Atomic Physics Models Research Articles

Extreme Ultraviolet Radiation Sources from Dense Plasmas

The concept of dense and hot plasmas can be used to build up powerful and brilliant radiation sources in the soft X-ray and extreme ultraviolet spectral range. Such sources are used for nanoscale imaging and structuring applications, such as EUV lithography in the semiconductor industry. An understanding of light-generating atomic processes and radiation transport within the plasma is mandatory for optimization. The basic principles and technical concepts using either a pulsed laser or a gas discharge for plasma generation are presented, and critical aspects in the ionization dynamics are outlined within the framework of a simplified atomic physics model.

Probing atomic physics at ultrahigh pressure using laser-driven implosions

Spectroscopic measurements of dense plasmas at billions of atmospheres provide tests to our fundamental understanding of how matter behaves at extreme conditions. Developing reliable atomic physics models at these conditions, benchmarked by experimental data, is crucial to an improved understanding of radiation transport in both stars and inertial fusion targets. However, detailed spectroscopic measurements at these conditions are rare, and traditional collisional-radiative equilibrium models, based on isolated-atom calculations and ad hoc continuum lowering models, have proved questionable at and beyond solid density. Here we report time-integrated and time-resolved x-ray spectroscopy measurements at several billion atmospheres using laser-driven implosions of Cu-doped targets. We use the imploding shell and its hot core at stagnation to probe the spectral changes of Cu-doped witness layer. These measurements indicate the necessity and viability of modeling dense plasmas with self-consistent methods like density-functional theory, which impact the accuracy of radiation transport simulations used to describe stellar evolution and the design of inertial fusion targets.

Homogeneous, Micron-Scale High-Energy-Density Matter Generated by Relativistic Laser-Solid Interactions.

Short-pulse, laser-solid interactions provide a unique platform for studying complex high-energy-density matter. We present the first demonstration of solid-density, micron-scale keV plasmas uniformly heated by a high-contrast, 400nm wavelength laser at intensities up to 2×10^{21} W/cm^{2}. High-resolution spectral analysis of x-ray emission reveals uniform heating up to 3.0keV over 1 μm depths. Particle-in-cell simulations indicate the production of a uniformly heated keV plasma to depths of 2 μm. The significant bulk heating and presence of highly ionized ions deep within the target are attributed to the few MeV hot electrons that become trapped and undergo refluxing within the target sheath fields. These conditions enabled the differentiation of atomic physics models of ionization potential depression in high-energy-density environments.

Reproducible Spectrum and Hyperspectrum Data Analysis Using NeXL.

NeXL is a collection of Julia language packages (libraries) for X-ray microanalysis data processing. NeXLCore provides basic atomic and X-ray physics data and models including support for microanalysis-related data types for materials and k-ratios. NeXLMatrixCorrection provides algorithms for matrix correction and iteration. NeXLSpectrum provides utilities and tools for energy-dispersive X-ray spectrum and hyperspectrum analysis including display, manipulation, and fitting. NeXL is integrated with the Julia language infrastructure. NeXL builds on the Gadfly plotting library and the DataFrames tabular data library. When combined with the DrWatson package, NeXL can provide a highly reproducible environment in which to process microanalysis data. Data availability and reproducible data analysis are two keys to scientific reproducibility. Not only should readers of journal articles have access to the data, they should also be able to reproduce the analysis steps that take the data to final results. This paper will both discuss the NeXL framework and provide examples of how it can used for reproducible data analysis.

Measuring the oscillator strength of intercombination lines of helium-like V ions in a laser-produced-plasma

We present results of measurements of the oscillator strength of intercombination lines of He-like Vanadium ions in high energy density (HED) laser-produced-plasmas and compare them with the simulations from commonly used codes and data from the NIST database. Whilst not yet sufficiently accurate to constrain different trusted atomic-physics models for the particular system studied, our results are in agreement with the available data within experimental error bars, yet differ from cruder approximations of the oscillator strength used in certain atomic-kinetics packages, suggesting that this general method could be further extended to be used as a measurement of the oscillator strength of additional atomic transitions under the extreme conditions that are achieved in HED experiments.

