An experimental platform for creating white dwarf photospheres in the laboratory

We present an experimental platform for measuring hydrogen Balmer emission and absorption line profiles for plasmas with white dwarf (WD) photospheric conditions (T_e ～1 eV, n_e ～10¹⁷ cm^?3). These profiles will be used to benchmark WD atmosphere models, which, used with the spectroscopic method, are responsible for determining fundamental parameters (e.g., effective temperature, mass) for tens of thousands of WDs. Our experiment, performed at the Z Pulsed Power Facility at Sandia National Laboratories, uses the large amount of X-rays generated from a z-pinch dynamic hohlraum to drive plasma formation in a gas cell. The platform is unique compared to past hydrogen line profile experiments in that the plasma is radiation-driven. This decouples the heating source from the plasma to be studied in the sense that the radiation temperature causing the photoionization is independent of the initial conditions of the gas. For the first time we measure hydrogen Balmer lines in absorption at these conditions in the laboratory for the purpose of benchmarking Stark-broadened line shapes. The platform can be used to study other plasma species and to explore non-LTE, time-dependent collisional-radiative atomic kinetics.     

Improvements to the RADIOM non-LTE model

In 1993, we proposed the RADIOM model [M. Busquet, Phys. Fluids 85 (1993) 4191] where an ionization temperature T_z is used to derive non-LTE properties from LTE data. T_z is obtained from an “extended Saha equation” where unbalanced transitions, like radiative decay, give the non-LTE behavior. Since then, major improvements have been made. T_z has been shown to be more than a heuristic value, but describes the actual distribution of excited and ionized states and can be understood as an “effective temperature”. Therefore we complement the extended Saha equation by introducing explicitly the auto-ionization/dielectronic capture. Also we use the SCROLL model to benchmark the computed values of T_z.     

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.     

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.     

Tungsten L transition line shapes and energy shifts resulting from ionization in warm dense matter

Spectra of the W L transitions in the energy range 8–12 keV from warm dense plasmas generated by the Naval Research Laboratory's Gamble II pulsed power machine were recorded by a newly developed high-resolution transmission-crystal X-ray spectrometer with ±2 eV accuracy. The discharges have up to 2 MV voltage, 0.5 MA current, and produce up to 2.4 MJ/cm^?3 energy density. The plasma-filled rod pinch (PFRP) diode produces a plasma with N_e ≈ 10²² cm^?3 and T_e ≈ 50 eV during the time of maximum X-ray emission. By analyzing the line shapes, it was determined that the Lβ₂ inner-shell transition from the 4d_5/2 level was shifted to higher energy by up to 23 eV relative to nearby Lβ transitions from n = 3 levels. In addition, the Lβ₂ transition was significantly broader and asymmetric compared to the n = 3 transitions. The energy shift of the Lβ₂ transition results from the ionization of electrons outside the 4d shell that perturbs the transition energies in the ions to higher values. The increased line width and asymmetry result from unresolved transitions from a range of ionization states up to +28. The ionization distribution was determined by comparison of the measured energy shifts and widths to calculated transition energies in W ions, and the ionization was correlated with Gamble discharge parameters such as the anode type and the high voltage delay time. This work demonstrates a new hard X-ray spectroscopic diagnostic technique for the direct measurement of the ionization distribution in warm dense plasmas of the heavy elements W through U that is independent of the other plasma parameters and does not require interpretation by hydrodynamic, atomic kinetics, and radiative simulation codes.     

The calculation of free electron density in Cassandra

Cassandra is an AWE opacity code used to model plasmas in local thermal equilibrium: there is a desire to expand its use to calculating plasma equations of state. Cassandra's self-consistent field calculation (scf) uses the local density approximation for bounds states and has a free electron contribution based upon the Thomas-Fermi model [B.J.B. Crowley et al., J. Quant. Spectro. Radiat. Trans. 71, 257(2001)]. Whilst this is applicable for very high temperature or low density plasmas; in hot and dense matter the effect of ionization will lead to discontinuities in the effective ionisation, Z^?. The electron contribution to hydrostatic pressure is associated with Z^?, thus these discontinuities produce unphysical jumps in the resulting calculated material pressure.We describe a procedure to mitigate the effect by calculating the free electron wave functions within the generalized ion-cell model [B.J.B. Crowley et al., Phys. Rev. A 41, 2179(1990)], and thus explicitly calculate free-electron resonances.     

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.     

