A study of the contribution of doubly excited ionic states to the properties of hot dense high-Z plasmas

The role of two-electron processes, i.e. dielectronic recombination and autoionization, in the ionization balance and X-ray emission of hot dense plasmas composed of various high-Z materials is explored. Tungsten, gold, lead and uranium are considered. It is shown that the average ion charge and the high-energy emissivity are both sensitive to the dielectronic recombination rate. A systematic study demonstrates the degree of this sensitivity. It is found that the complete neglect of these 2-electron processes introduces a large error but once included, the key physical properties are quite insensitive to the rate over the important 2–3 keV temperature range. The high-energy emissivity depends strongly on temperature, peaking at conditions corresponding to a closed shell system, and on the square of the electron density, as for a coronal system.     

The effects of ionization potential depression on the spectra emitted by hot dense aluminium plasmas

Recent experiments at the Linac Coherent Light Source (LCLS) X-ray Free-Electron-Laser (FEL) have demonstrated that the standard model used for simulating ionization potential depression (IPD) in a plasma (the Stewart–Pyatt (SP) model, J.C. Stewart and K.D. Pyatt Jr., Astrophysical Journal 144 (1966) 1203) considerably underestimates the degree of IPD in a solid density aluminium plasma at temperatures up to 200 eV. In contrast, good agreement with the experimental data was found by use of a modified Ecker–Kröll (mEK) model (G. Ecker and W. Kröll, Physics of Fluids 6 (1963) 62–69). We present here detailed simulations, using the FLYCHK code, of the predicted spectra from hot dense, hydrogenic and helium-like aluminium plasmas ranging in densities from 0.1 to 4 times solid density, and at temperatures up to 1000 eV. Importantly, we find that the greater IPDs predicted by the mEK model result in the loss of the n = 3 states for the hydrogenic ions for all densities above ≈0.8 times solid density, and for the helium-like ions above ≈0.65 solid density. Therefore, we posit that if the mEK model holds at these higher temperatures, the temperature of solid density highly-charged aluminium plasmas cannot be determined by using spectral features associated with the n = 3 principal quantum number, and propose a re-evaluation of previous experimental data where high densities have been inferred from the spectra, and the SP model has been used.     

Multi-electron-recombination rates estimated within dense plasmas

We investigate the rates for multielectron recombination within a dense plasma with Maxwellian electron energy distribution function. We find that these rates can be high within dense plasmas, and they should be treated in the simulations of the plasmas created by intense radiation, in particular for plasmas created by intense VUV radiation from free-electron-laser (FEL), or for modeling the inertial confinement fusion (ICF) plasmas.     

Equation of state of dense plasmas using a screened-hydrogenic model with ℓ-splitting

We present a self-consistent model based on a nonrelativistic screened-hydrogenic model with ℓ-splitting to calculate the equation of state of matter in local thermodynamic equilibrium. We take into account the quantum subshell effect to go beyond the simple semiclassical and statistical Thomas–Fermi approach to obtain the electronic properties. Arbitrary degeneracy is allowed for the free electrons. Pressure ionization mechanism, which plays a key role in the present ionization-equilibrium model, is carefully described. Ion properties and cold curve are determined using the QEOS multiphase equation of state. The whole model is fast, robust, and reasonably accurate over a wide range of temperatures and densities.     

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.     

Electron scattering in hot/warm plasmas

Electrical and thermal conductivities are presented for aluminum, iron and copper plasmas at various temperatures, and for gold between 15,000 and 30,000 K. The calculations are based on the continuum wave functions computed in the potential of the temperature and density dependent self-consistent ‘average atom’ (AA) model of the plasma. The cross-sections are calculated by using the phase shifts of the continuum electron wave functions and also in the Born approximation. We show the combined effect of the thermal and radiative transport on the effective Rosseland mean opacities at temperatures from 1 to 1000 eV. Comparisons with low temperature experimental data are also presented.     

Density effects in plasmas: Detailed atomic calculations and analytical expressions

In warm dense plasmas, the free-electron and ion spatial distribution may strongly affect atomic structure. To account for such effects we have implemented a potential correction based on the uniform electron gas model in the Flexible Atomic Code (FAC). This code has been applied to obtain energies, wave-functions and radiative rates modified by the plasma environment. In hydrogen-like ions, these numerical results have been successfully compared to an analytical calculation based on first-order perturbation theory. In the case of multi-electron ions, we observe level crossings in agreement with another recent model calculation.     

The reduced detailed configuration accounting (RDCA) model for NLTE plasma spectral calculations

The purpose of this work is to continue development of a model to provide a fast and accurate in-line NLTE capability for calculating plasma spectral properties in large-scale radiation-transport hydrodynamic simulations. A method has recently been developed to transform the large detailed atomic models into very small models that can be used for fast in-line calculations. The reduced model is more accurate than the average-atom models conventionally used in such simulations. In the present work, spectra calculated with the reduced model are compared to the original detailed model and the average-atom model. The spectra of iron and gold plasmas under various plasma conditions are compared.     

