Publications

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Simple formulas are given for the interior voltages appearing across bolted joints from exterior lightning currents. External slot and bolt inductances as well as internal slot and bolt diffusion effects are included. Both linear and ferromagnetic wall materials are considered. A useful simplification of the slot current distribution into linear stripline and cylindrical parts (near the bolts) allows the nonlinear voltages to be estimated in closed form.

In October 2005, an intensive three-year Laser Triggered Gas Switch (LTGS) development program was initiated to investigate and solve observed performance and reliability issues with the LTGS for ZR. The approach taken has been one of mission-focused research: to revisit and reassess the design, to establish a fundamental understanding of LTGS operation and failure modes, and to test evolving operational hypotheses. This effort is aimed toward deploying an initial switch for ZR in 2007, on supporting rolling upgrades to ZR as the technology can be developed, and to prepare with scientific understanding for the even higher voltage switches anticipated needed for future high-yield accelerators. The ZR LTGS was identified as a potential area of concern quite early, but since initial assessments performed on a simplified Switch Test Bed (STB) at 5 MV showed 300-shot lifetimes on multiple switch builds, this component was judged acceptable. When the Z{sub 20} engineering module was brought online in October 2003 frequent flashovers of the plastic switch envelope were observed at the increased stresses required to compensate for the programmatically increased ZR load inductance. As of October 2006, there have been 1423 Z{sub 20} shots assessing a variety of LTGS designs. Numerous incremental and fundamental switch design modifications have been investigated. As we continue to investigate the LTGS, the basic science of plastic surface tracking, laser triggering, cascade breakdown, and optics degradation remain high-priority mission-focused research topics. Significant progress has been made and, while the switch does not yet achieve design requirements, we are on the path to develop successively better switches for rolling upgrade improvements to ZR. This report summarizes the work performed in FY 2006 by the large team. A high-level summary is followed by detailed individual topical reports.

This paper examined the high frequency time harmonic localization of modal fields in two dimensional cavities along unstable periodic orbits. The elliptic formalism, combined with the random phase approach, allowed the treatment of both convex and concave boundary geometries.

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This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.

In this LDRD we examine techniques to analyze the electromagnetic scattering from structures that are nearly periodic. Nearly periodic could mean that one of the structure's unit cells is different from all the others--a defect. It could also mean that the structure is truncated, or butted up against another periodic structure to form a seam. Straightforward electromagnetic analysis of these nearly periodic structures requires us to grid the entire structure, which would overwhelm today's computers and the computers in the foreseeable future. In this report we will examine various approximations that allow us to continue to exploit some aspects of the structure's periodicity and thereby reduce the number of unknowns required for analysis. We will use the Green's Function Interpolation with a Fast Fourier Transform (GIFFT) to examine isolated defects both in the form of a source dipole over a meta-material slab and as a rotated dipole in a finite array of dipoles. We will look at the numerically exact solution of a one-dimensional seam. In order to solve a two-dimensional seam, we formulate an efficient way to calculate the Green's function of a 1d array of point sources. We next formulate ways of calculating the far-field due to a seam and due to array truncation based on both array theory and high-frequency asymptotic methods. We compare the high-frequency and GIFFT results. Finally, we use GIFFT to solve a simple, two-dimensional seam problem.

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We have developed a diagnostic system that measures the spectrally integrated (i.e. the total) energy and power radiated by a pulsed blackbody x-ray source. The total-energy-and-power (TEP) diagnostic system is optimized for blackbody temperatures between 50 and 350 eV. The system can view apertured sources that radiate energies and powers as high as 2 MJ and 200 TW, respectively, and has been successfully tested at 0.84 MJ and 73 TW on the Z pulsed-power accelerator. The TEP system consists of two pinhole arrays, two silicon-diode detectors, and two thin-film nickel bolometers. Each of the two pinhole arrays is paired with a single silicon diode. Each array consists of a 38 x 38 square array of 10-{micro}m-diameter pinholes in a 50-{micro}m-thick tantalum plate. The arrays achromatically attenuate the x-ray flux by a factor of {approx}1800. The use of such arrays for the attenuation of soft x rays was first proposed by Turner and co-workers [Rev. Sci. Instrum. 70, 656 (1999)RSINAK0034-674810.1063/1.1149385]. The attenuated flux from each array illuminates its associated diode; the diode's output current is recorded by a data-acquisition system with 0.6-ns time resolution. The arrays and diodes are located 19 and 24 m from the source, respectively. Because the diodes are designed to have an approximately flat spectral sensitivity, the output current from each diode is proportional to the x-ray power. The nickel bolometers are fielded at a slightly different angle from the array-diode combinations, and view (without pinhole attenuation) the same x-ray source. The bolometers measure the total x-ray energy radiated by the source and--on every shot--provide an in situ calibration of the array-diode combinations. Two array-diode pairs and two bolometers are fielded to reduce random uncertainties. An analytic model (which accounts for pinhole-diffraction effects) of the sensitivity of an array-diode combination is presented.

