Session 7S - ICF Physics: Simulations and Theory Simulation.
POSTER session, Thursday morning, November 14
Exhibit Hall - Concourse Level, Adam's Mark

We report calculations of the effects of random laser pointing and power balance errors on indirectly driven Nova capsule implosions. Drive asymmetry is calculated with a view factor code, and the implosions are calculated with the HYDRA 3-D radiation hydrodynamics code. Perfect laser power balance and alignment give, with vacuum transport, an intrinsic drive asymmetry dominated by the pole-to-waist variation (Y_2,0 spherical harmonic) and components associated with the laser spots which have an Y_l,m=5 azimuthal variation. Errors in the power balance and pointing between beams introduce a complex combination of spherical harmonics into the radiation drive asymmetry. The low mode perturbations which develop in the capsule are found to be as significant as those caused by the intrinsic azimuthal variation. Large variations in the shape of the fuel region result, making it more vulnerable to other perturbations seeded by surface roughness, which grow at the fuel-pusher interface. When the drive errors are sufficiently large, jets of pusher material form. We examine the impact of the overall drive asymmetry, acting alone or combined with other effects, on Nova capsule performance.

[7S.02] Two-Dimensional Radiation Hydrodynamics with Detailed Equations of State and Opacities

The University of Wisconsin presently models ICF targets and target chambers with the 1-D BUCKY computer code.(J.J. MacFarlane, G.A. Moses, and R.R. Peterson, Univ.\ of Wis.\ Report UWFDM-984 (1995).) Progress on incorporating the BUCKY physics models in the ZEUS-2D two-dimensional radiation-magnetohydrodynamics computer code(J.M. Stone, D. Mihalas, and M.L. Norman, Ap. J. Suppl.) \bf80, 753--845 (1992). will be reported. ZEUS-2D has been modified to use detailed equations of state and opacities, multigroup flux-limited radiation diffusion, and multiple materials. Selected studies of radiation burn-through, heat-pulse propagation, and x-ray emission from hohlraums will be presented. Cylindrically symmetric hohlraums exhibit primarily two-dimensional emission of x rays, with axial jets and conical lobes out the laser entrance holes. This information will be particularly useful for evaluating the response of the chamber wall and diagnostics to high-yield NIF shots.

[7S.03] Anomalous heat transport due to ion acoustic turbulence in laser-produced plasmas

Fokker-Planck simulations which include the return current-induced turbulence from the ion acoustic instability in laser-produced plasmas demonstrate significant modification of the transport phenomena as compared to that defined by Coulomb collisions. The plasma was heated due to the inverse bremsstrahlung absorption of the laser energy and for the first time the combined effect of two phenomena - the electron nonlocality and ion acoustic wave turbulence (IAT) - on the electron energy transport has been studied self-consistently. Electrons have been treated kinetically and coupled to hydrodynamic ions and to IAT in a quasilinear approximation. Ion hydrodynamics included turbulent collision ion heating due to IAT. The nonlocality and instability act constructively to enhance the electron heat flux inhibition. The development of IAT results in steepening of the electron temperature and density profiles, strong ion heating and excitation of broad spectrum of a rather high level (W/n_eT_e\sim 0.1) of the turbulence.

[7S.04] Modeling Lithium Plasma Formation by Laser Ionization Based on Resonance Saturation (LIBORS) And Implications for Extreme-Current Ion Sources

Key issues for light ion beam fusion are decreased ion beam divergence with increased ion beam current density. A satisfactory ion source for these kA/cm^2 beams is essential, and we are studying active lithium sources where an independent energy source is used to pre-form a lithium plasma against the anode. We are developing a comprehensive computer code for investigating lithium plasma formation by laser ionization based on resonance saturation (LIBORS) in the presence of large density gradients. In our computer code, a system of time-dependent rate equations, which couples the detailed atomic model with the external radiation field (laser), is solved self-consistently to predict the rapidly-changing ionization characteristics of the lithium vapor. In particular, time-dependent spectroscopy information will be provided so that the theoretical predictions can be comparied with the results of spectroscopy measurement. Details of the physical model and the preliminary results will be reported.