Monochromatic 2DKαEmission Images Revealing Short-Pulse Laser Isochoric Heating Mechanism

The rapid heating of a thin titanium foil by a high intensity, subpicosecond laser is studied by using a 2D narrow-band x-ray imaging and x-ray spectroscopy. A novel monochromatic imaging diagnostic tuned to 4.51keV Ti Kα was used to successfully visualize a significantly ionized area (⟨Z⟩>17±1) of the solid density plasma to be within a ∼35 μm diameter spot in the transverse direction and 2 μm in depth. The measurements and a 2D collisional particle-in-cell simulation reveal that, in the fast isochoric heating of solid foil by an intense laser light, such a high ionization state in solid titanium is achieved by thermal diffusion from the hot preplasma in a few picoseconds after the pulse ends. The shift of Kα and formation of a missing Kα cannot be explained with the present atomic physics model. The measured Kα image is reproduced only when a phenomenological model for the Kα shift with a threshold ionization of ⟨Z⟩=17 is included. This work reveals how the ionization state and electron temperature of the isochorically heated nonequilibrium plasma are independently increased.

Validating Continuum Lowering Models via Multi-Wavelength Measurements of Integrated X-ray Emission

X-ray emission spectroscopy is a well-established technique used to study continuum lowering in dense plasmas. It relies on accurate atomic physics models to robustly reproduce high-resolution emission spectra, and depends on our ability to identify spectroscopic signatures such as emission lines or ionization edges of individual charge states within the plasma. Here we describe a method that forgoes these requirements, enabling the validation of different continuum lowering models based solely on the total intensity of plasma emission in systems driven by narrow-bandwidth x-ray pulses across a range of wavelengths. The method is tested on published Al spectroscopy data and applied to the new case of solid-density partially-ionized Fe plasmas, where extracting ionization edges directly is precluded by the significant overlap of emission from a wide range of charge states.

Soledge2D‐Eirene simulations of the Pilot‐PSI linear plasma device compared to experimental data

Predictions for the operation of tokamak divertors are reliant on edge plasma simulations typically utilizing a fluid plasma code in combination with a Monte Carlo code for neutral species. Pilot‐PSI is a linear device operating with a cascaded arc plasma source that produces plasmas comparable to those expected in the ITER divertor (Te ∼ 1 eV, ne ∼ 1021 m−3). In this study, plasma discharges in Pilot‐PSI are modelled using the Soledge2D fluid plasma code coupled to the Eirene neutral Monte Carlo code. The plasma is generated using an external source of plasma density and power. These input parameters are tuned in order to match Thomson scattering (TS) measurements close to the cascaded arc source nozzle. The sensitivity of the simulations to different atomic physics models is explored. It is found that elastic collisions between ions and hydrogen molecules have a strong influence on calculated profiles. Without their inclusion, supersonic flow regimes are obtained with M ∼ 2 close to the target plate. Simulation results are compared with experimental findings using TS close to the target and, in the case of Pilot‐PSI, a Langmuir probe embedded in the target. Comparison between experimental trends observed in a background pressure scan and the simulations show that the inclusion of the elastic collision is mandatory for the trends to be reproduced.

Picosecond time-resolved measurements of dense plasma line shifts

Picosecond time-resolved x-ray spectroscopy is used to measure the spectral line shift of the 1s2p-1s^{2} transition in He-like Al ions as a function of the instantaneous plasma conditions. The plasma temperature and density are inferred from the Al He_{α} complex using a nonlocal-thermodynamic-equilibrium atomic physics model. The experimental spectra show a linearly increasing redshift for electron densities of 1-5×10^{23}cm^{-3}. The measured line shifts are broadly consistent with a generalized analytic line-shift model based on calculations of a self-consistent field ion-sphere model.

Low-energyR-matrix fits for theLi6(d,α)He4Sfactor

Background: The information about the 6Li(d,a)4He reaction rates of the astrophysical interest can be obtained by extrapolating direct data to the lower energies, or by indirect methods. The indirect Trojan Horse method, as well as various R-matrix and polynomial fits to direct data, estimate the electron screening energies much larger than the adiabatic limit. Calculations that include the subthreshold resonance estimate smaller screening energies. Purpose: Obtain the 6Li(d,a)4He reaction R-matrix parameters and the astrophysical S factor for the energies relevant to the stellar plasmas by fitting the R-matrix formulas for the subthreshold resonances to the S factor data above 60 keV. Methods: The bare S factor is calculated using the single and the two-level R-matrix formulas for the closest to the threshold 0+ and 2+ subthreshold states at 22.2, 20.2 and 20.1 MeV. The electron screening potential Ue is then obtained by fitting it as a single parameter to the low energy data. Results: The low energy S factor is dominated by the 2+ subthreshold resonance at 22.2 MeV. The influence of the other two subthreshold states is small. R-matrix fits result in the electron screening that is smaller than the adiabatic value. Neglecting the electron screening above 60 keV reduces the electron screening potential significantly. Calculations show a large ambiguity associated with a choice of the initial channel radius. Conclusions: The R matrix fits do not show a significantly larger Ue than predicted by the atomic physics models. The R-matrix best fit produces Ue=149.5 eV and Sb(0)=21.7 MeV b.