The later time phase of electrical breakdown in water is investigated for the purpose of improving understanding of the discharge characteristics. One dimensional simulations in addition to a zero dimensional lumped model are used to study the spark discharge. The goal is to provide better electrical models for water switches used in the pulse compression section of pulsed power systems. It is found that temperatures in the discharge channel under representative drive conditions, and assuming small initial radii from earlier phases of development, reach levels that are as much as an order of magnitude larger than those used to model discharges in atmospheric gases. This increased temperature coupled with a more rapidly rising conductivity with temperature than in air result in a decreased resistance characteristic compared to preceding models. A simple modification is proposed for the existing model to enable the approximate calculation of channel temperature and incorporate the resulting conductivity increase into the electrical circuit for the discharge channel. Comparisons are made between the theoretical predictions and recent experiments at Sandia. Although present and past experiments indicated that preceding late time channel models overestimated channel resistance, the calculations in this report seem to underestimate the resistance relative to recent experiments. Some possible reasons for this discrepancy are discussed.

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This report examines the problem of an antenna radiating from a cylindrical hole in the earth and the subsequent far-zone field produced in the upper air half space. The approach used for this analysis was to first examine propagation characteristics along the hole for surrounding geologic material properties. Three cases of sand with various levels of moisture content were considered as the surrounding material to the hole. For the hole diameters and sand cases examined, the radiation through the earth medium was found to be the dominant contribution to the radiation transmitted through to the upper half-space. In the analysis presented, the radiation from a vertical and a horizontal dipole source within the hole is used to determine a closed-form expression for the radiation in the earth medium which represents a modified element factor for the source and hole combination. As the final step, the well-known results for a dipole below a half space, in conjunction with the use of Snell's law to transform the modified element factor to the upper half space, determine closed-form expressions for the far-zone radiated fields in the air region above the earth.

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This report presents a modification of a previous model for the statistical distribution of linear antenna impedance. With this modification a simple formula is determined which yields accurate results for all ratios of modal spectral width to spacing. It is shown that the reactance formula approaches the known unit Lorentzian in the lossless limit.

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Approximate formulas are constructed and numerical simulations are carried out for electric field derivative probes that have the form of flush mounted monopoles. Effects such as rounded edges are included. A method is introduced to make results from two-dimensional conformal mapping analyses accurately apply to the three-dimensional axisymmetric probe geometry

By using a multipole-conformal mapping expansion for the wire currents we examine the accuracy of approximations for the transfer inductance of a one dimensional array of wires (wire grid). A simple uniform fit is constructed by introduction of the decay factor from bipolar coordinates into existing formulas for this inductance.

This report assembles models for the response of a wire interacting with a conducting ground to an electromagnetic pulse excitation. The cases of an infinite wire above the ground as well as resting on the ground and buried beneath the ground are treated. The focus is on the characteristics and propagation of the transmission line mode. Approximations are used to simplify the description and formulas are obtained for the current. The semi-infinite case, where the short circuit current can be nearly twice that of the infinite line, is also examined.

Transverse electromagnetic (TEM) wave analysis is used to estimate the efficiencies of the coax to triplate transition in Sandia's Z-20 test module. The structure of both the TEM mode and higher order TE modes in the triplate transmission line are characterized. In addition, three dimensional time domain simulations are carried out and used in conjunction with the modal analysis to provide insight into the wave structure excited in the triplate transmission line.