A two-step methodology for predicting the radiated fields from lines radiating in the presence of conductor-backed substrates is presented. The method employs the use of transmission line theory to find the current distributions on the lines forming the interconnects of a circuit. These currents are used to evaluate the far-fields of the circuit through the use of dipole theory and superposition. The method was tested and validated by comparison to full-wave models. Investigations established that radiation from common-mode currents, which are not accounted for by the circuit analysis, are found to be dominated by the radiation due to differential mode currents, and thus EMI prediction based on the two-step methodology is found to have good engineering accuracy. A full-wave method based on the Finite-Difference Time-Domain (FDTD) is presented for the evaluation of radiation from structures of such geometrical complexity that the transmission line model is not applicable. The Perfectly Matched Layer truncation scheme is implemented in the FDTD and investigated for radiating structures found in printed circuit boards (PCBs). Proximity effects of the PML dictate careful attention to the proper implementation of this absorbing boundary condition. Also, the FDTD subcell model for thin wires is investigated for modelling thin microstrip interconnect lines. To evaluate the far-fields from radiating structures found in multilayer electronic packages, a novel near-to-far field transform at a single frequency is developed and implemented for sources in stratified medium. This transform is validated and investigated with regard to PML and structure proximity. The near-to-far field transform is also implemented in a methodology for obtaining the radiated emissions from a radiating structure. This methodology is used to address important concerns regarding the grounding of heat sinks, "floating" conducting planes, and the electromagnetic behavior of split ground planes.

In many applications it is necessary to determine coupling from a line current source to a nearby wire. Applications include current coupling in high-speed interconnects and wire interaction with a charged particle beam. A common physical configuration occurs when the source and wire are perpendicular to each other. In this dissertation, we investigate the scattered field and coupled current that result from such a configuration. We solve the problem for three different sources: a dipole, an array of dipoles, and a continuous line current. We detail the solution for the line current source where we obtain the scattered field by numerical integration, the far-zone approximation using steepest descents, and the excited current by numerical integration. We also show that the solution of an infinite number of phased dipoles approaches the continuous line source excitation. For the continuous line source case, we assume an infinite traveling wave line current. We also assume that the current magnitude and phase are not affected by the existence of the nearby wire. The current travels with a speed less than the speed of light in the surrounding medium. The wire is infinitely long and infinitesimally thin, and is located a distance d from the line source. We solve for the scattered field both numerically and approximately using steepest descents. We then add corrections to the saddle point approximation through two different approaches. We also solve numerically for the coupled current on the wire. Finally, we produce plots that allow us to compare the levels of the field with and without the wire present. Our problem could serve as a prelude to investigation of a traveling wave of current and an array of parallel wires. However, such a problem is quite different since the physical configuration would then allow the presence of guided waves.

The formation and propagation of hotspots in a cylindrical medium that is undergoing microwave heating is studied in detail. A mathematical model developed by Garcia-Reimbert, C., Minzoni, A. A. and Smyth, N. in Hotspot formation and propagation in Microwave Heating, IMA, Journal of Applied Mathematics (1996), 37, p. 165-179 is used. The model consists of Maxwell's wave equation coupled to a temperature diffusion equation containing a bistable nonlinear term. When the thermal diffusivity is sufficiently small the leading order temperature solution of a singular perturbation analysis is used to reduce the system to a free boundary problem. This approximation accurately predicts the steady-state solutions for the temperature and electric fields in closed form. These solutions are valid for arbitrary values of the electric conductivity, and thus extend the previous (small conductivity) results of Garcia-Reimbert et.al. A time-dependent approximate profile for the electric field is used to obtain an ordinary differential equation for its relaxation to the steady-state. This equation appears to accurately describe the time scale of the electric field's evolution even in the absence of a temperature front (with zero coupling to the temperature), and can be of wider interest than the model for microwave heating studied here. With sufficiently small thermal diffusivity and strong coupling, the differential equation also accurately describes the time evolution of the temperature front's location. A closed form expression for the time scale of the formation of the hotspot is derived for the first time in the literature of hotspot modeling. Finally, a rigorous proof of the existence of steady-state solutions of the free boundary problem is given by a contraction mapping argument.

