Session UI3: High Energy Density Laboratory Plasmas

Ab initio calculations of the equations of state for hydrogen, helium, and water and the relevance to the giant planets

Since the interior structure of giant planets inside or outside our solar system cannot be probed directly by experiments, planetary models have been developed to gain further insight. Such models require accurate equations of state (EOS) for the major components (H, He, and heavier compounds like water) up to extreme thermodynamic conditions (pressures of several ten megabars and temperatures of more than ten thousand degrees Kelvin) [1]. Ab initio methods that combine finite temperature density functional theory (FT-DFT) for the electrons with classical molecular dynamics (MD) for the ions have proven to be a powerful tool to calculate such accurate EOS data. In addition, the FT-DFT-MD also generates structural information, transport and optical properties and, most important, information on phase diagrams and demixing regions. Based on our recently calculated ab initio data for H, He, and water, we derive interior models of Saturn and Jupiter and discuss the role of H-He demixing [2] and of the plasma phase transition in hydrogen on the planetary interiors. We also present new models for Uranus and Neptune which offer conditions to allow the formation of the exotic superionic phase of water [3]. The ab initio data can also be applied in planetary evolution scenarios and dynamo simulations of solar and extrasolar planets.\\[4pt] [1] J. J. Fortney, N. Nettelmann, Space Sci. Rev. 152, 423 (2010)\\[0pt] [2] W. Lorenzen, B. Holst, R. Redmer, Phys. Rev. Lett. 102, 115701 (2009)\\[0pt] [3] M. French, T. R. Mattsson, N. Nettelmann, R. Redmer, Phys. Rev. B 79, 054107 (2009)   

Ab Initio Determination of Thermal Conductivities for Dense Hydrogen and CH Plasmas at ICF conditions

Among the numerous parameters that condition the success of future inertial confinement fusion (ICF) experiments, electronic thermal conductivity plays a central role. It is however poorly known in the hot and dense regime. Most of the models interpolate between weakly coupled regime and strongly degenerated plasmas. They disagree at high densities so that an independent determination is needed. Quantum molecular dynamics has been proved to be a powerful tool to finely study matter in warm dense regime. We will present ab initio calculations of thermal and electrical conductivities for hydrogen at densities between 10 g/cc and 160 g/cc and temperatures up to 800 eV, i.e. thermodynamical conditions relevant to ICF. The ionic structure is obtained using molecular dynamics simulations based on an orbital-free treatment for the electrons. The transport properties were computed using ab initio simulation in the DFT/LDA approximation. The thermal and electrical conductivities are evaluated using Kubo-Greenwood formulation. These calculations are then used to check various analytical models (Hubbard, Lee-More, Ichimaru) widely used in hydrodynamics simulations of ICF capsule implosions. The Lorentz number, which is the ratio between thermal and electrical conductivities, is also computed and compared to the well-known Wiedemann-Franz law in different regimes ranging from the highly degenerated to the kinetic one. Evaluations of electronic transport properties for CH are also presented.   

Measurements of magneto-Rayleigh-Taylor instability growth in solid liners on the 20 MA Z facility

The magneto-Rayleigh-Taylor (MRT) instability is the most important instability for determining whether a cylindrical liner can be compressed to its axis in a relatively intact form, a requirement for achieving the high pressures needed for inertial confinement fusion (ICF) and other high energy-density physics applications. While there are many published RT studies, there are a handful of well-characterized MRT experiments at time scales $>$1 $\mu$s and none for 100 ns z-pinch implosions. Experiments used solid Al liners with outer radii of 3.16 mm and thicknesses of 292 $\mu$m, dimensions similar to magnetically-driven ICF target designs [1]. In most tests the MRT instability was seeded with sinusoidal perturbations ($\lambda$=200, 400 $\mu$m, peak-to-valley amplitudes of 10, 20 $\mu$m, respectively), wavelengths similar to those predicted to dominate near stagnation. Radiographs show the evolution of the MRT instability and the effects of current-induced ablation of mass from the liner surface. Additional Al liner tests used 25-200 $\mu$m wavelengths and flat surfaces. Codes being used to design magnetized liner ICF loads [1] match the features seen except at the smallest scales ($<$50 $\mu$m). Recent experiments used Be liners to enable penetrating radiography using the same 6.151 keV diagnostics and provide an in-flight measurement of the liner density profile.\\[4pt] [1] S.A. Slutz et al., Phys. Plasmas 17, 056303 (2010).   

Magnetic field threshold for thermal plasma formation from an aluminum surface pulsed to multi-megagauss magnetic field

The first measurement of the thermal ionization threshold of a thick-metal surface by pulsed multi-megagauss magnetic field is reported. Whether plasma should form from intensely ohmically heated thick metal has been of interest since at least 1959, when Fowler \textit{et al}. first reported producing fields above 10 MG. Plasma formation from thick metal is uncertain, even for megagauss field, because fresh, cold, high conductivity metal persists within, reducing the electric field, current density, and ohmic heating at the surface. The phase-state of thick metal subjected to ultra-high field has been examined by pulsing Al rods of initial diameter 0.50-2.00 mm to 1.0 MA peak current in 100 ns. Experiments accessed the surface-heating regime, where the magnetic penetration depth is less than the conductor radius, and current flows in a skin layer. Shot hardware with novel electrical contacts mitigated or eliminated the non-thermal precursor plasma produced by electric-field-driven electron avalanche and arcing electrical contacts in earlier experiments. Rod surfaces were examined with time-resolved imaging, visible and EUV radiometry and spectroscopy, and laser shadowgraphy. For magnetic field rise rates from 30-80 MG/$\mu $s, thermal plasma forms from 6061-alloy Al when the surface field reaches the threshold level of 2.2 MG, in qualitative agreement with simulation results by Garanin \textit{et al}. [J. Appl. Mech. Tech. Phys. 46, 153 (2005)] which suggest that a thick Cu surface will ionize when the imposed magnetic field reaches 1.5-3 MG. Measurements of the time-evolution of the surface temperature, Al expansion rate, and ionization state, as functions of applied field, significantly constrain the choice of models used in rad-MHD simulations.   

Kinetic simulations of a deuterium-tritium z pinch with $>$10$^{16}$ neutron yield

Fully kinetic, collisional, and electromagnetic simulations of the time evolution of an imploding z-pinch plasma have been performed as first reported in D. R. Welch, \textit{et al.} [\textit{Phys. Rev. Lett}. \textbf{103}, 255002 (2009)]. Using the implicit particle-in-cell (PIC) code L\textsc{sp,} multi-dimensional (1-3D) simulations of deuterium and deuterium-tritium z-pinches provide insight into the mechanisms of neutron production. The PIC code allows non-Maxwellian particle distributions, simulates finite mean-free-path effects, performs self-consistent calculations of anomalous resistivity, and permits charge separation. At pinch current $I <$ 7 MA, neutron production is dominated by high energy ions driven by instabilities. The instabilities produce a power-law ion-energy distribution function in the distribution tail. At higher currents, roughly half of the neutrons are thermonuclear in origin and follow a $I ^{4}$ neutron yield scaling. High-current, multi-dimension simulations ($>$ 40 MA with $>$ 10$^{16}$ neutron yield) suggest that the fraction of thermonuclear neutrons is not sensitive to $I$, and the strong dependence of neutron yield on current will continue at still higher currents. Scenarios for fusion breakeven and possible ignition will be discussed.