This report will describe an improved computer code for two-photon opacity. The new code incorporates many recent advances and is ready to start to face the experiments. It incorporates the difficult mathematical techniques for handling free states and free-free matrix elements.
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Physical Review Letters
We report on the first accurate validation of low-Z ion-stopping formalisms in the regime ranging from low-velocity ion stopping - through the Bragg peak - to high-velocity ion stopping in well-characterized high-energy-density plasmas. These measurements were executed at electron temperatures and number densities in the range of 1.4-2.8 keV and 4×1023-8×1023 cm-3, respectively. For these conditions, it is experimentally demonstrated that the Brown-Preston-Singleton formalism provides a better description of the ion stopping than other formalisms around the Bragg peak, except for the ion stopping at vi∼0.3vth, where the Brown-Preston-Singleton formalism significantly underpredicts the observation. It is postulated that the inclusion of nuclear-elastic scattering, and possibly coupled modes of the plasma ions, in the modeling of the ion-ion interaction may explain the discrepancy of ∼20% at this velocity, which would have an impact on our understanding of the alpha energy deposition and heating of the fuel ions, and thus reduce the ignition threshold in an ignition experiment.
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Atoms
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.
Physics of Plasmas
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.