Opacity calculation for target physics using the ABAKO/RAPCAL code

Radiative properties of hot dense plasmas remain a subject of current interest since they play an important role in inertial confinement fusion (ICF) research, as well as in studies on stellar physics. In particular, the understanding of ICF plasmas requires emissivities and opacities for both hydro-simulations and diagnostics. Nevertheless, the accurate calculation of these properties is still an open question and continuous efforts are being made to develop new models and numerical codes that can facilitate the evaluation of such properties. In this work the set of atomic models ABAKO/RAPCAL is presented, as well as a series of results for carbon and aluminum to show its capability for modeling the population kinetics of plasmas in both LTE and NLTE regimes. Also, the spectroscopic diagnostics of a laser-produced aluminum plasma using ABAKO/RAPCAL is discussed. Additionally, as an interesting application of these codes, fitting analytical formulas for Rosseland and Planck mean opacities for carbon plasmas are reported. These formulas are useful as input data in hydrodynamic simulation of targets where the computation task is so hard that in line computation with sophisticated opacity codes is prohibitive.     

K-α emission spectroscopic analysis from a Cu Z-pinch

Advances in diagnostic techniques at the Sandia Z-facility have facilitated the production of very detailed spectral data. In particular, data from the copper nested wire-array shot Z1975 provides a wealth of information about the implosion dynamics and ionization history of the pinch. Besides the dominant valence K- and L-shell lines in Z1975 spectra, K-α lines from various ionization stages were also observed. K-shell vacancies can be created from inner-shell excitation and ionization by hot electrons and from photo-ionization by high-energy photons; these vacancies are subsequently filled by Auger decay or resonance fluorescence. The latter process produces the K-α emission. For plasmas in collisional equilibrium, K-α emission usually occurs from highly charged ions due to the high electron temperatures required for appreciable excitation of the K-α transitions. Our simulation of Z1975 was carried out with the NRL 1-D DZAPP non-LTE radiation-hydrodynamics model, and the resulting K- and L-shell synthetic spectra are compared with measured radiation data. Our investigation will focus on K-α generation by both impacting electrons and photons. Synthetic K-α spectra will be generated either by self-consistently calculating the K-shell vacancy production in a full Z-pinch simulation, or by post-processing data from a simulation. The analysis of these K-α lines as well as K- and L-shell emission from valence electrons should provide quantitative information about the dynamics of the pinch plasma.     

Criterion for establishing deviations from the local thermodynamic equilibrium in atmospheric pressure plasma jets

In this paper a dimensionless parameter is defined which allows the prediction of the thermodynamic state in the field-free plasma jet of D. C. operated plasma torches of various designs. This dimensionless parameterP is derived from the conservation equations applied to a two-step temperature and velocity model and contains only quantities which can be experimentally determined without using sophisticated equipment. Critical values ofP based on a critical electron density of 10¹⁶ cm^?3 have been calculated for argon, hydrogen, nitrogen, oxygen, and helium and corresponding values of P_crit have been determined experimentally for two different D. C. operated argon plasma torches using various diagnostic techniques. The experimental values corroborate the assumptions made for the calculation of P_crit. ForP < P_crit, substantial deviations from the local thermodynamic equilibrium (LTE) may occur.     

The effect of bound states on X-ray Thomson scattering for partially ionized plasmas

X-ray Thomson scattering is being developed as a method to measure the temperature, electron density, and ionization state of high energy density plasmas such as those used in inertial confinement fusion. X-ray laser sources have always been of interest because of the need to have a bright monochromatic X-ray source to overcome plasma emission and eliminate other lines in the background that complicate the analysis. With the advent of the X-ray free electron laser (X-FEL) at the SNAL Linac Coherent Light Source (LCLS) and other facilities coming online worldwide, we now have such a source available in the keV regime. An important challenge with X-ray Thomson scattering experiments is understanding how to model the scattering for partially ionized plasmas. Most Thomson scattering codes used to model experimental data greatly simplify or neglect the contributions of the bound electrons to the scattered intensity. In this work we take the existing models of Thomson scattering that include elastic ion–ion scattering and inelastic electron–electron scattering and add the contribution of bound electrons in the partially ionized plasmas. Except for hydrogen plasmas, most plasmas studied today have bound electrons and it is important to understand their contribution to the Thomson scattering, especially as new X-ray sources such as an X-FEL will allow us to study much higher Z plasmas. To date, most experiments have studied hydrogen or beryllium plasmas. We first analyze existing experimental data for beryllium to validate the code. We then consider several higher Z materials such as Cr and predict the existence of additional peaks in the scattering spectrum that require new computational tools to understand. For a Sn plasma, we show that bound contributions change the shape of the scattered spectrum in a way that would change the plasma temperature and density inferred from experiment.     

