalized population kinetics and spectral model for rapid spectroscopic analysis for all elements

FLYCHK is a straightforward, rapid tool to provide ionization and population distributions of plasmas in zero dimension with accuracy sufficient for most initial estimates and in many cases is applicable for more sophisticated analysis. FLYCHK solves rate equations for level population distributions by considering collisional and radiative atomic processes. The code is designed to be straightforward to use and yet is general enough to apply for most laboratory plasmas. Further, it can be applied for low-to-high Z ions and in either steady-state or time-dependent situations. Plasmas with arbitrary electron energy distributions, single or multiple electron temperatures can be studied as well as radiation-driven plasmas. To achieve this versatility and accuracy in a code that provides rapid response we employ schematic atomic structures, scaled hydrogenic cross-sections and read-in tables. It also employs the jj configuration averaged atomic states and oscillator strengths calculated using the Dirac–Hartree–Slater model for spectrum synthesis. Numerous experimental and calculational comparisons performed in recent years show that FLYCHK provides meaningful estimates of ionization distributions, well within a charge state for most laboratory applications.     

Understanding the anomalous dispersion of doubly ionized carbon plasmas near 47 nm

Over the last several years we have predicted and observed plasmas with an index of refraction greater than 1 in the soft X-ray regime. These plasmas are usually a few times ionized and have ranged from low-Z carbon plasmas to mid-Z tin plasmas. Our main calculational tool has been the average-atom code. We have recently observed C²⁺ plasmas with an index of refraction greater than 1 at a wavelength of 46.9 nm (26.44 eV). In this paper we compare the average-atom method, AVATOMKG, against two more detailed methods, OPAL and CAK, for calculating the index of refraction for the carbon plasmas and discuss the different approximations used. We present experimental measurements of carbon plasmas that display this anomalous dispersion phenomenon. It is shown that the average-atom calculation is a good approximation when the strongest lines dominate the dispersion. However, when weaker lines make a significant contribution, the more detailed calculations such as OPAL and CAK are essential. During the next decade X-ray free electron lasers and other X-ray sources will be available to probe a wider variety of plasmas at higher densities and shorter wavelengths so understanding the index of refraction in plasmas will be even more essential. With the advent of tunable X-ray lasers the frequency-dependent interferometer measurements of the index of refraction may enable us to determine the absorption coefficients and lineshapes and make detailed comparisons against our atomic physics codes.     

Large-scale molecular dynamics simulations of dense plasmas: The Cimarron Project

We describe the status of a new time-dependent simulation capability for dense plasmas. The backbone of this multi-institutional effort – the Cimarron Project – is the massively parallel molecular dynamics (MD) code “ddcMD,” developed at Lawrence Livermore National Laboratory. The project’s focus is material conditions such as exist in inertial confinement fusion experiments, and in many stellar interiors: high temperatures, high densities, significant electromagnetic fields, mixtures of high- and low-Z elements, and non-Maxwellian particle distributions. Of particular importance is our ability to incorporate into this classical MD code key atomic, radiative, and nuclear processes, so that their interacting effects under non-ideal plasma conditions can be investigated. This paper summarizes progress in computational methodology, discusses strengths and weaknesses of quantum statistical potentials as effective interactions for MD, explains the model used for quantum events possibly occurring in a collision, describes two new experimental efforts that play a central role in our validation work, highlights some significant results obtained to date, outlines concepts now being explored to deal more efficiently with the very disparate dynamical timescales that arise in fusion plasmas, and provides a careful comparison of quantum effects on electron trajectories predicted by more elaborate dynamical methods.     

Partially resolved transition array model for atomic spectra

The unresolved transition array (UTA) model of atomic spectra describes the lines in a configuration-to-configuration transition array with a single feature that conserves the total strength as well as the energy first and second strength-weighted moments. A new model is proposed that uses a relatively small detailed line-by-line calculation together with the extant variance formula to generate a series of Gaussians to describe the transition array. This partially resolved transition array (PRTA) model conserves the known array properties, yields improved higher moments, and systematically accounts for initial level populations. Numerical examples show that the PRTA model provides excellent fidelity to line-by-line methods using only a small fraction of the computational effort for the full calculations.     

