Publications

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This report documents calculations conducted to determine if 42 low-power transmitters located within a metallic enclosure can initiate electro-explosive devices (EED) located within the same enclosure. This analysis was performed for a generic EED no-fire power level of 250 mW. The calculations show that if the transmitters are incoherent, the power available is 32 mW - approximately one-eighth of the assumed level even with several worst-case assumptions in place.

This report examines the interactions involved with flashover along a surface in high density electronegative gases. The focus is on fast ionization processes rather than the later time ionic drift or thermalization of the discharge. A kinetic simulation of the gas and surface is used to examine electron multiplication and includes gas collision, excitation and ionization, and attachment processes, gas photoionization and surface photoemission processes, as well as surface attachment. These rates are then used in a 1.5D fluid ionization wave (streamer) model to study streamer propagation with and without the surface in air and in SF6. The 1.5D model therefore includes rates for all these processes. To get a better estimate for the behavior of the radius we have studied radial expansion of the streamer in air and in SF6. The focus of the modeling is on voltage and field level changes (with and without a surface) rather than secondary effects, such as, velocities or changes in discharge path. An experiment has been set up to carry out measurements of threshold voltages, streamer velocities, and other discharge characteristics. This setup includes both electrical and photographic diagnostics (streak and framing cameras). We have observed little change in critical field levels (where avalanche multiplication sets in) in the gas alone versus with the surface. Comparisons between model calculations and experimental measurements are in agreement with this. We have examined streamer sustaining fields (field which maintains ionization wave propagation) in the gas and on the surface. Agreement of the gas levels with available literature is good and agreement between experiment and calculation is good also. Model calculations do not indicate much difference between the gas alone versus the surface levels. Experiments have identified differences in velocity between streamers on the surface and in the gas alone (the surface values being larger).

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It is generally acknowledged that once a highly conductive channel is established between two charged and conducting materials, electrical breakdown is well established and difficult to interrupt. An understanding of the initiation mechanism for electrical breakdown is crucial for devising mitigating methods to avoid catastrophic failures. Both volumetric and surface discharges are of interest. An effort is underway where experiments and theory are being simultaneously developed. The experiment consists of an impedance matched discharge chamber capable of investigating various gases and pressures to ten atmospheres. In addition to current and voltage measurements, a high dynamic range streak camera records streamer velocities. The streamer velocities are particularly valuable for comparison with theory. A streamer model is being developed which includes photo-ionization and particle interactions with an insulating surface. The combined theoretical and experimental effort is aimed at detailed comparisons of streamer development as well as a quantitative understanding of how streamers interact with dielectric surfaces and the resulting effects on breakdown voltage. © 2008 IEEE.

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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.

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.

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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.

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.

This report summarizes the work on breakdown modeling in nonuniform geometries by the ionization coefficient approach. Included are: (1) fits to primary and secondary ionization coefficients used in the modeling; (2) analytical test cases for sphere-to-sphere, wire-to-wire, corner, coaxial, and rod-to-plane geometries; a compilation of experimental data with source references; comparisons between code results, test case results, and experimental data. A simple criterion is proposed to differentiate between corona and spark. The effect of a dielectric surface on avalanche growth is examined by means of Monte Carlo simulations. The presence of a clean dry surface does not appear to enhance growth.

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The research discussed in this report was conceived during our earlier attempts to simulate breakdown across a dielectric surface using a Monte Carlo approach. While cataloguing the various ways that a dielectric surface could affect the breakdown process, we found that one obvious effect--photoemission from the surface--had been ignored. Initially, we felt that inclusion of this effect could have a major impact on how an ionization front propagates across a surface because of the following argument chain: (1) The photon energy required to release electrons from a surface via photoemission is less than the photon energy required to ionize gas molecules directly. (2) The mean free path of a photon in gas is longer for low-energy photons than for high-energy photons. (3) Photoionization is a major effect in advancing the ionization front for breakdown in gas without a surface, therefore, we know that even high-energy photons can be released from the head of a streamer and propagate some distance through the gas. Our hypothesis, therefore, was that photons with energies near the threshold of photoemission could travel further in front of the streamer before being absorbed than higher-energy photons needed for photoionization, yet the lower-energy photons, with the help of the surface, could still create seed electrons for new avalanches. Thus, the streamer would advance more rapidly next to a surface than in gas alone. Additionally, the photoemission from the surface would add to the electrons in the avalanche and cause the avalanche to grow faster. After some study, however, we are forced to conclude that although photoemission does contribute to avalanche growth at fields near breakdown threshold, secondary electron emission causes electrons to stick to the surface and cancels out the growth due to photoemission. This conclusion assumes a discharge that occurs over a short period of time so that charging of the surface, which could alter its secondary electron emission characteristics, does not occur. This report documents the numerical work we did on investigating this effect and the experimental work we did on pre-breakdown phenomena in gas.

