Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Target Area design basis and system performance for the National Ignition Facility. Revision 1

The NIF Target Area is designed to confine the ICF target experiments leading up to and including fusion ignition and gain. The Target Area will provide appropriate in-chamber conditions before, during, and after each shot. The repeated introduction of large amounts of laser energy into the chamber and emission of fusion energy from targets represents a new challenge in ICF facility design. Prior to a shot, the facility provides proper illumination geometry, target chamber vacuum, and a stable platform for the target and its diagnostics. During a shot, the impact of the energy introduced into the chamber is minimized, and workers and the public are protected from excessive prompt radiation doses. After the shot, the residual radioactivation is managed to allow required accessibility. Tritium and other radioactive wastes are confined and disposed of. Diagnostic data is also retrieved, and the facility is readied for the next shot. The Target Area will accommodate yields up to 20 MJ, and its design lifetime is 30 years. The Target Area provides the personnel access needed to support the use precision diagnostics. The annual shot mix for design purposes is shown. Designing to this experimental envelope ensures the ability and flexibility to move through the experimental campaign to ignition efficiently

Mobile, scanning x-ray source for mine detection using backscattered x-rays

A continuously operating, scanning x-ray machine is being developed for landmine detection using backscattered x-rays. The source operates at 130 kV and 650 mA. The x-rays are formed by electrons striking a high Z target. Target shape is an approximate 5 cm wide by 210 cm long racetrack. The electron beam is scanned across this target with electromagnets. There are 105, 1-cm by 1-cm collimators in each leg of the racetrack for a total of 210 collimators. The source is moved in the forward direction(the direction perpendicular to the 210-cm dimension) at 3 mi/h. The forward velocity and collimator spacing are such that a grid of collimated x-rays are projected at normal incidence to the soil. The spacing between the collimators and the ground results in a 2-cm by 2-cm x-ray pixel on the ground. A unique detector arrangement of collimated and uncollimated detectors allows surface features to be recognized and removed, leaving an image of a buried landmine. Another detector monitors the uncollimated x-ray output and is used to normalize the source output. The mine detector is being prepared for an Advanced Technology Demonstration (ATD). The ATD is scheduled for midyear of 1998. The results of the source performance in pre ATD tests will be presented

Design and evaluation of coils for a 50 mm diameter induction coilgun launcher

Coilguns have the ability to provide magnetic pressure to projectiles which results in near constant acceleration. However, to achieve this performance and control projectile hearing, significant constraints are placed on the design of the coils. We are developing coils to produce an effective projectile base pressure of 100 MPa (1kbar) as a step toward reaching base pressures of 200 MPa. The design uses a scalable technology applicable to the entire range of breech to muzzle coils of a multi-stage launcher. This paper presents the design of capacitor-driven coils for launching nominal 50 mm, 350 gram projectiles. Design criteria, constraints, mechanical stress analysis, launcher performance, and test results are discussed

Sandia National Laboratories participation in the National Ignition Facility project

The National Ignition Facility is a $1.1B DOE Defense Programs Inertial Confinement Fusion facility supporting the Science Based Stockpile Stewardship Program. The goal of the facility is to achieve fusion ignition and modest gain in the laboratory. The NIF project is responsible for the design and construction of the 192 beam, 1.8 MJ laser necessary to meet that goal. - The project is a National project with participation by Lawrence Livermore National Laboratory (LLNL), Los Alamos National Laboratory (LANL), Sandia National Laboratory (SNL), the University of Rochester Laboratory for Laser Energetics (URLLE) and numerous industrial partners. The project is centered at LLNL which has extensive expertise in large solid state lasers. The other partners in the project have negotiated their participation based on the specific expertise they can bring to the project. In some cases, this negotiation resulted in the overall responsibility for a WBS element; in other cases, the participating laboratories have placed individuals in the project in areas that need their individual expertise. The main areas of Sandia`s participation are in the management of the conventional facility design and construction, the design of the power conditioning system, the target chamber system, target diagnostic instruments, data acquisition system and several smaller efforts in the areas of system integration and engineering analysis. Sandia is also contributing to the technology development necessary to support the project by developing the power conditioning system and several target diagnostics, exploring alternate target designs, and by conducting target experiments involving the ``foot`` region of the NIF power pulse. The project has just passed the mid-point of the Title I (preliminary) design phase. This paper will summarize Sandia`s role in supporting the National Ignition Facility and discuss the areas in which Sandia is contributing. 3 figs

55-TW magnetically insulated transmission-line system: Design, simulations, and performance

We describe herein a system of self-magnetically insulated vacuum transmission lines (MITLs) that operated successfully at 20 MA, 3 MV, and 55 TW. The system delivered the electromagnetic-power pulse generated by the Z accelerator to a physics-package load on over 1700 Z shots. The system included four levels that were electrically in parallel. Each level consisted of a water flare, vacuum-insulator stack, vacuum flare, and 1.3-m-radius conical outer MITL. The outputs of the four outer MITLs were connected in parallel by a 7.6-cm-radius 12-post double-post-hole vacuum convolute. The convolute added the currents of the four outer MITLs, and delivered the combined current to a single 6-cm-long inner MITL. The inner MITL delivered the current to the load. The total initial inductance of the stack-MITL system was 11 nH. A 300-element transmission-line-circuit model of the system has been developed using the tl code. The model accounts for the following: (i) impedance and electrical length of each of the 300 circuit elements, (ii) electron emission from MITL-cathode surfaces wherever the electric field has previously exceeded a constant threshold value, (iii) Child-Langmuir electron loss in the MITLs before magnetic insulation is established, (iv) MITL-flow-electron loss after insulation, assuming either collisionless or collisional electron flow, (v) MITL-gap closure, (vi) energy loss to MITL conductors operated at high lineal current densities, (vii) time-dependent self-consistent inductance of an imploding z-pinch load, and (viii) load resistance, which is assumed to be constant. Simulations performed with the tl model demonstrate that the nominal geometric outer-MITL-system impedance that optimizes overall performance is a factor of ∼3 greater than the convolute-load impedance, which is consistent with an analytic model of an idealized MITL-load system. Power-flow measurements demonstrate that, until peak current, the Z stack-MITL system performed as expected. tl calculations of the peak electromagnetic power at the stack, stack energy, stack voltage, outer-MITL current, and load current, as well as the pinch-implosion time, agree with measurements to within 5%. After peak current, tl calculations and measurements diverge, which appears to be due in part to the idealized pinch model assumed by tl. The results presented suggest that the design of the Z accelerator’s stack-MITL system, and the tl model, can serve as starting points for the design of stack-MITL systems of future superpower accelerators