Aluminium Lyman-beta satellite emission in non-Maxwellian dense laser produced plasmas

High-energy decay channels of the Al Lyman-β satellite have been observed in X-ray emission from highly ionized plasma jets created by intense laser irradiation of aluminium foil targets. Atomic structure calculations show that the Lyman β satellite emission consists from six emission groups close to the He-like Al 1s²-1s4p (He_γ) and 1s²-1s5p (He_δ) resonance lines. This provides new possibilities for space resolved analysis of high density plasmas. Non-Maxwellian simulations of the plasma emission carried out with the MARIA code demonstrate that the intensity ratios of the Lyman-β satellites and the He_γ and He_δ resonance lines are very sensitive to the bulk electron temperature. In contrast to standard diagnostic methods, parameter studies show that this bulk electron diagnostics is practically unaffected by suprathermal electrons having less than 10% of the bulk electron density.     

Thomson scattering in dense plasmas with density and temperature gradients

Collective X-ray Thomson scattering has become a versatile tool for the diagnostics of dense plasmas. Assuming homogeneous density and temperature throughout the target sample, these parameters can be determined directly from the plasmon dispersion and the ratio of plasmon amplitudes via detailed balance. In inhomogeneous media, the scattering signal is an average of the density and temperature dependent scattering cross-section weighted with the density and temperature profiles. We analyse Thomson scattering spectra in the XUV range from near solid density hydrogen targets generated by free electron laser radiation. The influence of plasma inhomogeneities on the scattering spectrum is investigated by comparing density and temperature averaged scattering signals to calculations assuming homogeneous targets. We find discrepancies larger than 10% between the mean electron density and the effective density as well as between the mean temperature and the effective temperature.     

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.     

A thermodynamical model of conductivity dispersion in plasmas and semiconductors

Summary In this paper, we first introduce a relation between the kinetic energy and the relaxation time, given by the Arrhenius equation, into the electrical conductivity equation of plasmas and semiconductors. Second, we investigate mathematically the change of the conductivity in the frequency and the time domains, and the nature of the distribution of relaxation times, of this new model of conductivity dispersion.     

A Configurationally-Resolved-Super-Transition-Arrays method for calculation of the spectral absorption coefficient in hot plasmas

A new method, ‘Configurationally-Resolved-Super-Transition-Arrays’, for calculation of the spectral absorption coefficient in hot plasmas is presented. In the new method, the spectrum of each Super-Transition-Array is evaluated as the Fourier transform of a single Complex Pseudo Partition Function, which represents the exact analytical sum of the contributions of all constituting unresolved transition arrays sharing the same set of one-electron solutions. Thus, in the new method, the spectrum of each Super-Transition-Array is resolved down to the level of the (unresolved) transition arrays. It is shown that the corresponding spectrum, evaluated by the traditional Super-Transition-Arrays (STA) method [14], is just the coarse-grained Gaussian approximation of the Configurationally-Resolved-Super-Transition-Array. A new computer program is presented, capable of evaluating the absorption coefficient by both the new configurationally resolved and the traditional Gaussian Super-Transition-Arrays methods. A numerical example of gold at temperature 1 keV and density 0.5 gr/cm³, is presented, demonstrating the simplicity, efficiency and accuracy of the new method.     

Stopping power modeling in warm and hot dense matter

A model is presented to calculate the stopping power of ions propagating in dense matter. Comparisons with experiment in the cold dense regime are presented and discussed. Further, we present results from the warm dense matter regime and the field of high energy density physics.     

Thermodynamic conditions of shock Hugoniot curves in hot dense matter

We use a self-consistent model combining the Quotidian Equation Of State and a nonrelativistic screened-hydrogenic model with ?-splitting to study the thermodynamic conditions encountered along shock Hugoniot curves. We focus on the maximum compression ratio reached on shock Hugoniot curves for simple elements that are solid at normal temperature and pressure. Electron shell effect and pressure ionization can have a strong impact on the results. Numerical calculations are presented and discussed. Some of the physical points addressed in this work could be tested experimentally when the National Ignition Facility laser in the USA attains full power or when the Laser Mégajoule in France comes online.     

Critical datasets for benchmarking atomic codes: Calibrated line intensities emitted by well-diagnosed solar plasmas

The accuracy of available spectral codes is dependent on the quality of the atomic data and transition rates that they include, and can only be tested by benchmarking predicted line emissivities with observations from plasmas whose physical properties are known with precision. In the present work we describe a few high-resolution spectra emitted by solar flare plasmas under condition of ionization equilibrium, and one quiet Sun off-disk region spectrum, and we propose these datasets as benchmarks for the assessment of the accuracy of existing spectral codes in the 1.84–1.90 Å and 3.17–3.22 Å X-ray ranges and in the 500–1600 Å far ultraviolet range.     

Thermodynamic model of a dense fluid

In this paper we derive an approximate equation of state of a dense fluid in which the thermal pressure is completely determined by the pressure dependence of the volume at 0 ° K. We also consider some generalizations (which take into account the attractive forces of the atoms and the presence of mixtures).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 119–122, January–February, 1971.