Corrections to statistical modeling of spectra for plasmas at moderate or low temperatures

For plasmas in LTE at moderate or low temperatures (1–50 eV), the statistical approach for calculating emission or absorption spectra may become inaccurate and need improvement to account for the Boltzmann factor in the population of the levels. In this work, corrections to the transition rates are computed by using the moments of emission or absorption zones, which represent the set of levels within a configuration that provide the dominant part of the emissivity (or opacity). Partition functions are also improved by using high-order moments of level energy distributions. Corrections to the statistical models are derived in a non-relativistic framework as a function of these moments, which can be deduced from already published formulas. Numerical comparisons of detailed line-by-line and statistical calculations are presented that clearly illustrate the importance of correcting the models at low temperatures. Thus, these corrections are of great interest for applications such as Warm Dense Matter, LTE photo-absorption experiments where the targets are heated to ∼T_e = 20 eV and astrophysical plasmas.     

Atomic modeling of the plasma EUV sources

We present the development of population kinetics models for tin plasmas that can be employed to design an EUV source for microlithography. The atomic kinetic code is constrained for the requirement that the model must be able to calculate spectral emissivity and opacity that can be used in radiation hydrodynamic simulations. Methods to develop compact and reliable atomic model with an appropriate set of atomic states are discussed. Specifically, after investigation of model dependencies and comparison experiment, we improve the effect of configuration interaction and the treatment of satellite lines. Using the present atomic model we discuss the temperature and density dependencies of the emissivity, as well as conditions necessary to obtain high efficiency EUV power at λ = 13.5 nm.     

Versatile code DLAYZ for investigating population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium

A versatile code DLAYZ based on collisional-radiative model is developed for investigating the population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium. DLAYZ is implemented on the detailed level accounting (DLA) approach and can be extended to detailed configuration accounting (DCA) and hybrid DLA/DCA approaches. The code can treat both steady state and time-dependent problems. The implementation of the main modules of DLAYZ is discussed in detail including atomic data, rates, population distributions and radiative properties modules. The complete set of basic atomic data is obtained using relativistic quantum mechanics. For dense plasmas, the basic atomic data with plasma screening effects can be obtained. The populations are obtained by solving the coupled rate equations, which are used to calculate the radiative properties. A parallelized version is implemented in the code to treat the large-scale rate equations. Two illustrative examples of a steady state case for carbon plasmas and a time-dependent case for the relaxation of a K-shell excited argon are employed to show the main features of the present code.     

Effect of third- and fourth-order moments on the modeling of unresolved transition arrays

The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram–Charlier, Normal Inverse Gaussian and Generalized Gaussian distributions. It is shown that the modeling of unresolved transition arrays with non-Gaussian distributions may reveal more detailed structures, due essentially to the large value of the kurtosis. In the present work, focus is put essentially on the Generalized Gaussian, the power of the argument in the exponential being constrained by the kurtosis value. The relevance of the new statistical line distribution is checked by comparisons with smoothed detailed line-by-line calculations and through the analysis of 2p → 3d transitions of recent laser or Z-pinch absorption measurements. The issue of calculating high-order moments is also discussed (Racah algebra, Jucys graphical method, semi-empirical approach…).     