Six thunderstorms that occurred at the NASA Kennedy Space Center, Florida, have been studied in an attempt to characterize their electrical structure and electrification. Ground-based measurements of the cloud electric fields, the locations of lightning VHF radio sources, cloud-to-ground lightning strike points, and dual-polarization radar data were used in this study. Changes in the electric field due to lightning were used to determine the locations and magnitudes of changes in cloud charge. The fields themselves were used to compute displacement current densities following lightning flashes. The altitudes of negative charge regions were between 6.5 and 8.5 km and were almost constant. The altitude of upper positive charge exhibited more variability, and usually increased as cells developed. Amounts of charge removed by lightning increased during each cell in large storms but were nearly constant during the early part of small storms. A lower positive charge center (LPCC) usually appeared in the fields before any other charge regions could be detected at the ground. A LPCC appeared to be involved in the initiation of the majority of CG flashes. During periods of lightning, a LPCC was sometimes created by a flash, but more typically, LPCCs were produced by a cloud charge separation process. Displacement current densities were used to estimate charge accumulation rates in the cloud. The rates derived for the main negative and upper positive charge regions were compared to the average rate of charge removal by lightning. The generation rates and average lightning currents each had values ranging from 0.2 to 1.5 A and were approximately equal within expected errors in single-cell storms. Once the storm was multicellular, however, the lightning current was larger than the cloud charging rate, possibly because lightning was removing residual charge from older cells. The cloud charging rates and average lightning currents were compared with the currents computed using a non-inductive ice-graupel charging mechanism and radar-derived cloud microphysical data. This mechanism provided currents that were comparable to the observed charging rates and lightning currents and appeared to be capable of producing the LPCC.

In this work we solve two new matrix models, using standard and new techniques. The two models are based on matrix ensembles not previously considered. They are represented by special forms of antisymmetric matrices and are classified in the DIII generator ensemble. It is shown that, in the double scaling limit, their free energy has the same behavior as previous models describing oriented and unoriented surfaces. We also found an additional solution for the chapter 3 model.

<p> Edge magnetoplasmons (EMPs) and pinning mode resonances in two dimensional electron systems (2DESs) can both be thought of as lower hybrid modes of cyclotron and plasma resonances. This dissertation describes low temperature microwave spectroscopy of both of these modes. EMPs have oscillating charge confined at the 2DES edge by the combination of the perpendicular magnetic field and the electrostatic potential that produces the edge. Pinning mode resonances are from electron solids oscillating against confinement provided by disorder in the bulk of the 2DES. </p><p> The first part of this dissertation concerns the search for a mode similar to an EMP but confined solely by a linear magnetic inhomogeneity in the perpendicular magnetic field (<i>B_z</i>). While we do not observe such an excitation, we do observe a marked reduction in the velocity of an EMP in the presence of a <i>B_z</i>-inhomogeneity. </p><p> In the second part of this dissertation, we investigate pinning modes in &ldquo;wide'' quantum well samples, for which the effective electron-electron interaction is softened at short range due to the vertical extent of the wavefunction. We observe a pinning mode resonance whose peak frequency (<i>f_pk</i>) vs Landau level filling (&nu;) shows an anomalous increase as &nu; moves away from &nu; = 1 under roughly the same conditions as anomalous quantum Hall effects observed previously in DC transport. A region of &nu; with enhanced <i>f_pk</i> is interpreted as evidence for a new electron solid phase.</p>

<p> This dissertation proposes three novel bandpass filter structures to protect systems exposed to damaging levels of electromagnetic (EM) radiation from intentional and unintentional high-power microwave (HPM) sources. This is of interest because many commercial microwave communications and sensor systems are unprotected from high power levels. Novel technologies to harden front-end components must maintain existing system performance and cost. The proposed concepts all use low-cost printed circuit board (PCB) fabrication to create compact solutions that support high integration.</p><p> The first proposed filter achieves size reduction of 46% using a technology that is suitable for low-loss, narrowband filters that can handle high power levels. This is accomplished by reducing a substrate-integrated waveguide (SIW) loaded evanescent-mode bandpass filter to a half-mode SIW (HMSIW) structure. Demonstrated third-order SIW and HMSIW filters have 1.7 GHz center frequency and 0.2 GHz bandwidth. Simulation and measurements of the filters utilizing combline resonators prove the underlying principles.</p><p> The second proposed device combines a traditional microstrip bent hairpin filter with encapsulated gas plasma elements to create a filter-limiter: a novel narrowband filter with integral HPM limiter behavior. An equivalent circuit model is presented for the ac coupled plasma-shell components used in this dissertation, and parameter values were extracted from measured results and EM simulation. The theory of operation of the proposed filter-limiter was experimentally validated and key predictions were demonstrated including two modes of operation in the on state: a constant output power mode and constant attenuation mode at high power. A third-order filter-limiter with center frequency of 870 MHz was demonstrated. It operates passively from incident microwave energy, and can be primed with an external voltage source to reduce both limiter turn-on threshold power and output power variation during limiting. Limiter functionality has minimal impact on filter size, weight, performance, and cost.</p><p> The third proposed device demonstrates a large-area, light-weight plasma device that interacts with propagating X-band (8-12 GHz) microwave energy. The structure acts as a switchable EM aperture that can be integrated into a radome structure that shields enclosed antenna(s) from incident energy. Active elements are plasma-shells that are electrically excited by frequency selective surfaces (FSS) that are transparent to the frequency band of interest. The result is equivalent to large-area free-space plasma confined in a discrete layer. A novel structure was designed with the aid of full-wave simulation and was fabricated as a 76.2 mm square array. Transmission performance was tested across different drive voltages and incidence angles. Switchable attenuation of 7 dB was measured across the passband when driven with 1400 V_pp at 1 MHz. Plasma electron density was estimated to be 3.6 &times; 10¹² cm^-3 from theory and full-wave simulation. The proposed structure has potential for use on mobile platforms.</p>

