Frank Graziani

Frontiers and challenges in warm dense matter

Carsten A. Ullrich, Time-dependent density-functional theory: features and challenges, with a special view on matter under extreme conditions.- Aurora Pribram-Jones, Stefano Pittalis, E.K.U. Gross, and Kieron Burke, Thermal Density Functional Theory in Context.- Valentin V. Karasiev, Travis Sjostrom, Debajit Chakraborty, James W. Dufty, Keith Runge, Frank E. Harris, and S.B. Trickey, Innovations in Finite-Temperature Density Functionals.- Hannes Schulz and Andreas Gorling, Toward a comprehensive treatment of temperature in electronic structure calculations: Non-zero-temperature Hartree-Fock and exact-exchange Kohn-Sham methods.- Ethan Brown, Miguel A Morales, Carlo Pierleoni, and David Ceperley, Quantum Monte Carlo techniques and applications for warm dense matter.- D. Saumon, C.E. Starrett, J.A. Anta, W. Daughton and G. Chabrier, The structure of warm dense matter modeled with an average atom model with ion-ion correlations.- Carsten Fortmann, Dynamical structure factor in High Energy Density Plasmas and application to X-Ray Thomson Scattering.- Winfried Lorenzen, Andreas Becker, and Ronald Redmer, Progress in Warm Dense Matter and Planetary Physics.- Tomorr Haxhimali and Robert E. Rudd, Diffusivity of Mixtures in Warm Dense Matter Regime.- Paul E. Grabowski, A Review of Wave Packet Molecular Dynamics.

Molecular dynamics simulations of temperature equilibration in dense hydrogen.

The temperature equilibration rate between electrons and protons in dense hydrogen has been calculated with molecular dynamics simulations for temperatures between 10 and 600eV and densities between 10;{20}cm;{-3}to10;{24}cm;{-3} . Careful attention has been devoted to convergence of the simulations, including the role of semiclassical potentials. We find that for Coulomb logarithms L greater, similar1 , a model by Gericke-Murillo-Schlanges (GMS) [D. O. Gericke, Phys. Rev. E 65, 036418 (2002)] based on a T -matrix method and the approach by Brown-Preston-Singleton [L. S. Brown, Phys. Rep. 410, 237 (2005)] agrees with the simulation data to within the error bars of the simulation. For smaller Coulomb logarithms, the GMS model is consistent with the simulation results. Landau-Spitzer models are consistent with the simulation data for L>4 .

Quantum hydrodynamics for plasmas - a Thomas-Fermi theory perspective

The idea to describe quantum systems within a hydrodynamic framework (quantum hydrodynamics, QHD) goes back to Madelung and Bohm. While such a description is formally exact for a single particle, more recently the concept has been applied to many-particle systems by Manfredi and Haas [Phys. Rev. B 64, 075316 (2001)] and received high popularity in parts of the quantum plasma community. Thereby, often the applicability limits of these equations are ignored, giving rise to unphysical predictions. Here we demonstrate that modified QHD equations for plasmas can be derived from Thomas-Fermi theory including gradient corrections. This puts QHD on firm grounds. At the same time this derivation yields a different prefactor, γ = (D – 2/3D), in front of the quantum (Bohm) potential which depends on the system dimensionality D. Our approach allows one to identify the limitations of QHD and to outline systematic improvements. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Benchmarks and models for time-dependent grey radiation transport with material temperature in binary stochastic media

Abstract We present benchmark calculations for radiation transport coupled to a material temperature equation in a slab geometry binary random media. The mixing statistics are taken to be homogeneous Markov statistics where the material chunk sizes are described by Poisson distribution functions. The material opacities are taken to be constant. Benchmark values for time evolution of the ensemble average values of material temperature energy density and radiation transmission are computed via a Monte Carlo-type method. These benchmarks are used as a basis for comparison with three other approximate methods of solution. One of these approximate methods is simple atomic mix which is seen to consistently over absorb resulting in lower steady-state radiation transmission and material temperature. The second approximate model is an adaptation of what is commonly called the Levermore–Pomraning model and which we refer to as the standard model. It is shown to consistently under absorb resulting in higher steady-state radiation transmission and material temperature. We show that recasting the temperature coupling as a type of effective scattering can be useful in formulating the third approximate model, an adaptation of a model due to Su and Pomraning which attempts to account for the effects of scattering in a stochastic context. We show this last adaptation shows consistent improvement over both the atomic mix and standard models.

Molecular dynamic simulations with radiation

Hot dense radiative (HDR) plasmas common to inertial confinement fusion (ICF) and stellar interiors have high temperature (a few hundred eV to tens of keV), high density (tens to hundreds of g/cc) and high pressure (hundreds of Megabars to thousands of Gigabars). Typically, such plasmas undergo collisional, radiative, atomic and possibly thermonuclear processes. In order to describe HDR plasmas, computational physicists in ICF and astrophysics use atomic-scale microphysical models implemented in various simulation codes. Experimental validations of the models used for describing HDR plasmas are difficult to perform. Direct numerical simulation (DNS) of the many-body interactions of plasmas is a promising approach to model validation, but previous work either relies on the collisionless approximation or ignores radiation. We present a first attempt at a new numerical simulation technique to address a currently unsolved problem: the extension of molecular dynamics to collisional plasmas including emission and absorption of radiation. The new technique passes a key test: it relaxes to a blackbody spectrum for a plasma in local thermodynamic equilibrium. This new tool also provides a method for assessing the accuracy of energy and momentum exchange models in hot dense plasmas. As an example, we simulate the evolution of non-equilibrium electron, ion and radiation temperatures for a hydrogen plasma using the new molecular dynamics simulation capability.

