Super Transition Array Research Articles

Monte Carlo Simulation of Opacities of Hot and Dense Au Plasmain the Unresolved Transition Array Approximation

The opacity, and its Planck and Rosseland mean values, of the hotand dense Au plasma in local thermodynamics equilibrium are studied bythe Monte Carlo method based on the unresolved transition array (UTA)approximation. The average ion model and the Saha equation are used todetermine the atomic level populations. The result gives a moredetailed structure for frequency-dependent opacity than the popularlyused super transition array or UTA in the photon energy range of 500 eVto 2000 eV. The Monte Carlo method can give a result better than thatof the UTA, with almost the same computation effort.

Recent developments in atomic physics for the simulation of hot plasmas

Simulations of plasmas in which atoms are not completely stripped require atomic data, like average charge, ionization energies, and radiative properties (emissivity, opacity). These depend on populations of energy levels. The basic framework for obtaining the latter is the collisional radiative model (CRM), which bridges the gap between the low-density Corona Equilibrium (CE) and Local Thermodynamic Equilibrium (LTE). However, for nearly all but the simplest ions, the number of relevant bound states and cross sections is prohibitive. In this review we summarize some recent methods for handling complex ions: By focusing on an exact evaluation of relevant information and ignoring unobservable features, unresolved transition arrays (UTA) are obtained. The supertransition arrays (STA) model combines many UTAs in LTE. The STA code was recently extended to a non-LTE CRM called SCROLL. Using these models could improve radiation simulation in hot plasmas, even for simple spectra.

Analysis of the M-shell spectra emitted by a short-pulse laser-created tantalum plasma

The spectrum of tantalum emitted by a subpicosecond laser-created plasma, was recorded in the regions of the 3d-5f, 3d-4f, and 3d-4p transitions. The main difference with a nanosecond laser-created plasma spectrum is a broad understructure appearing under the 3d-5f transitions. An interpretation of this feature as a density effect is proposed. The supertransition array model is used for interpreting the spectrum, assuming local thermodynamic equilibrium (LTE) at some effective temperature. An interpretation of the 3d-4f spectrum using the more detailed unresolved transition array formalism, which does not assume LTE, is also proposed. Fitted contributions of the different ionic species differ slightly from the LTE-predicted values.

Unresolved Spectral Structures Emitted From Heavy Atom Plasmas Produced by Short Pulse Laser

Spectra of rare earth elements emitted from ultra short pulse laser produced plasma were recorded using simultaneously high and low resolution, spectrometers. A study of the broad band emission of the Δn = 1 transitions in highly ionized Ba and Sm plasma showed that this band is completely unresolved. The spectra were analyzed using the LTE based on super-transition array (STA) model. The theory reconstructs the entire Ba spectrum using a single temperature and density, whereas for Sm the discrepancies between the theory and experiment are not reconcilable. The agreement in the Ba case is attributed to the fact that BaF2 target is transparent to the laser's prepulse effects, producing a homogeneous dense plasma, whereas for Sm the dilute plasma created by the prepulse is far from LTE. The obtained results posses a significant implication to the applicability of the STA model, in particular for calculations of opacities and conversion of laser light to x-rays.

Effect of configuration interaction on shift widths and intensity redistribution of transition arrays

Opacity calculations are generally restricted to single configurations approximation with no configuration interaction (CI). The theory for the inclusion of the CI effect on intensity distribution on transition arrays has recently been developed and added to the supertransition array model. However, in an experiment performed recently at NRL, presented in this work, it became apparent that the global shift and width of transition arrays, due to the CI effect, are significant and must be included in the calculations. This feature was also noticed in an LLNL experiment published recently on iron plasma. In these cases the dominant arrays originate from {Delta}n=0 transitions where this effect is particularly significant. In this work we extend the theory, bypassing the impractical need for matrix diagonalizations, and derive analytic expressions for the CI-corrected array moments including CI shifts, widths, and the adjusted intensity distribution. Examples are presented comparing the theoretical results with detailed calculations and with the experiments. {copyright} {ital 1999} {ital The American Physical Society}

Calculation of plasma transmission spectra using the superconfiguration method with orbital relaxation effects

We describe a program developed at CEA Limeil-Valenton for the calculation of absorption spectra. This program is based on the idea of the Superconfiguration method proposed by Bar-Shalom et al. and implemented in their Super Transition Arrays code (STA). We address several points that we consider as important and new in our approach. Examples of calculated transmission spectra are shown and compared with experimental results. The effect of orbital relaxation in the final superconfiguration on optical transition frequencies is emphasized.

Operator technique for calculating superconfiguration-averaged quantities of atoms in plasmas

An operator technique for performing superconfiguration averages is presented. This technique is applicable in the calculation of local thermodynamic equilibrium (LTE) spectral moments as well as average rates for the various atomic processes in non-LTE collisional radiative models. It is shown that for any moment or rate the configuration average polynomials, in the shell occupation numbers, can be regarded as derivative operators that average over superconfigurations when acting on their corresponding partition functions. The superconfiguration-averaged quantities are obtained as generalized partition functions for which a set of recursion formulas is presented allowing a short calculation path. Using this technique, analytic expressions for thermodynamical quantities, such as internal energy and specific heat, are obtained, taking into account orbital relaxation and first-order energies in the Boltzmann factors. This allows for the supertransition array code to yield accurate and consistent data for the equation of state used in hydrodynamic simulations, in addition to radiative properties.

Photoelectric effect in the super transition array model.