[7S.05] Nonlinear Laser Filamentation Simulation in 3D

Recent application of our laser filamentation code to high temperature hohlraums (e.g., I = 10^16 W/cm^2, T_e = 10 keV), or channeling experiments where nearly all of the mass is evacuated from a cavity, have motivated the development, and integration into F3d, of a 3D nonlinear eulerian hydrodynamics (Nh3). We have also added a linearized nonlocal thermal heat conduction model, allowing simulation of thermally driven, as well as ponderomotively driven, filamentation, and a 2^nd order wave equation solver.

The specifics of Nh3 and some applications to beam deflection were reported last year. (C. H. Still et al., ``3D Nonlinear Hydrodynamics with Beam Deflection Applications'', APS/DPP, Louisville KY, 6-11 November, 1995.) In this presentation, we will show F3d simulations for high temperature hohlraums where the filamentation gain per speckle is large, when an extremely tight focus in a plasma is achieved (similar to Peter Young's experiments on Janus) (P. E. Young et al., ``Laser beam propagation and channel formation in underdense plasmas'', Phys. of Plasmas, 2) 7 (1995). and in channeling experiments where near vacuum is achieved.

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[7S.06] Particle-in-Cell Simulations of Stimulated Brillouin Scattering in Two and Three Spatial Dimensions.

The results arising from numerical simulations of Stimulated Brillouin Scattering (SBS) in two and three spatial dimensions using HERCULES, a particle ion/adiabatic fluid-electron particle-in cell code(H. X. Vu, J. Comput. Phys.) 124, 417 (1996)., are presented. We compare the results of these simulations against the solutions of a linearized fluid model of SBS in homogeneous plasmas(C. J. McKinstrie, R. Betti, R. E. Giacone, T. Kolber and J. S. Li, Phys. Rev. E) 50, 2182 (1994).. Multidimensional effects on the angular dependance of SBS are studied. The results obtained from numerical simulations are in good agreement with the linear model. Comparisons of beam bending (H. A. Rose, Phys. Plasmas) 3, 1709 (1996). and cross laser beams effects in two and three dimensions will be also presented. \vskip 0.1truein Work performed under the auspices of the US Department of Energy.

[7S.07] ICF3D-Hydro: 3D Parallel Unstructured Mesh Hydrodynamics Code

ICF3D is a three dimensional unstructured mesh, arbitrary Lagrangian-Eulerian (ALE) code to simulate inertial confinement fusion (ICF) plasmas. We describe its hydrodynamic module which discretizes space using discontinuous finite elements and time using an explicit Runge-Kutta scheme. It uses a second order Godunov scheme with a 3D generalization of Van Leer's slope limiting for shock stabilization. ICF3D is written in the object oriented programming language C++. It runs on a variety of computers: uniprocessors, symmetric multiprocessors (SMP) and massively parallel processors (MPP) architectures. We Parallelize using domain decomposition and message passing. A distributed computing environment controls the calculation on a remote computer from a desktop workstation. We present results on problems relevant to ICF target design: shock propagation, Rayleigh-Taylor instabilities and spherical implosions. We also describe parallel scaling obtained on up to 256 processors.

[7S.08] Laser Energy Deposition Model for the ICF3D Code

We have built a laser deposition module for the new ICF physics design code, ICF3D(``3D Unstructured Mesh ALE Hydrodynamics with the Upwind Discontinuous Finite Element Method,'' D. S. Kershaw, M. K. Prasad and M. J. Shaw,'' LLNL Report UCRL-JC-122104, (1995)), being developed at LLNL. The code uses a 3D unstructured grid on which hydrodynamic quantities are represented in terms of discontinuous linear finite elements (hexahedrons, prisms, tetrahedrons or pyramids). Because of the complex mesh geometry and (in general) non-uniform index of refraction (i.e., plasma density), the geometrical-optical ray-tracing problem is quite complicated. To solve it we have developed a grid-cell-face-crossing detection algorithm, an integrator for the ray equations of motion and a path-length calculator that are encapsulated in a C++ class that is used to create ray-bundle objects. Additional classes are being developed for inverse-bremsstrahlung and resonance-absorption heating models. A quasi-optical technique will be used to include diffractive effects. We use the ICF3D Python shell, a very flexible interface that allows command-line invocation of member functions.

