Publications

This report examines the localization of high frequency electromagnetic fields in general three-dimensional convex walled cavities along periodic paths between opposing sides of the cavity. The report examines the three-dimensional case where the mirrors at the end of the orbit have two different radii of curvature. The cases where these orbits lead to unstable localized modes are known as scars.

Use of insensitive high explosives (IHEs) has significantly improved ammunition safety because of their remarkable insensitivity to violent cook-off, shock and impact. Triamino-trinitrobenzene (TATB) is the IHE used in many modern munitions. Previously, lightning simulations in different test configurations have shown that the required detonation threshold for standard density TATB at ambient and elevated temperatures (250 C) has a sufficient margin over the shock caused by an arc from the most severe lightning. In this paper, the Braginskii model with Lee-More channel conductivity prescription is used to demonstrate how electrical arcs from lightning could cause detonation in TATB. The steep rise and slow decay in typical lightning pulse are used in demonstrating that the shock pressure from an electrical arc, after reaching the peak, falls off faster than the inverse of the arc radius. For detonation to occur, two necessary detonation conditions must be met: the Pop-Plot criterion and minimum spot size requirement. The relevant Pop-Plot for TATB at 250 C was converted into an empirical detonation criterion, which is applicable to explosives subject to shocks of variable pressure. The arc cross-section was required to meet the minimum detonation spot size reported in the literature. One caveat is that when the shock pressure exceeds the detonation pressure the Pop-Plot may not be applicable, and the minimum spot size requirement may be smaller.

This paper provides an overview of the electromagnetic frequency domain simulation capabilities of the Electromagnetic Theory department at Sandia National Laboratories via a description of two of its codes. EIGER is a Method of Moments code for electromagnetic simulations, but it only runs on traditional CPUs, not on new architectures. Gemma is in development to replace EIGER and will run on many architectures, including CPUs, GPUs, and MICs, by leveraging the Kokkos library.

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In this paper we investigate full-wave simulations of realistic implementations of multifunctional nanoantenna enabled detectors (NEDs). We focus on a 2x2 pixelated array structure that supports two wavelengths of operation. We design each resonating structure independently using full-wave simulations with periodic boundary conditions mimicking the whole infinite array. We then construct a supercell made of a 2x2 pixelated array with periodic boundary conditions mimicking the full NED; in this case, however, each pixel comprises 10-20 antennas per side. In this way, the cross-talk between contiguous pixels is accounted for in our simulations. We observe that, even though there are finite extent effects, the pixels work as designed, each responding at the respective wavelength of operation. This allows us to stress that realistic simulations of multifunctional NEDs need to be performed to verify the design functionality by taking into account finite extent and cross-talk effects.

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A block base sparse approximate inverse preconditioner for the electric field integral equations is documented and tested. It utilized the Kokkos library for performance portability and shows superior performance when compared to a direct method, 36x faster for a 112K DOF problem. Furthermore, due to the abstractions available in the Kokkos library it allows one to migrate from CPU to GPU in a trivial way.

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The goal of this paper is to investigate full-wave simulations of realistic implementations of multifunctional nanoantenna enabled detectors (NEDs). We realize a 2×2 pixelated array structure that supports two wavelengths of operation. After designing each resonating structure independently using full-wave simulations with periodic boundary conditions mimicking the whole infinite array, we construct a supercell made of a 2×2 pixelated array with periodic boundary conditions mimicking the full NED. In the NED, each pixel comprises 10-20 nanoantennas. Our simulations account for the cross-talk between contiguous pixels. We observe that, even though there are finite extent effects, the pixels work as designed, each responding at the respective wavelength of operation. We want to stress that realistic simulations of multifunctional NEDs need to be performed to verify the design functionality by taking into account finite extent and cross-talk effects.

The growth of a cylindrical s park discharge channel in water and Lexan is studied using a series of one - dimensional simulations with the finite - element radiation - magnetohydrodynamics code ALEGRA. Computed solutions are analyzed in order to characterize the rate of growth and dynamics of the spark c hannels during the rising - current phase of the drive pulse. The current ramp rate is varied between 0.2 and 3.0 kA/ns, and values of the mechanical coupling coefficient K p are extracted for each case. The simulations predict spark channel expansion veloc ities primarily in the range of 2000 to 3500 m/s, channel pressures primarily in the range 10 - 40 GPa, and K p values primarily between 1.1 and 1.4. When Lexan is preheated, slightly larger expansion velocities and smaller K p values are predicted , but the o verall behavior is unchanged.

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This report examines bounds on the penetrant power through ports of entry into a conductive cavity. We first replace the cavity by a load and consider the maximum power transfer properties of an antenna or an aperture. We consider how limitations on the load quality factor place limits on received power. For general frequency ranges we model the backing region by means of a uniformly distributed matched load along a slot aperture and adjust its value for maximum power transfer. This result is derived in closed form using a transmission line model for the aperture. This result illustrates the reduction in received power for low frequencies with finitely conducting wall materials. At high frequencies it approaches the receiving cross section of a linear array having the slot length dimension. Next we examine a slot aperture in a conducting rectangular enclosure and determine how the cavity wall losses and resulting quality factor limit the penetrant power. Detailed simulations and experimental measurements are compared with each other and with the bounding results to assess the accuracy of the bounds. These comparisons also indicate limitations on the accuracy of the models due to perturbing influences in construction, such as bolted joints.