Light element opacities from ATOMIC

We present new calculations of local-thermodynamic-equilibrium (LTE) light element opacities from the Los Alamos ATOMIC code. ATOMIC is a multi-purpose code that can generate LTE or non-LTE quantities of interest at various levels of approximation. A program of work is currently underway to compute new LTE opacity data for all elements H through Zn. New opacity tables for H through Ne are complete, and a new Fe opacity table will be available soon. Our calculations, which include fine-structure detail, represent a systematic improvement over previous Los Alamos opacity calculations using the LEDCOP legacy code. Our opacity calculations incorporate atomic structure data computed from the CATS code, which is based on Cowan's atomic structure codes, and photoionization cross section data computed from the Los Alamos ionization code GIPPER. We make use of a new equation-of-state (EOS) model based on the chemical picture. ATOMIC incorporates some physics packages from LEDCOP and also includes additional physical processes, such as improved free–free cross sections and additional scattering mechanisms. In this report, we briefly discuss the physics improvements included in our new opacity calculations and present comparisons of our new opacities with other work for C, O, and Fe at selected conditions.     

A comparison of theory and experiment for high density,high temperature germanium spectra

This paper compares results from theoretical predictions to experimental emission data from germanium obtained on the HELEN laser at AWE. The aim of the comparison was to test opacity predictions of highly stripped, medium Z elements, a regime which has received relatively little attention due the difficulty of achieving conditions near LTE at high temperatures. The data show emission from the 2p–3d and 2s–3p transitions from a layer of germanium buried in plastic and heated by the HELEN CPA beam. Predictions of spectra constructed using data generated by the grasp2K atomic structure code coupled to Saha–Boltzman population dynamics were compared to the experimental emission. It was found that the grasp2K calculations match the position of all the features in the experiment well, but non-LTE effects in the experiment make it unreasonable to expect a match to line strengths. Two opacity codes, CASSANDRA and DAVROS, were benchmarked against the grasp2K simulations. It was shown that the major difference in the two opacity codes is due to different approaches to calculating total ion energies. For this reason the DAVROS line positions are significantly more accurate than those of CASSANDRA.     

Applied plasma spectroscopy: Laser-fusion experiments

High-energy-density plasmas created in laser-fusion experiments are diagnosed with X-ray spectroscopy. Hans Griem, considered the father of modern plasma spectroscopy, provided an excellent foundation for this research. He studied the effect of plasma particles, in particular the fast-moving free electrons, on the Stark-broadening of spectral line shapes in plasmas [H. Griem, Phys. Rev. 125 (1962) 177]. Over the last three decades, X-ray spectroscopy has been used to record the remarkable progress made in inertial confinement fusion research. Four areas of X-ray spectroscopy for laser-fusion experiments are highlighted in this paper: Kα emission spectroscopy to diagnose target preheat by suprathermal electrons, Stark-broadened K-shell emissions of mid-Z elements to diagnose compressed densities and temperatures of implosion cores, K- and L-shell absorption spectroscopy to diagnose the relatively cold imploding shell (the “piston”) that does not emit X rays, and multispectral monochromatic imaging of implosions to diagnose core temperature and density profiles. The seminal research leading to the original X-ray spectroscopy experiments in these areas will be discussed and compared to current state-of-the-art measurements.     

A hybrid detailed level and configuration accounting model for investigating the radiative opacity of gold plasmas with open 4d and 4f shells

A hybrid model combining the detailed level accounting (DLA) and detailed relativistic configuration accounting (DCA) methods is developed to investigate the radiative opacity of gold plasmas with open 4d and 4f shells. Due to the collapse of 4f shells, the configurations with multi-electron excited from 4d and 4f shells are bound and can form a huge number of fine-structure levels and detailed transition lines. A full DLA calculation is time-consuming and intractable and thus a hybrid DLA and DCA method is needed. To obtain accurate radiative opacity, the transitions within the collapsed orbitals and transitions to the relatively lowly excited orbitals are treated by a DLA method, while the transitions to the higher excited orbitals are treated by a DCA method. As an illustrative example, the spectrally resolved, Rosseland and Planck mean opacity of gold plasmas at 100 eV and 0.001 g/cm³ are calculated by using the hybrid model. The present results are compared with those obtained by pure DCA and average atom models, where large discrepancies in the line intensities and positions are found for the strongest 4d–4f transitions due to the collapse of 4f shells indicating the importance of detailed treatment to obtain the accurate opacity.