[7S.09] HED: An Inertial Confinement Fusion Modelling Code for High Energy Density Simulations

A new code for high energy density (\tt HED) simulation is under construction at LLNL in support of the Advanced Strategic Computing Initiative. This code represents the aggregation of physics modelling techniques developed previously in the \tt ICF3D and \tt FLAG codes into a unified framework for ICF computational modelling and other high energy density applications. The new code exploits object oriented design techniques to support the coexistence of multiple physics algorithms for various subsystems such as hydrodynamics, diffusion, radiation transport, etc. For example, either finite volume or discontinuous finite element hydrodynamcis may be selected. Advanced C++ techniques are used to support efficient execution in the face of replaceable subsystem components. The Python script language is employed to support programmable simulations and diagnostics, and to facilitate user interaction.

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[7S.10] Integrated Computational Modeling of Liner-on-Plasma Fusion Experiments

Magnetized Target Fusion (MTF) experiments, in which a preheated and magnetized plasma is hydrodynamically compressed to fusion conditions, present a challenging computational modeling problem. Modeling of magnetized target plasmas must accurately predict plasma densities, temperatures, fields, and lifetime; dense plasma interactions with wall materials must be characterized. Modeling of ``liner-on-plasma'' compressions of such target plasmas to fusion conditions must then accurately characterize competing processes of compression heating, radiative and conductive cooling, wall instabilities and interactions, and fusion. Ongoing target plasma and liner driver experiments at Los Alamos National Laboratory are being computationally modeled, using a number of computational tools. In addition to their significance for this innovative approach to controlled fusion, such experiments provide important opportunities to validate computational codes used in high energy density physics research.

[7S.11] Improvements to Busquet's Non LTE algorithm in NRL's Hydro code

Implementation of the Non LTE model RADIOM (M. Busquet, Phys. Fluids B, 5, 4191 (1993)) in NRL's RAD2D Hydro code in conservative form was reported previously(M. Klapisch et al., Bull. Am. Phys. Soc., 40, 1806 (1995)).While the results were satisfactory, the algorithm was slow and not always converging. We describe here modifications that address the latter two shortcomings. This method is quicker and more stable than the original. It also gives information about the validity of the fitting. It turns out that the number and distribution of groups in the multigroup diffusion opacity tables - a basis for the computation of radiation effects in the ionization balance in RADIOM- has a large influence on the robustness of the algorithm. These modifications give insight about the algorithm, and allow to check that the obtained average charge state is the true average. In addition, code optimization resulted in greatly reduced computing time: The ratio of Non LTE to LTE computing times being now between 1.5 and 2.

[7S.12] Modeling and Experiment of NIF Target Debris with First Wall Materials

The target chamber of the National Ignition Facility must be designed to operate after the explosion of ignited ICF targets, which a minimal delay. The deposition of debris ions from the explosion of NIF targets can damage and contaminate with tritium target chamber materials, including the first walls and the debris shields. The primary candidate for the first wall material is B_4C with the debris shield is made of SiO_2. The response of these two materials to the debris from ignited NIF targets has been calculated with the BUCKY computer code. BUCKY is a 1-D Lagrangian radiation-hydrodynamics computer code that models ICF targets and vaporization and melting of the first wall. BUCKY and the accompanying equation-of-state and opacity codes were written at the University of Wisconsin. Recent experiments have been performed at Sandia National Laboratories on NIF sample materials provided by Lawrence Livermore National Laboratory. BUCKY Simulations of these experiments are compared with experimental results.

