Adiabatic invariants and Mixmaster catastrophes

We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical results. We also present a new formulation of the dynamics via Catastrophe Theory. We find that the change from one era to the next corresponds to a fold catastrophe, during the Kasner shifts the potential is an Implicit Function Form whereas, as the anisotropy dissipates, the Mixmaster potential must become a Morse 0--saddle. We compare and contrast our results to many known works on the Mixmaster problem and indicate how extensions could be achieved. Further exploitation of this formulation may lead to a clearer understanding of the global Mixmaster dynamics.Comment: 24 pages, LaTeX, 5 figures (which can be obtained by sending a message to the first author), submitted to Phys.Rev.

Higher-Derivative Quantum Cosmology

The quantum cosmology of a higher-derivative derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler-DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques for solving the Wheeler-DeWitt equation with appropriate boundary conditions shall be described, and implications for semiclassical theories of inflationary cosmology will be outlined.Comment: 11 pages TeX. A term has been removed from equation (13

Performance of a 500 watt Nd:GGG zigzag slab oscillator

Realization of practical multi-kilowatt Nd:garnet lasers will require the scale-up of crystal dimensions as well as more powerful pumping sources. A high average power zigzag slab crystal amplifier testing facility has been established at LLNL which employs two 100 kW{sub e} vortex stabilized arc lamps, cooled reflectors and a cooled, spectrally filtered, crystal slab mounting fixture. The operational characteristics of the first crystal laser to be tested in this setup, a Nd:GGG zigzag oscillator, are presented. A Nd:GGG crystal of dimensions 18 {times} 7 {times} 0.5 cm{sup 3}, doped at 2 {times} 10{sup 20} cm{sup {minus}3} Nd{sup 3+} atomic density, was pumped by up to 40 kW of filtered argon line emission. A small-signal single pass gain (losses excluded) of 1.09 was measured with a probe laser when the DC input to the lamps was 43 kW{sub e}. Our power supply was then modified to operate in a pulsed mode and provided one to three milliseconds pulses at 120 Hz. An average optical output power of 490 watts was obtained at a lamp input power of 93 kW{sub e} in an unoptimized resonator. The laser output power declined after a few tens of seconds since the slab tips were not properly cooled. A birdhouse specular lamp reflector and a contoured diffuse reflector were tested; in both cases the pump illuminated crystal surface was smaller than the total crystal face area. Fluorescence imaging of the zigzag amplifier's output aperture registered a smoother, more uniform pumping profile when the diffuse reflector was used. Uniformity of pumping results in decreased resonator loss and yields higher laser output power. Thermo-optic distortions observed in these preliminary tests are analyzed with the aid of computer simulations of the thermal fields, stresses, and surface displacements of our crystal slab. 3 refs., 12 figs

Software Engineering Processes Used to Develop the NIF Integrated Computer Control System

We have developed a new target platform to study Laser Plasma Interaction in ignition-relevant condition at the Omega laser facility (LLE/Rochester)[1]. By shooting an interaction beam along the axis of a gas-filled hohlraum heated by up to 17 kJ of heater beam energy, we were able to create a millimeter-scale underdense uniform plasma at electron temperatures above 3 keV. Extensive Thomson scattering measurements allowed us to benchmark our hydrodynamic simulations performed with HYDRA [1]. As a result of this effort, we can use with much confidence these simulations as input parameters for our LPI simulation code pF3d [2]. In this paper, we show that by using accurate hydrodynamic profiles and full three-dimensional simulations including a realistic modeling of the laser intensity pattern generated by various smoothing options, fluid LPI theory reproduces the SBS thresholds and absolute reflectivity values and the absence of measurable SRS. This good agreement was made possible by the recent increase in computing power routinely available for such simulations

Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1

The present work considers (4+1)-dimensional spatially homogeneous vacuum cosmological models. Exact solutions -- some already existing in the literature, and others believed to be new -- are exhibited. Some of them are the most general for the corresponding Lie group with which each homogeneous slice is endowed, and some others are quite general. The characterization ``general'' is given based on the counting of the essential constants, the line-element of each model must contain; indeed, this is the basic contribution of the work. We give two different ways of calculating the number of essential constants for the simply transitive spatially homogeneous (4+1)-dimensional models. The first uses the initial value theorem; the second uses, through Peano's theorem, the so-called time-dependent automorphism inducing diffeomorphismsComment: 26 Pages, 2 Tables, latex2

Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio

Orchestrating Shots for the National Ignition Facililty (NIF)