The goal of this project was to develop a device that uses electric fields to grasp and possibly levitate LIGA parts. This non-contact form of grasping would solve many of the problems associated with grasping parts that are only a few microns in dimensions. Scaling laws show that for parts this size, electrostatic and electromagnetic forces are dominant over gravitational forces. This is why micro-parts often stick to mechanical tweezers. If these forces can be controlled under feedback control, the parts could be levitated, possibly even rotated in air. In this project, we designed, fabricated, and tested several grippers that use electrostatic and electromagnetic fields to grasp and release metal LIGA parts. The eventual use of this tool will be to assemble metal and non-metal LIGA parts into small electromechanical systems.

One of the tasks performed routinely by the Electromagnetics and Plasma Physics Analysis Department at Sandia National Laboratories is analyzing the effects of direct-strike lightning on Faraday cages that protect sensitive items. The Faraday cages analyzed thus far have many features in common. This report is an attempt to collect equations and other information that have been routinely used in the past in order to facilitate future analysis.

This paper presents models and measurements of antenna input impedance in resonant cavities at high frequencies.The behavior of input impedance is useful in determining the transmission and reception characteristics of an antenna (as well as the transmission characteristics of certain apertures). Results are presented for both the case where the cavity is undermoded (modes with separate and discrete spectra) as well as the over moded case (modes with overlapping spectra). A modal series is constructed and analyzed to determine the impedance statistical distribution. Both electrically small as well as electrically longer resonant and wall mounted antennas are analyzed. Measurements in a large mode stirred chamber cavity are compared with calculations. Finally a method based on power arguments is given, yielding simple formulas for the impedance distribution.

The purpose of this research was to develop a science-based understanding of the early-time behavior of electric surface arcing in air at atmospheric pressure. As a first step towards accomplishing this, we used a kinetic approach to model an electron swarm as it evolved in a neutral gas under the influence of an applied electric field. A computer code was written in which pseudo-particles, each representing some number of electrons, were accelerated by an electric field. The electric field due to the charged particles was calculated efficiently using a tree algorithm. Collision of the electrons with the background gas led to the creation of new particles through the processes of ionization and photoionization. These processes were accounted for using measured cross-section data and Monte Carlo methods. A dielectric half-space was modeled by imaging the charges in its surface. Secondary electron emission from the surface, resulting in surface charging, was also calculated. Simulation results show the characteristics of a streamer in three dimensions. A numerical instability was encountered before the streamer matured to form branching.

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The simple formula, {l_angle}P{sub r}{r_angle}=(E{sub o}{sup 2}/{eta})({lambda}{sup 2}/8{pi}), for the received power of an antenna with a matched load in an over-moded cavity actually holds for an antenna of any shape and size. This can be seen from the close connection between the correlation tensor of the cavity field at two different points and the imaginary part of the free-space dyadic Green's function.

A hybrid FEM/MoM model has been implemented to compute the coupling of fields into a cavity through narrow slot apertures having depth. The model utilizes the slot model of Warne and Chen [23]-[29] which takes into account the depth of the slot, wall losses, and inhomogeneous dielectrics in the slot region. The cavity interior is modeled with the mixed-order, covariant-projection hexahedral elements of Crowley [32]. Results are given showing the accuracy and generality of the method for modeling geometrically complex slot-cavity combinations.

Test data on canonical weapon-like fixtures are used to validate previously developed analytical bounding results. The test fixtures were constructed to simulate (but be slightly worse than) weapon ports of entry but have known geometries (and electrical points of contact). The exterior of the test fixtures exhibited exterior resonant enhancement of the incident fields at the ports of entry with magnitudes equal to those of weapon geometries. The interior consisted of loaded transmission lines adjusted to maximize received energy or voltage but incorporating practical weapon geometrical constraints. New analytical results are also presented for bounding the energies associated with multiple bolt joints and for bounding the exterior resonant enhancement of the exciting fields.