This work is supported by the U.S. Department of Energy.

[7S.13] NIF Capsule Design Candidates

We describe several ignition capsule designs, for use in the National Ignition Facility. We will compare these designs for ablator efficiency ignition margin, implosion and stability performance. This study includes capsule designs driven by x-ray drive profiles with both 300 eV and 250 eV peak temperature. All of the 300 eV designs are tuned to implode the DT fuel in a nearly identical manner. Some issues relating to material properties and fabrication will be described.

[7S.14] Modeling of Hydrodynamic Instabilities on Indirect Drive Ignition Targets

We have done a variety of simulations of Rayleigh-Taylor and Richtmyer-Meshkov instabilities on indirect drive ignition targets that have been designed for the proposed National Ignition Facility. Modeling has been done that combines variations in drive profile, in irradiation asymmetry, and RT/RM growth at a full spectrum of wavelengths. The simulations are used to determine surface finish specifications for the capsules. We have considered a variety of ablator materials and peak drive temperatures, with various resulting surface finish specifications.

[7S.15] Three-Dimensional Simulations of National Ignition Facility Capsule Implosions

Hydrodynamic instabilities on ignition targets designed for the National Ignition Facility have been modeled previously using weakly nonlinear saturation analysis and two dimensional single mode and multimode LASNEX simulations. We present here the first three-dimensional simulations of the NIF point design capsule, performed with the HYDRA radiation hydrodynamics code. These examine the growth of multimode perturbations seeded by roughness on both the inner and outer surfaces. The spectrum of modes, simulated over a portion of the capsule, extends up to values equivalent to spherical harmonic mode number l = 120. Simulations show that perturbation growth progresses well into the nonlinear regime, underscoring the importance of an accurate treatment of saturation effects. We compare simulations performed using a variety of surface perturbations having different spectrum shapes and amplitudes. Results indicate that spikes can penetrate up to 10 \mum into the 30 \mum radius hot spot before ignition is quenched. Yields of up to 12 MJ have been obtained in simulations with realistic surface roughnesses.

[7S.16] Studies of Beryllium Capsules in NIF Hohlraums

We present results from our calculations of two dimensional beryllium capsules in NIF design hohlraums as part of a comparative study of beryllium and plastic ablator capsule implosions. First, we describe our results for beryllium capsules in hohlraums with a 1.66 mg cm^-3 gas fill and show that we can control implosion symmetry by changing the relative laser power in the inner and outer cones. Then we show that beryllium is a better ablator material because the implosion is on a lower adiabat than for a plastic capsule with a comparable laser pulse. We will also give a progress report on our Be ablator capsule design for a 250 eV drive temperature.

Work performed for the U.S. Department of Energy by Los Alamos National Laboratory under Contract W-7405-ENG-36.

[7S.17] Non-Linear Growth Factor Analysis of NIF Capsule Hydrodynamic Instabilities

Stability of NIF capsules during indirectly driven implosion may be limited by the Raleigh Taylor growth of short wavelength non-spherical surface perturbations. The growth rate of individual modes with an initially small amplitude has been studied. The non-linear growth of simultaneous perturbation modes has been modeled. The sensitivity of the non-linear model growth rate to capsule composition and environment will be discussed.

[7S.18] Generation of shear flow by a compression wave propagating through a left-right asymmetric structure.