Investigation of characteristics of hard x-rays produced during implosions of wire array loads on 1.6 MA Zebra generator

Experimental study of the characteristics of hard x-ray (HXR) emission from multi-planar wire arrays and compact-cylindrical wire arrays (CCWA) plasmas on the 1.6 MA Zebra generator at UNR has been carried out. The characteristics of HXR produced by multi-planar wire arrays such as single, double, and triple planar as well as compact-cylindrical wire arrays made from Al, Cu, brass, Mo, and W were analyzed. Data from spatially resolved time-integrated and spatially integrated time-gated x-ray spectra recorded by LiF spectrometers, x-ray pinhole images, and signals from fast x-ray detectors have been used to study spatial distribution and time history of HXR emission with different loads. The dependence of the HXR yield and power on the wire material, geometry of the load and load mass is observed. Both HXR yield and power are minimum for Al and maximum for W loads. The HXR yield increases with the rise of the atomic number of the material for all loads. The presence of aluminum wires in the load with the main material such as Cu, Mo, or W in combined wire arrays decreases HXR yield. For W plasma, the intensity of cold L-shell spectral lines (1–1.5 Å) correlates with corresponding amplitude of HXR signals which may suggest the evidence of generation of electron beams in plasma. It is found that HXRs are generated from different plasma regions by the interaction of electron-beam with the plasma trailing mass, with the material of anode and due to thermal radiation from plasma bright spots. The theoretical assumption of thermal mechanism of HXR emission predicts the different trends for dependency of HXR power on atomic number and load mass.     

Absorption spectroscopy of mid and neighboring Z plasmas: Iron, nickel,copper and germanium

Opacities of four medium Z element plasmas (iron, nickel, copper and germanium) have been measured at the LULI-2000 facility in similar conditions: temperatures between 15 and 25 eV and densities between 2 and 10 mg/cm³, in a wavelength range (8–18 Å) including the strong 2p–3d structures.Two laser beams from the LULI facility were used in the nanosecond-picosecond configuration. The NANO-2000 beam (at λ = 0.53 μm) heated a gold hohlraum with an energy between 30 and 150 J with a duration of 0.6 ns. Samples covering half a hohlraum hole were thus radiatively heated. The picosecond pulse PICO-2000 beam (at λ = 1.053 μm) has been used to produce a short (about 10 ps) X-ray backlighter in order to reduce time variations of temperatures and densities during the measurement. A crystal high-resolution spectrometer was used as the main diagnostic to record at the same time the non-absorbed and the absorbed backlighter spectra. Radiation temperatures were measured using a broadband spectrometer. 1D and 2D simulations have been performed in order to estimate hydrodynamic plasmas parameters.The measured spectra have been compared with theoretical ones obtained using either the superconfiguration code SCO or the detailed term accounting code HULLAC. These comparisons allow us to check the modeling of the statistical broadening and of the spin-orbit splitting of the 2p–3d transitions and related effects such as the interaction between relativistic subconfigurations belonging to the same non-relativistic configuration.     

Measurements of niobium absorption spectra in plasmas with nearly full M-shell configurations

A systematic study has been carried out on the changes in the L-shell absorption structure of niobium as a result of changing the population of the n = 3 shell from full to having vacancies in the 3d level. The niobium spectra were measured in the 2–3 keV frequency range, which spanned the 2p-nd transitions where 3 ≤ n ≤ 11. In addition to the detailed structure in these arrays the data also show 2s-4p and 2p-4s transitions and the bound-free L edge. The frequencies and widths of transition arrays, transmission between arrays, and the absorption due to the bound-free edge, can be seen in the data. The sample conditions were found from a combination of two-dimensional radiation-hydrodynamics calculations using the AWE NYM code and flux measurements using X-ray diodes, measurements of 1s-2p absorption spectra in aluminium and mixed aluminium/niobium samples. The electron temperature error, inferred from the modelling, is ±2 eV, with a density error of 30%. The data were recorded over the temperature range from 28 to 45 eV and show marked changes in the spectra over this range.The data were compared to spectra predicted by the AWE CASSANDRA [B.J.B. Crowley, J.W.O. Harris, J. Quant. Spectrosc. Radiat. Transfer 71 (2000) p. 257] opacity code. The calculated spectra were able to reproduce the measurements reasonably well. However, there are some differences in line positions that cannot be accounted for by gradients and there are differences in the array structure in the prediction and the measurements, with additional structure predicted but not seen in the measurements. There is also lower transmission on the blue side of the 2p-3d transition arrays compared to prediction.     

