Publications

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Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

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The MagLIF campaign operated by Sandia conducted a total of four shot days in FY17 (one on OMEGA and three on OMEGA-EP) aimed at characterizing the laser heating of underdense plasmas (D2, Ar) at parameters that are relevant to the Magnetized Liner Inertial Fusion (MagLIF) ICF scheme being pursued at Sandia National Laboratories [1] [2]. MagLIF combines fuel preheat, magnetization and pulsed power implosion to significantly relax the implosion velocity and pR required for self-heating. Effective fuel preheat requires coupling several kJ of laser energy into the 10 mm long, underdense (typically ne/nc<0.1) fusion fuel without introducing significant mix. Barriers to achieving this include the presence laser plasma instabilities (LPI) as laser energy is coupled to the initially cold fuel, and the presence of a thin, polyimide laser entrance hole (LEH) foil that the laser must pass through and that can be a significant perturbation.

The burning core of an inertial confinement fusion (ICF) plasma produces bright x-rays at stagnation that can directly diagnose core conditions essential for comparison to simulations and understanding fusion yields. These x-rays also backlight the surrounding shell of warm, dense matter, whose properties are critical to understanding the efficacy of the inertial confinement and global morphology. In this work, we show that the absorption and fluorescence spectra of mid-Z impurities or dopants in the warm dense shell can reveal the optical depth, temperature, and density of the shell and help constrain models of warm, dense matter. This is illustrated by the example of a high-resolution spectrum collected from an ICF plasma with a beryllium shell containing native iron impurities. Lastly, analysis of the iron K-edge provides model-independent diagnostics of the shell density (2.3 × 10²⁴ e/cm³) and temperature (10 eV), while a 12-eV red shift in Kβ and 5-eV blue shift in the K-edge discriminate among models of warm dense matter: Both shifts are well described by a self-consistent field model based on density functional theory but are not fully consistent with isolated-atom models using ad-hoc density effects.

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The recent iron opacity measurements performed at Sandia National Laboratory by Bailey and collaborators have raised questions about the completeness of the physical models normally used to understand partially ionized hot dense plasmas. We describe calculations of two-photon absorption, which is a candidate for the observed extra opacity. Our calculations do not yet match the experiments but show that the two-photon absorption process is strong enough to require careful consideration.

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Iron opacity calculations presently disagree with measurements at an electron temperature of ∼180-195 eV and an electron density of (2-4)×1022cm-3, conditions similar to those at the base of the solar convection zone. The measurements use x rays to volumetrically heat a thin iron sample that is tamped with low-Z materials. The opacity is inferred from spectrally resolved x-ray transmission measurements. Plasma self-emission, tamper attenuation, and temporal and spatial gradients can all potentially cause systematic errors in the measured opacity spectra. In this article we quantitatively evaluate these potential errors with numerical investigations. The analysis exploits computer simulations that were previously found to reproduce the experimentally measured plasma conditions. The simulations, combined with a spectral synthesis model, enable evaluations of individual and combined potential errors in order to estimate their potential effects on the opacity measurement. The results show that the errors considered here do not account for the previously observed model-data discrepancies.

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