In this work we present the super transition array (STA) approach for calculating the detailed photoelectric spectra under local thermodynamic equilibrium conditions. We define the bound-free STAs and obtain analytic expressions for their moments (total intensity, average energy, and variance). It is shown that the various STAs connected with a specific photoelectron can be combined first, and then integration over the continuum is carried out only once. The various initial superconfigurations give rise to the structure of the photoelectric spectrum near the ionization edges. The details of this structure are gradually revealed by the convergence procedure inherent in the STA model. The efficiency of the method is discussed. Results of a few examples are given in comparison with the average atom method and with detailed term accounting in cases where this approach is possible. \textcopyright{} 1996 The American Physical Society.

The science applications of the high-energy density plasmas created on the Nova laser

Since the late 1970s it has been realized that the laser-heated hohlraums envisioned for indirect drive Inertial Confinement Fusion (ICF) could also serve as ‘‘physics factories’’ by providing a high-energy density environment for the study of a wide variety of physics with important applications. In this review we will describe some of these studies, accomplished in the early 1990s using the Nova laser [J. T. Hunt and D. R. Speck, Opt. Eng. 28, 461 (1989)] at the Lawrence Livermore National Laboratory. They include measuring the opacity of Fe, thus confirming that the OPAL low Z opacity code [C. A. Iglesias and F. J. Rogers, Astrophys. J. 443, 460 (1995)] is quantitatively more accurate than ‘‘standard’’ models, with important astrophysical implications such as modeling the Cepheid variables [F. J. Rogers and C. A. Iglesias, Science 263, 50 (1994)]; measuring the Rosseland mean opacity of Au, confirming the correctness of the ‘‘Super Transition Array’’ (STA) high-Z code [Bar Shalom et al., Phys. Rev. A 40, 3183 (1989)] with important implications for ignition targets designed for the National Ignition Facility (NIF); sophisticated Rayleigh–Taylor and other hydrodynamic turbulence experiments and analysis that serve as a test bed for understanding astrophysical observations such as supernova explosions; using laboratory x-ray lasers for probing high-density ICF plasmas as well as biology; and creating near Gbar pressures [Cauble et al. Phys. Rev. Lett. 70, 2102 (1993)]. Expanded opportunities for such research on the NIF will also be described.

Effect of configuration widths on the spectra of local thermodynamic equilibrium plasmas

We present the extension of the supertransition-array (STA) theory to include configuration widths in the spectra of local thermodynamic equilibrium (LTE) plasmas. Exact analytic expressions for the moments of a STA are given, accounting for the detailed contributions of individual levels within the configurations that belong to a STA. The STA average energy is shifted and an additional term appears in its variance. Various cases are presented, demonstrating the effect of these corrections on the LTE spectrum.

Relation between the super-transition-array method in opacity calculations and the Hartree-Fock approximation at nonzero temperature.

We consider the photoabsorption cross section of dense plasmas in thermodynamic equilibrium. We transform the exact expression of this cross section into a form suitable for the calculation of moments with respect to frequency. We show that the super-transition-array (STA) method, which is successfully applied in opacity calculations, is consistent with the thermal Hartree-Fock approximation. The Hartree-Fock theory justifies the use of the noninteracting partition function inside each superconfiguration, which is an important approximation in the STA method.

Thick winds from Wolf-Rayet stars

When the effective opacity becomes sufficiently great, a qualitatively different type of radiatively driven wind solution appears, in which a high wind thickness and trapping of radiation cause each other in a bootstrap fashion. It is proposed that the thick winds from Wolf-Rayet stars can be understood in this manner. Opacity computations using the method of super transition arrays (STA) are presented that show that outflows from WR stars can attain the needed opacities.

Modeling of Nova indirect drive Rayleigh–Taylor experiments

The growth due to the Rayleigh–Taylor (RT) instability of single-wavelength surface perturbations on planar foils of brominated CH [CH(Br)] and fluorosilicone (FS) was measured. The foils were accelerated by x-ray ablation with temporally shaped drive pulses. A range of initial amplitudes (a0) and wavelengths (λ) have been used. This paper focuses upon foils with small a0/λ, which exhibit substantial growth in the linear regime, and are most sensitive to the calculated growth rate. The CH(Br) foils exhibit slower RT perturbation growth because opacity differences result in a larger ablation velocity and a longer density scale length than for FS. Tabulated opacities from detailed atomic models, OPAL [Astrophys. J. 397, 717 (1992)] and super transition array (STA) [Phys. Rev. A 40, 3183 (1989)] were employed. Unlike previous simulations which employed the average atom (XSN) opacity treatment, parameter adjustments to fit experimental data no longer appear necessary. Nonlocal thermodynamic equilibrium (NLTE) effects do not appear to be important. Other variables which may affect the modeling, such as changes of the equation of state and radiation drive spectrum, were also examined. The current calculational model, which incorporates physically justified choices for these calculational ingredients, agrees with the Nova single wavelength RT perturbation growth data.

Configuration interaction in LTE spectra of heavy elements

We present a method for including the effects of configuration interaction (CI) between relativistic subconfigurations of an electron configuration in the calculation of emission and absorption spectra of plasmas in local thermodynamic equilibrium (LTE). Analytical expressions for the correction to the intensities, owing to CI, of an unresolved transition array (UTA) and of a supertransition array (STA) are obtained when the correction is small compared to the spin-orbit splitting, bypassing the need to diagonalize energy matrices. These expressions serve as working formulas in the STA model and, in addition, reveal a priori the conditions under which CI effects are significant. Examples of the effect are presented.

Fractional parentage coefficients for equivalent f shell electrons

The partially resolved transition array model for radiative transitions between ordinary electronic configurations is extended to the super configuration approach. The specific application incorporates intermediate coupling effects into transition arrays to describe the transition from LS to JJ coupling without the ad hoc approximations introduced in past formulations. More generally, the extended concept permits stepwise refinement of the super transition array method towards the line-by-line limit in ordinary configurations. Thus, the formalism forms a framework for a hybrid scheme to combine detailed line accounting and statistical methods.