Modelling of non-LTE atomic physics processes in hot dense plasmas during the interaction with an intense short pulse laser

The implicit 2D3V particle-in-cell (PIC) code developed to study the interaction of intense lasers with matter (Petrov and Davis 2008 Comput. Phys. Commun. 179 868–80; 2011 Phys. Plasmas 18 073102) has been extended to include atomic physics under extreme energy density conditions. The atomic physics model is applied to aluminium. Each ionization stage contains two levels: one ground and one lumped excited state, for which various atomic physics processes such as optical field ionization, collisional ionization, excitation, de-excitation and radiative decay describe the population density. Two-dimensional PIC simulations have been carried out for laser pulses with peak intensity 1 × 1020 W cm−2, pulse duration 60 fs, spot size 3 µm and energy 0.75 J interacting with ultrathin (0.2 µm) Al foil. Radiation emitted during the laser–target interaction is computed by accounting for both bound–bound transitions and bremsstrahlung radiation. We demonstrate that the radiation signature of laser-produced plasma can be used as a complementary tool to other diagnostic techniques used in laser–plasma interactions. Finally, results from the PIC model are compared to equilibrium calculations (Maxwell–Boltzmann and Saha). In the early stages of laser–plasma interactions (<100 fs) the plasma is far from equilibrium and equilibrium models can not be applied with confidence to model the plasma.

Calculation of unit tensor operators using a restricted set of Slater determinants

In this paper we present a new result involving the properties of the Clebsch–Gordan coefficients well-used in atomic physics. We also demonstrate a practical use of this result: a new and simple method of calculation of unit tensor operators of multi-electron atoms while working within the Slater–Condon scheme. This results in a significant increase in the ease of implementation of multi-electron atomic physics models, and we discuss the computational complexity of the resulting algorithm.

Photometric and Thermal Cross-calibration of Solar EUV Instruments

We present an assessment of the accuracy of the calibration measurements and atomic physics models that go into calculating the SDO/AIA response as a function of wavelength and temperature. The wavelength response is tested by convolving SDO/EVE and {\it Hinode}/EIS spectral data with the AIA effective area functions and comparing the predictions with AIA observations. For most channels, the AIA intensities summed over the disk agree with the corresponding measurements derived from the current Version (V2) of the EVE data to within the estimated 25% calibration error. This agreement indicates that the AIA effective areas are generally stable in time. The AIA 304 \AA\ channel, however, does show degradation by a factor of almost 3 from May 2010 through September 2011, when the throughput apparently reached a minimum. We also find some inconsistencies in the 335 \AA\ passband, possibly due to higher-order contamination of the EVE data. The intensities in the AIA 193 \AA\ channel agree to within the uncertainties with the corresponding measurements from EIS full CCD observations. Analysis of high-resolution X-ray spectra of the solar-like corona of Procyon, and of EVE spectra, allows us to investigate the accuracy and completeness of the CHIANTI database in the AIA shorter wavelength passbands. We find that in the 94 \AA\ channel, the spectral model significantly underestimates the plasma emission owing to a multitude of missing lines. We derive an empirical correction for the AIA temperature responses by performing differential emission measure (DEM) inversion on a broad set of EVE spectra and adjusting the AIA response functions so that the count rates predicted by the full-disk DEMs match the observations.

Spectral modeling of supernova remnants

We report on recent efforts to generate high quality, self-consistent atomic physics models for L-shell ion stages for iron and the use of these data in collisional-radiative modeling of X-ray spectra of supernova remnants. As a specific example, we present comparisons between observed and theoretical X-ray spectra produced by Tycho's supernova remnant.

Collisional particle-in-cell modeling for energy transport accompanied by atomic processes in dense plasmas

Fully relativistic collisional Particle-in-Cell (PIC) code, PICLS, has been developed to study extreme energy density conditions produced in intense laser-solid interaction. Recent extensions to PICLS, such as the implementation of dynamic ionization, binary collisions in a partially ionized plasma, and radiative losses, enhance the efficacy of simulating intense laser plasma interaction and subsequent energy transport in resistive media. Different ionization models are introduced and benchmarked against each other to check the suitability of the model. The atomic physics models are critical to determine the energy deposition and transport in dense plasmas, especially when they consist of high Z (atomic number) materials. Finally we demonstrate the electron transport simulations to show the importance of target material on fast electron dynamics.