X-ray absorption spectroscopy for wire-array Z-pinches at the non-radiative stage

Absorption spectroscopy was applied to wire-array Z-pinches on the 1 MA pulsed-power Zebra generator at the Nevada Terawatt Facility (NTF). The 50 TW Leopard laser was coupled with the Zebra generator for X-ray backlighting of wire arrays at the ablation stage. Broadband X-ray emission from a laser-produced Sm plasma was used to backlight Al star wire arrays in the range of 7–9 Å. Two time-integrated X-ray conical spectrometers recorded reference and absorption spectra. The spectrometers were shielded from the bright Z-pinch X-ray burst by collimators. The comparison of plasma-transmitted spectra with reference spectra indicates absorption lines in the range of 8.1–8.4 Å. Analysis of Al K-shell absorption spectra with detailed atomic kinetics models shows a distribution of electron temperature in the range of 10–30 eV that was fitted with an effective two-temperature model. Temperature and density distributions in wire-array plasma were simulated with a three-dimension magneto-hydrodynamic code. Post-processing of this code’s output yields synthetic transmission spectrum which is in general agreement with the data.     

Opacity calculations in ICF plasmas

Germanium may be used as a possible dopant in the ablator of inertial confinement fusion ignition targets, the knowledge of its opacity is crucial. We have calculated the opacity by two approaches: 1) a detailed line calculation is used in which the atomic database is provided by the MCDF code. A line shape code was adapted to perform the calculation of opacity profile, which leads to a prohibitively long calculation time when the number of lines is large. 2) to alleviate the computationally burden a second approach, combining detailed line calculations and statistical calculations is used. The latter approach requires much smaller calculation times than the first approach and is well suited for extensive calculations. The monochromatic opacity and the Rosseland and Planck mean opacities are calculated for various relevant densities and temperatures.     

Modeling of K-shell Al and Mg radiation from compact single, double planar and cylindrical alloyed Al wire array plasmas produced on the 1 MA Zebra generator at UNR

Radiative emission from alloyed Al single, double and compact cylindrical wire arrays have been studied using the 1 MA Zebra UNR generator. Single planar wire arrays using ten wires and double planar wire arrays and compact cylindrical wire arrays (CCWA) that both had sixteen wires were utilized. The wire composition is Al-5056 (95% of Al and 5% of Mg). We have observed that implosion of these alloyed Al wire loads generated optically thick Al plasmas that can be diagnosed using K-shell Mg lines. In particular, among the considered loads, the K-shell lines of Al from implosions of the double planar wire arrays have the highest optical depth for He-like Al resonance transitions, which occurred near the stagnation phase. X-ray time-gated and time-integrated spectra and pinhole images as well as photoconductive detectors signals were analyzed to provide information on the plasma parameters; electron temperatures and densities, implosion dynamics features and power and yields of the X-ray radiation. Previously developed non-LTE models were applied to model axially-resolved time-integrated, as well as time-gated spatially-integrated, K-shell spectra from Al and Mg. The derived time-dependent electron temperature, density and axial opacity were studied and compared. In addition, the wire ablation dynamics model (WADM) was used to calculate the kinetic energy of the plasma, which with the aid of a Local Thermal Equilibrium (LTE) magneto-hydrodynamics (MHD) simulation, allowed to estimate the precursor and stagnated z-pinch plasma electron temperatures from implosions of wire array loads.     

Statistical line-by-line model for atomic spectra in intermediate coupling

A statistical method to simulate detailed line accounting (DLA) calculations of complex spectra is proposed. The method is based on the recently developed partially resolved transition array model. Numerical examples show that spectrum calculations using the statistical approach are in good agreement with DLA results. In particular, the statistical method conserves systematic line coincidences across transition arrays differing only in the subshell occupation of excited spectator electrons important in opacity calculations. In addition, it is computationally efficient; hence, it can accelerate spectrum calculations without introducing significant uncertainties whenever the DLA method is considered impractical.