The National Ignition Facility (NIF), currently under construction at the Lawrence Livermore National Laboratory, is a stadium-sized facility containing a 192-beam, 1.8 Megajoule, 500-Terawatt, ultra-violet laser system together with a 10-meter diameter target chamber with room for nearly 100 experimental diagnostics. When completed, NIF will be the world's largest and most energetic laser experimental system, providing an international center to study inertial confinement fusion and physics of matter at extreme densities and pressures. The NIF is operated by the Integrated Computer Control System (ICCS), which is a layered architecture of over 700 lower-level front-end processors attached to nearly 60,000 control points and coordinated by higher-level supervisory subsystems in the main control room. A shot automation framework has been developed and deployed during the past year to orchestrate and automate shots performed at the NIF using the ICCS. The Shot Automation framework is designed to automate 4-8 hour shot sequences, that includes deriving shot goals from an experiment definition, set up of the laser and diagnostics, automatic alignment of laser beams, and a countdown to charge and fire the lasers. These sequences consist of set of preparatory verification shots, leading to amplified system shots followed by post-shot analysis and archiving. The framework provides for a flexible, model-based work-flow execution, driven by scripted automation called macro steps. The shot director software is the orchestrating component of a very flexible automation layer which allows us to define, coordinate and reuse simpler automation sequences. This software provides a restricted set of shot life cycle state transitions to 26 collaboration supervisors that automate 8-laser beams (bundle) and a common set of shared resources. Each collaboration supervisor commands approximately 10 subsystem shot supervisors that perform automated control and status verification. Collaboration supervisors translate shot life cycle state commands from shot director into sequences of ''macro steps'' to be distributed to each of its shot supervisors, maintains order of macro steps for each subsystem, and supports collaboration between macro steps. They also manage failure, restarts, and rejoining into the shot cycle (if necessary) and manage auto/manual macro step execution and collaborations between other collaboration supervisors. Each macro step has database-driven verification phases and a scripted perform phase. This provides for a highly flexible framework for performing a variety of NIF shot types. Database tables define the order of work and dependencies (workflow) of macro steps to be performed for a shot. A graphical model editor facilitates the definition and viewing of an execution model. A change manager tool enables ''de-participation'' of individual devices, of entire laser segments (beams, quads, or bundles of beams) or individual diagnostics. This software has been deployed to the NIF facility and is currently being used to support NIF main laser commissioning shots and build-out of the NIF laser. This will be used to automate future target and experimental shot campaigns

Shot Automation for the National Ignition Facility

A shot automation framework has been developed and deployed during the past year to automate shots performed on the National Ignition Facility (NIF) using the Integrated Computer Control System This framework automates a 4-8 hour shot sequence, that includes inputting shot goals from a physics model, set up of the laser and diagnostics, automatic alignment of laser beams and verification of status. This sequence consists of set of preparatory verification shots, leading to amplified system shots using a 4-minute countdown, triggering during the last 2 seconds using a high-precision timing system, followed by post-shot analysis and archiving. The framework provides for a flexible, model-based execution driven of scriptable automation called macro steps. The framework is driven by high-level shot director software that provides a restricted set of shot life cycle state transitions to 25 collaboration supervisors that automate 8-laser beams (bundles) and a common set of shared resources. Each collaboration supervisor commands approximately 10 subsystem shot supervisors that perform automated control and status verification. Collaboration supervisors translate shot life cycle state commands from the shot director into sequences of ''macro steps'' to be distributed to each of its shot supervisors. Each Shot supervisor maintains order of macro steps for each subsystem and supports collaboration between macro steps. They also manage failure, restarts and rejoining into the shot cycle (if necessary) and manage auto/manual macro step execution and collaborations between other collaboration supervisors. Shot supervisors execute macro step shot functions commanded by collaboration supervisors. Each macro step has database-driven verification phases and a scripted perform phase. This provides for a highly flexible methodology for performing a variety of NIF shot types. Database tables define the order of work and dependencies (workflow) of macro steps to be performed for a shot. A graphical model editor facilitates the definition and viewing of an execution model. A change manager tool enables ''de-participation'' of individual devices, of entire laser segments (beams, quads, or bundles of beams) or individual diagnostics. This software has been deployed to the NIF facility and is currently being used to support NIF main laser commissioning shots and build-out of the NIF laser. This will be used to automate future target and experimental shot campaigns

Status of the National Ignition Facility Integrated Computer Control System (ICCS) on the Path to Ignition

The National Ignition Facility (NIF) at the Lawrence Livermore National Laboratory is a stadium-sized facility under construction that will contain a 192-beam, 1.8-Megajoule, 500-Terawatt, ultraviolet laser system together with a 10-meter diameter target chamber with room for multiple experimental diagnostics. NIF is the world's largest and most energetic laser experimental system, providing a scientific center to study inertial confinement fusion (ICF) and matter at extreme energy densities and pressures. NIF's laser beams are designed to compress fusion targets to conditions required for thermonuclear burn, liberating more energy than required to initiate the fusion reactions. NIF is comprised of 24 independent bundles of 8 beams each using laser hardware that is modularized into more than 6,000 line replaceable units such as optical assemblies, laser amplifiers, and multifunction sensor packages containing 60,000 control and diagnostic points. NIF is operated by the large-scale Integrated Computer Control System (ICCS) in an architecture partitioned by bundle and distributed among over 800 front-end processors and 50 supervisory servers. NIF's automated control subsystems are built from a common object-oriented software framework based on CORBA distribution that deploys the software across the computer network and achieves interoperation between different languages and target architectures. A shot automation framework has been deployed during the past year to orchestrate and automate shots performed at the NIF using the ICCS. In December 2006, a full cluster of 48 beams of NIF was fired simultaneously, demonstrating that the independent bundle control system will scale to full scale of 192 beams. At present, 72 beams have been commissioned and have demonstrated 1.4-Megajoule capability of infrared light. During the next two years, the control system will be expanded to include automation of target area systems including final optics, target positioners and diagnostics, in preparation for project completion in 2009. Additional capabilities to support fusion ignition shots in a National Ignition Campaign (NIC) beginning in 2010 will include a cryogenic target system, target diagnostics, and integrated experimental shot data analysis with tools for data visualization and archiving. This talk discusses the current status of the control system implementation and discusses the plan to complete the control system on the path to ignition