Intense magnetic fields exist in the immediate vicinity of a lightning strike (and near power lines). Conducting barriers increase the rise time (and thus decrease the rise rate) interior to the barrier, but typically do not prevent penetration of the magnetic field, since the lightning current fall time may be larger than the barrier diffusion time. Thus, substantial energy is present in the interior field, although the degradation of rise rate makes it more difficult to couple into electrical circuits. This report assesses the threat posed by the diffusive magnetic field to interior components and wire loops (where voltages are induced). Analytical and numerical bounding analyses are carried out on a pill box shaped conducting barrier to develop estimates for the worst case magnetic field threats inside the system. Worst case induced voltages and energies are estimated and compared with threshold charge voltages and energies on the output capacitor of the system. Variability of these quantities with respect to design parameters are indicated. The interior magnetic field and induced voltage estimates given in this report can be used as excitations for more detailed interior and component models.

A radial transmission line material measurement sample apparatus (sample holder, offset short standards, measurement software, and instrumentation) is described which has been proposed, analyzed, designed, constructed, and tested. The purpose of the apparatus is to obtain accurate surface impedance measurements of lossy, possibly anisotropic, samples at low and intermediate frequencies (vhf and low uhf). The samples typically take the form of sections of the material coatings on conducting objects. Such measurements thus provide the key input data for predictive numerical scattering codes. Prediction of the sample surface impedance from the coaxial input impedance measurement is carried out by two techniques. The first is an analytical model for the coaxial-to-radial transmission line junction. The second is an empirical determination of the bilinear transformation model of the junction by the measurement of three full standards. The standards take the form of three offset shorts (and an additional lossy Salisbury load), which have also been constructed. The accuracy achievable with the device appears to be near one percent.

This paper develops corrections to the impedance per unit length when the conductor cross section includes sharp corners. The case of a right internal angle is treated in detail. Corrections are given for all values of the ratio of internal to external magnetic permeabilities. Both the real and imaginary parts of the corrections are determined. Application of the results to a conductor of square cross section is given. Higher order terms are developed and compared to a numerical solution.

Typical aerospace joints lead to apertures which are very narrow and thick. We develop a systematic analytical treatment of this type of aperture (precise conditions of validity given in the text), although the results are also applicable to apertures on a thin conducting body. An antenna integral equation with an equivalent antenna radius is used to describe the voltage across a narrow and thick aperture in a perfectly conducting plane. The result shows the voltage across the aperture has very high Q (quality-factor) resonances, because the equivalent radius is exponentially small. Transmitted power also exhibits similar behavior. When metallic and gasket losses are included, a nonlocal antenna model together with a local transmission line model is used to describe the voltage across the aperture. Good metallic walls, such as aluminum, are found to significantly reduce the penetration of an aperture of typical dimensions. Gaskets with relatively small loss tangents also result in significant penetration reductions. A simple transmission line with uniform loading is used to approximate the governing equation described in. In the lossless limit and for moderate fatness parameter this simple transmission line model is comparable in accuracy to King's three-term theory. The loading of the bolts or hinges is demonstrated to act in many cases as a short. Finally, the low frequency penetration for a narrow slot aperture of arbitrary depth is characterized by the equivalent polarizabilities (dominating longitudinal component) as a function of the ratio of the depth to the width and ratio of the length to the width. A general relationship is shown to exist between the equivalent radius and the transverse line dipole moments of a slot aperture with depth. The longitudinal equivalent polarizabilities of antennas and slot apertures are used to derive a coupling energy bound for a step function EMP. 9 refs., 8 figs.

Electromagnetic coupling to electronic components or subsystems is a concern in modern system design. Undesired coupling can cause interference or, in the extreme, system upset. To be able to characterize the coupling is an important step to understanding the limitations on system performance. Often the approach is taken to shield the electronic equipment inside some kind of enclosure. However, there are usually inadvertent cracks or bowing at mechanical interfaces. These gaps are apparent slot apertures. An equivalent antenna/local transmission line model for narrow slot apertures with depth including losses has been developed. It may be applied tortuous paths and hence may be used to model practical situations. This model has been previously verified by measuring the coupling through narrow slot apertures with varying width and depth. These measurements were performed for brass slots radiating into a half-space. The results were in good agreement with the model of Warne and Chen. The models, as well as the measurements showed that for very narrow slots the wall loss becomesdominant -- it has been demonstrated that the inclusion of loss is important in making realistic coupling estimates in practical configurations. This paper presents results showing the effects of varying conductivity and surface preparations for half-space coupling as well as different loadings of the narrow slot apertures. The coupling through narrow slot apertures having depth was measured for a variety of resonant cavity loadings. The loadings were chosen such that the cavity resonant frequencies were above, near and below the resonant peak of the half-space coupling curve. Measurements were made in the 2--4 GHz band with vertical polarization. 3 refs., 6 figs., 1 tab.