Shear viscosity for dense plasmas by equilibrium molecular dynamics in asymmetric Yukawa ionic mixtures

We present molecular dynamics (MD) calculations of shear viscosity for asymmetric mixed plasma for thermodynamic conditions relevant to astrophysical and inertial confinement fusion plasmas. Specifically, we consider mixtures of deuterium and argon at temperatures of 100-500 eV and a number density of 10^{25} ions/cc. The motion of 30,000-120,000 ions is simulated in which the ions interact via the Yukawa (screened Coulomb) potential. The electric field of the electrons is included in this effective interaction; the electrons are not simulated explicitly. Shear viscosity is calculated using the Green-Kubo approach with an integral of the shear stress autocorrelation function, a quantity calculated in the equilibrium MD simulations. We systematically study different mixtures through a series of simulations with increasing fraction of the minority high-Z element (Ar) in the D-Ar plasma mixture. In the more weakly coupled plasmas, at 500 eV and low Ar fractions, results from MD compare very well with Chapman-Enskog kinetic results. In the more strongly coupled plasmas, the kinetic theory does not agree well with the MD results. We develop a simple model that interpolates between classical kinetic theories at weak coupling and the Murillo Yukawa viscosity model at higher coupling. This hybrid kinetics-MD viscosity model agrees well with the MD results over the conditions simulated, ranging from moderately weakly coupled to moderately strongly coupled asymmetric plasma mixtures.

Effects of nonequilibrium particle distributions in deuterium-tritium burning

We investigate the effects of non-equilibrium particle distributions resulting from rapid deuterium-tritium burning in plasmas using a Fokker-Planck code that incorporates small-angle Coulomb scattering, Brehmsstrahlung, Compton scattering, and thermal-nuclear burning. We find that in inertial confinement fusion environments, deviations away from Maxwellian distributions for either deuterium or tritium ions are small and result in 1% changes in the energy production rates. The deuterium and tritium effective temperatures are not equal, but differ by only about 2.5% near the time of peak burn rate. Simulations with high Z (Xe) dopants show that the dopant temperature closely tracks that of the fuel. On the other hand, fusion product ion distributions are highly non-Maxwellian, and careful treatments of energy-exchange between these ions and other particles is important for determining burn rates.

The quantum radiative transfer equation: quantum damping, Kirchoff's Law, and the approach to equilibrium of photons in a quantum plasma

Abstract A method is presented based on the theory of quantum damping, for deriving a self-consistent but approximate form of the quantum transport for photons interacting with a fully ionized electron plasma. Specifically, we propose in this paper a technique for approximately including the effects of a background plasma on a photon distribution function by replacing the influence of the plasma degrees of freedom with quantum fluctuation and damping terms in the radiation transport equation. We consider the Markov limit where the electron relaxation time scale is short compared to the photon relaxation time scale. The result is a quantum Langevin equation for the photon number operator; the quantum radiative transfer equation. A dissipation term appears which is the imaginary part of the dielectric function for an electron gas undergoing electron scattering due to emission and absorption of photons. It depends only on the initial state of the plasma. A quantum noise operator also appears as a result of spontaneous emission of photons from the electron plasma. The thermal expectation value of this noise operator yields the emissivity which is exactly of the form of the Kirchoff–Planck relation. This non-zero thermal expectation value is a direct consequence of a fluctuation–dissipation relation. The fluctuations of the quantum noise operator yield the deviations from the Kirchoff–Planck relation. Using the quantum radiative transfer equation, transient fluctuations in the photon number are computed.

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

Summary form only given. The quantum Lenard-Balescu (QLB) equation provides an accurate description of weakly-couple plasmas. Unlike Landau/Fokker-Planck, the QLB equation is fully convergent and thus requires no input Coulomb logarithm. However, it contains a dielectric function that depends on the distribution, leading to a very complicated integro-differential equation. We present what we believe is the first numerical solution of the quantum Lenard-Balescu equation. We use a spectral expansion in Laguerre polynomials, which gives automatic conservation of particles and energy and enables an accurate integration over the dielectric function. Our method can also be used to solve the Landau/Fokker-Planck equation and we present comparisons with the QLB system for various equilibration problems.

Proposed pushered single shell capsule design for the investigation of mid/high Z mix on the NIF

The CD Mix campaign has given a detailed explination of the mix mechanics in the current ignition capsule designs by investigating the relationship between material mixing, shell-fuel interfaces, and the change in thermonuclear yield given a deuterated layer in the capsule. Alternative ignition scenarios include the use of double shell designs that incorporate high-Z material in the capsule. Simulations are conducted on a proposed capsule platform using the ARES code on a scaled capsule design using a partially reduced glass capsule design. This allows for the inclusion of deuterium on the inner surface of the pusher layer similar to the CD mix experiments. The presence of silicon dioxide allows for the investigation of the influence of higher Z material on the mixing characteristics.