Streamers are a type of ionization wave occurring during the early time phase of a gas discharge. They are typically launched when the evolving space charge of an electron avalanche reaches a certain critical level, beyond which the fi eld of the space charge itself is su ffi cient to drive further evolution of the ionization process. One of the most common ways to model streamers is known as a 1.5D model where the fi eld of a uniformly charged set of discs of chosen radius is evaluated along the cylinder axis. This fi eld drives a one-dimensional kinetic ionization process, which results in the nonlinear evolution of the streamer. This model is e ffi cient, but has the drawback of fi xing the radius and requiring it as an input parameter. Previously, we tried to extend t he 1.5D model to include evolution of its radius by developing a two-step process of axial and radial exp ansion but we encountered stability issues with the model that we thought could have been due to decoupling the two steps. In this report we introduce a new formulation of a streamer model that includes radial expansion. The goal is to take radial moments of the starting axisymmetric fl uid equations and thereby include the radial evolution of the streamer naturally and self-consistently from the beginning. We fi rst develop the fl uid model moments without electron attachment. We review the calculation of the electric fi elds required for the model and investigate approximations to improve computational e ffi ciency. We discuss the code implementation of the model and fi nally, we add attachment to allow the treatment of electronegative gases. Intentionally Left Blank

The di ff usion through shells consisting of either a single conducting or double conducting layers are examined. Exterior drives resulting from Electromagn etic Radiation (EMR), Electromagnetic Pulse (EMP), nearby (indirect) lightning, and DC (low frequency) magnetic fi eldsareused. Boththeinterior fi eld and the induced voltage from a maximally oriented and sized single turn loop are estimated. It is shown that the loop voltage with the empty cavity bounds the case where the center region is excluded by a conducting object. The cases of interior magnetic and electric fi elds from an exterior magnetic drive and the interior electric fi eld from an exterior electric drive are both solved; the magnetic interior fi eldfromanexterior magnetic drive is the only case that results in a nonzero low frequency penetration. Intentionally Left Blank

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This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric 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 report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank

When emitters of electromagnetic energy are operated in the vicinity of sensitive components, the electric field at the component location must be kept below a certain level in order to prevent the component from being damaged, or in the case of electro-explosive devices, initiating. The V-Curve is a convenient way to set the electric field limit because it requires minimal information about the problem configuration. In this report we will discuss the basis for the V-Curve. We also consider deviations from the original V-Curve resulting from inductive versus capacitive antennas, increases in directivity gain for long antennas, decreases in input impedance when operating in a bounded region, and mismatches dictated by transmission line losses. In addition, we consider mitigating effects resulting from limited antenna sizes.

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This report documents work conducted in FY13 on electrical discharge experiments performed to develop predictive computational models of the fundamental processes of surface breakdown in the vicinity of high-permittivity material interfaces. Further, experiments were conducted to determine if free carrier electrons could be excited into the conduction band thus lowering the effective breakdown voltage when UV photons (4.66 eV) from a high energy pulsed laser were incident on the rutile sample. This report documents the numerical approach, the experimental setup, and summarizes the data and simulations. Lastly, it describes the path forward and challenges that must be overcome in order to improve future experiments for characterizing the breakdown behavior for rutile.

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A lightning flash consists of multiple, high-amplitude but short duration return strokes. Between the return strokes is a lower amplitude, continuing current which flows for longer duration. If the walls of a Faraday cage are made of thin enough metal, the continuing current can melt a hole through the metal in a process called burnthrough. A subsequent return stroke can couple energy through this newly-formed hole. This LDRD is a study of the protection provided by a Faraday cage when it has been compromised by burnthrough. We initially repeated some previous experiments and expanded on them in terms of scope and diagnostics to form a knowledge baseline of the coupling phenomena. We then used a combination of experiment, analysis and numerical modeling to study four coupling mechanisms: indirect electric field coupling, indirect magnetic field coupling, conduction through plasma and breakdown through the hole. We discovered voltages higher than those encountered in the previous set of experiments (on the order of several hundreds of volts).

Continuum calculations are used to understand the avalanche growth of electrical current in a composite insulator consisting of an air gap and a solid dielectic. The results show that trapped charge can quench the electrical breakdown. The results are compared with phenomena found in dielectric barrier discharge (DBD) devices. © 2011 IEEE.

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This article 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 article examines the enhancements for these unstable orbits when the opposing mirrors are convex, constructing the high-frequency field in the scar region using elliptic cylinder coordinates in combination with a random reflection phase from the outer chaotic region. The enhancements when the cavity is symmetric as well as asymmetric about the orbit are examined. © Taylor & Francis Group, LLC.

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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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This report constructs simple circuit models for a hairpin shaped resonant plasma probe. Effects of the plasma sheath region surrounding the wires making up the probe are determined. Electromagnetic simulations of the probe are compared to the circuit model results. The perturbing effects of the disc cavity in which the probe operates are also found.

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.

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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.

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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 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.

This report discusses a set of verification test cases for the frequency-domain, boundary-element, electromagnetics code Eiger based on the analytical solution of plane wave scattering from a sphere. Three cases will be considered: when the sphere is made of perfect electric conductor, when the sphere is made of lossless dielectric and when the sphere is made of lossy dielectric. We outline the procedures that must be followed in order to carefully compare the numerical solution to the analytical solution. We define an error criterion and demonstrate convergence behavior for both the analytical and numerical cases. These problems test the code's ability to calculate the surface current density and secondary quantities, such as near fields and far fields.

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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.

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.

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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