<p> Electromagnetic equations pertaining to electrically small dipole antennas and electrically small monopole antennas with small circular ground planes are reviewed. Two electrically small antenna designs are analyzed numerically and the results are compared. The first is a frequency agile version of the two-dimensional (2D) planar Egyptian axe dipole (EAD) antenna. The second is its three-dimensional (3D) counterpart. The frequency agile performance characteristics of both the 2D and 3D EAD designs are studied and compared. The potential for non-Foster augmentation to achieve large instantaneous fractional impedance bandwidths is detailed for each antenna. In addition, details are given on how to run frequency agile simulations in both ANSYS HFSS and Agilent's ADS. Details are also provided on how to generate an antenna's non-Foster |S₁₁| and radiation efficiency curves using HFSS, and how to generate an antenna's non-Foster |S₁₁| curve using ADS. </p>

Dielectric losses and dielectric constants at radio frequencies for nitrobenzene, water and xylene. The method of resistance variation was used to measure the phase difference psi and dielectric constant K for frequencies between 2 x 105 and 14 x 105 cycles/sec. Special cells were required. (1) Variation with frequency. The results agree approximately with the equations: For carefully dried nitrobenzene at 30&deg;C, psi = .028&deg; + 6.03 x 104/f; for distilled water at 23.5&deg;, psi = 0.8&deg; + 2.09 x 106/ f. These indicate that in addition to the true dielectric loss there is a leakage through the liquid proportional to 1/f. For xylene, psi was too small to measure, less than .01&deg; at 3 x 10 5 cycles. K was found to be practically independent of the frequency, being 2.24 for xylene and of the order of 100 for water. (2) Variation with temperature, for nitrobenzene. K decreased from 42 at 20&deg; to 24 at 14.2&deg;, while psi increased in the same range in the ratio of 7 to 1. These values were obtained, however, for a sample of nitrobenzene for which psi was 12 times as great as for a carefully dried sample.

Interchange instability is an important dynamic mechanism in plasma physics and has been advanced as an explanation of a variety of phenomena in the magnetospheric physics. This work derives a new instability criterion for interchange motion in a plasma that connects to a finite-conductivity wall. The new criterion is for a arbitrary magnetic &lt;beta> (ratio between thermal pressure and magnetic pressure averaged within flux tube) system, which contains background shear flow, whereas most classical criteria did not consider all of these conditions. Thus this new result is more appropriate to be applied in a real plasma system like the Earth's plasma sheet, which exhibits a wide range of &lt;beta> values and background shear flow. Based on magnetosphere-ionosphere coupling theory and ideal MHD adiabatic theory in the inner plasma sheet, a theoretical model was constructed in the ionosphere region. A finite boundary layer was set up between two regions of uniform-content flux tubes, and a perturbation on the boundary layer was investigated. Both analytical and numerical approaches are used to study the stability of the plasma configuration. The flux tubes are interchange unstable when the angle between the gradient of flux tube volume, defined as V = dsB , and the gradient of adiabatic specific entropy PV 5/3 is larger than arccos&lt;b&gt; 1lnPV5/3 1ln V/ 21+5&lt;b&gt;/6 . Combining this new criterion with the statistical calculation of the plasma sheet characteristics by using the Tsyganenko magnetic field model (the 1996 version) and the Tsyganenko-Mukai plasma model, it is found that, in the Earth's inner plasma sheet, the angle between the two gradients is typically of the order of 15&deg;, which indicates that the statistical-average Earth's plasma sheet is interchange stable. This result is applicable to the study of interchange instability and plasma transport in the global-MHD and other large-scale magnetosphere simulations, and provides a theoretical base for the study of analogous dynamic processes in the magnetospheres of other planets like Jupiter.