Shear flows embedded in the shell of the ICF pellet may partly stabilize Rayleigh-Taylor perturbations and slow down the mix process (D.E.Baldwin, D.D.Ryutov. "Comments on Plasma Phys. and Contr. Fus.", v.17, 1, 1995). One possible technique of generating shear flows consists in impregnating a left-right asymmetric structure into the shell material; when a compression wave generated at the surface of the shell reaches the structure, the wave imparts a tangential momentum to those layers of a shell where the structure is situated, thereby creating embedded shear flow. The paper contains analysis of this process. The following issues are assessed: optimum spatial period of the fine structure; dependence of the imparted tangential momentum on the "density contrast" of the structure; dissipative processes (thermal conductivity, viscosity); perturbations "imprinted" into transmitted wave; rate of broadening of the layer occupied by shear flow. Estimates are also presented for the case when compression wave steepens to a shock wave before reaching the layer with the impregnated fine structure. It is shown that shock wave can very effectively generate shear flow. A rough estimate of the optimum parameters of the structure is presented. This work was supported by DoE contract No. W-7405-ENG-48 at LLNL.

[7S.19] Weakly nonlinear evolution of interface instabilities*

We have developed a Hamiltonian formulation for hydrodynamic interface instabilities in incompressible liquids. The interface evolution equations of Haan^1 are extended to third order. Our nonlinear theory is applied to an embedded interface, and takes into account the temporal variation of the acceleration, final layer thickness, and material thinning due to ablation. The analytical descriptions of 3D hexagonal and rectangular structures are also developed. We evaluate the instability evolution by post processing the output from a one dimensional radiative hydrodynamics code, HYADES. The growth of the fundamental mode and higher harmonics are followed during the early nonlinear stages of perturbation evolution into bubbles and spikes. These results were used to interpret experiments done on the Nova laser to compare the Rayleigh-Taylor instability evolution at an ablation front versus at an embedded interface.^2 \scriptsize *Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livemore National Laboratory under Contract W-7405-ENG-48 ^1S.W. Haan, Phys. Fluids B 3, 2349 (1991). ^2K.S. Budil et al., Phys. Rev. Lett. 76, 4536 (1996).

[7S.20] Progress in Refining Simulations of Perturbation Growth in ICF Ignition Capsules

Numerical simulations of perturbation growth are done to evaluate the impact of surface roughnesses on capsule performance. While these hydro instability calculations are straightforward in concept, it is difficult to obtain definitive results because of (i) numerical difficulties associated with distorted meshes and (ii) sensitivities to mesh refinement. While there are other challenges too, it is these two that we address in the present work. We model, in 2-D using the code LASNEX, two capsules: the NIF PT and the French Limeil 1000. Both consist of a bromine doped plastic shell encapsulating a shell of DT ice which in turn contains DT gas. We model the surface roughness on the outside of the plastic ablator and that on the inside of the DT ice. These are multimode calculations in that 24 modes (up to l=96) are imposed on each surface. These calculations follow the evolution of perturbation growth into the nonlinear regime. Early work showed surprising behaviour which has now been traced to an interaction between mesh hourglassing and the perturbations. We now know that perturbation growth seeds hourglassing just outside the ablation surface and that such hourglassing can enhance the growth of the perturbations. Results with and without this instability will be discussed. We are also exploring the convergence of computed results with mesh refinement.

[7S.21] Hydrodynamic Simulations of Rayleigh-Taylor Instabilities in Magnetically-accelerated Cylindrical Liners Driven by the Atlas Capacitor Bank Applying SPLAT, a Two-dimensional Finite-element Code for High-performance Personal Computers with Support for Sesame and Analytic Equations-of-state, Temperature-dependent Resistivity, and Self-consistent Driving Circuits.

[7S.22] Growth of perturbations in the start-up problem

An analytic model is presented that studies perturbation evolution in the start up phase before the onset of the acceleration phase in ICF targets. It is studied the propagation of a rippled shock generated either by non-uniform irradiation on a smooth surface or by uniform irradiation on a rough surface. Good agreement for the oscillation period of the deformed shock front and perturbation decay is observed between the model and experimental results. The dependence of the shock front, ablation front and mass areal density perturbation on laser intensity is addressed. In the case of non-uniform irradiation it is found that the normalized shock front perturbation to the intensity non uniformity follows aproximately the relation k a_a / (\delta I / I_0) \sim 0.5.

Part 7 of program listing