Direct, spectroscopic measurement of electric fields in a plasma-RF antenna interaction region in Tore Supra

Balmer-series spectral line profiles of deuterium emission near a lower-hybrid (3.7 GHz) wave, high power (1–4 MW) launcher were measured with high-spectral resolution in the Tore Supra tokamak and fitted to an atomic physics model which includes both Zeeman and dynamic Stark effects. The magnetic field is static and the electric field is assumed to be monochromatic at 3.7 GHz. The determined strength and direction of the high-frequency electric field is found to be in good agreement with the results of a simulation that computes the propagation of these lower hybrid waves into the plasma in the region around the launch antenna and specifically in the region of estimated peak emission contributing to the measurement. This agreement indicates feasibility for the use of dynamic Stark effect spectroscopy to study interaction at the plasma antenna interactions in a fusion plasma environment.

Multi-keV X-ray sources from metal-lined cylindrical hohlraums

In 2009 a series of metal-lined hohlraums were tested on the Omega laser facility. The main aims of the campaign were to improve our understanding of the multi-keV energy production and our capability to numerically reproduce the measured conversion efficiencies (CE's). Two studies have been primarily planned: the effect of the metallic plasma mean ionization states and that of hydrodynamics. Six targets were experimented for which the metallic materials (titanium, copper, germanium), the cavity diameter, and the irradiation energy were varied. Here we compare experimental and calculated results. The numerical simulations are performed with the 2D hydro-radiative code FCI2. For all the cavities, the measured multi-keV x-ray powers versus time are qualitatively well reproduced by the simulations, indicating that hohlraum hydrodynamics seems to be well calculated. But we have an underestimation by a factor of ∼2 for the calculated CEs versus experimental values for titanium and copper hohlraums. By contrast there is a good agreement between measurements and calculations for the germanium hohlraum. To explain these results, we have calculated off-line integrated emissivities for couples of (ρ, Te) values contributing to the multi-keV production with several non-local-thermal-equilibrium (NLTE) atomic physics models.

Coupling of detailed configuration kinetics and hydrodynamics in materials submitted to x-ray free-electron-laser irradiation

We describe a model for the study of the interaction of short x-ray free-electron laser (XFEL) pulses with matter. Hydrodynamics is solved in one-dimensional planar geometry together with XFEL energy deposition, transport by thermal conduction and electron-ion energy exchange. Along with XFEL energy deposition, a proper detailed configuration accounting atomic physics model has been implemented in line with the calculations. Simulations typical of current XFEL conditions of irradiation are presented and discussed. Finally, the corresponding spectral emission of this XFEL-heated matter is calculated with the unresolved transition array formalism.

Multi-keV x-ray sources from metal-lined cylindrical hohlraums

As multi-keV x-ray sources, plastic hohlraums with inner walls coated with titanium, copper, and germanium have been fired on Omega in September 2009. For all the targets, the measured and calculated multi-keV x-ray power time histories are in a good qualitative agreement. In the same irradiation conditions, measured multi-keV x-ray conversion rates are ∼6%-8% for titanium, ∼2% for copper, and ∼0.5% for germanium. For titanium and copper hohlraums, the measured conversion rates are about two times higher than those given by hydroradiative computations. Conversely, for the germanium hohlraum, a rather good agreement is found between measured and computed conversion rates. To explain these findings, multi-keV integrated emissivities calculated with RADIOM [M. Busquet, Phys. Fluids 85, 4191 (1993)], the nonlocal-thermal-equilibrium atomic physics model used in our computations, have been compared to emissivities obtained from different other models. These comparisons provide an attractive way to explain the discrepancies between experimental and calculated quantitative results.

Stimulated Raman scatter analyses of experiments conducted at the National Ignition Facility

Recent experiments conducted at the National Ignition Facility achieved two main goals: providing radiation drive and symmetry suitable for subsequent ignition experiments. Of the many diagnostics fielded, one provided a time-resolved wavelength spectrum of light reflected from the target by stimulated Raman scatter (SRS). SRS occurs when incident light reflects off self-generated electron plasma waves. Analyses indicate that synthetic SRS spectra better match those of experiments when an atomic physics model with greater emissivity is utilized in target modeling, along with less inhibited electron transport (higher flux, with, ideally, nonlocal electron transport). With these models, SRS occurs in a target region where nearest-neighbor quads of laser beams significantly overlap the diagnosed quad. This increases SRS gain at lower density (lower wavelength), a feature consistent with experimental results. Inclusion of this effect of multiple quads sharing a reflected SRS light wave has resulted in improved capabilities used to successfully predict (preshot) the SRS spectrum from the first target driven with 1.25 MJ of laser energy. Additional resonant amplification of SRS light in the overlap intensity region is demonstrated in beam propagation simulations. Such effects will be reduced in a target optimized for these less dense and cooler plasma conditions.