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Thesis--University of Michigan, 1971.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 235-242).

Le but de cette thèse est d'améliorer les techniques d'analyse de données de la réflectométrie à balayage de fréquence pour la détermination du profil de densité des plasmas de fusion. Au cours des deux dernières décennies, des améliorations significatives ont été apportées sur la partie matérielle et sur d'extraction des signaux, mais l'analyse des données est en retard et nécessite d'autres améliorations pour répondre aux spécifications exigées pour un fonctionnement en continu des futurs réacteurs. Les améliorations obtenues lors de ce travail de thèse sur la reconstruction des profils de densité fournissent une meilleure précision en un temps plus court ceci même en présence de trou de densité conduisant à une mesure des propriétés de la turbulence suffisamment précise pour valider des modèles numériques et permettant la surveillance en temps réel de la forme et de la position du plasma / The goal of this PhD is to improve the data analysis techniques of frequency swept reflectometry for determination of the density profile of fusion plasmas. There has been significant improvements in the last two decades on the hardware design and signal extraction techniques, but the data analysis is lagging behind and require further improvements to meet the required standards for continuous operation in future reactors. The improvements obtained in this thesis on the reconstruction of density profiles provide a better accuracy in a shorter time, even in the presence of a density hole, also enabling sufficiently precise measurements of the properties of turbulence used to validate numerical models, and allowing real-time monitoring of the shape and position of the plasma

<p dir="ltr">Calculating space-charge limited current (SCLC) is a critical problem in plasma physics and intense particle beams. Accurate calculations are important for validation and verification of particle-in-cell (PIC) simulations. The theoretical assessment of SCLC is complicated by the nonlinearity of the Poisson equation when combined with the energy balance and continuity equations. This dissertation provides several theoretical tools to convert the nonlinear Poisson equation into a corresponding linear differential equation, which is then solved for numerous geometries of practical interest.</p><p dir="ltr">The first and second chapters briefly summarize the application of variational calculus (VC) to solve for one-dimensional (1D) SCLC in cylindrical and spherical diode geometries by extremizing the current in the gap. Next, conformal mapping (CM) is presented to convert the concentric cylindrical diode geometry into a planar geometry to obtain the same SCLC solution as VC. In the next chapter, SCLC is determined for several geometries with curvilinear electron flow that cannot be solved using VC because the Poisson equation cannot be written easily. We then map a hyperboloid tip onto a plane to form a non-Euclidean disk (Poincaré disk). These mappings on to Poincaré disk are utilized to solve for SCLC in tip-to-tip and tip-to-plane geometries. Lie symmetries are then introduced to solve for SCLC with nonzero monoenergetic injection velocity, recovering the solutions for concentric cylinders, concentric spheres, tip-to-plane, and tip-to-tip for zero injection velocity. We then extend the SCLC calculations to account for any geometry in multiple dimensions by using VC and vacuum capacitance. First, we derive a relationship between the space-charge limited (SCL) potential and vacuum potential that holds for any geometry. This relationship is utilized to obtain exact closed-form solutions for SCLC in two-dimensional (2D) and three-dimensional (3D) planar geometries considering emission from the full surface of the cathode. PIC simulations using VSim were performed that agreed with the SCLC in 2D diode with a maximum error of 13%. In the final chapters, we extend these multidimensional SCLC calculations to nonzero monoenergetic emission. The SCLC in any orthogonal diode in any number of dimensions is obtained by relating it to the vacuum capacitance. The current in the bifurcation regime is also derived from first-principles from vacuum capacitance. The simulations performed in VSim agreed with the theory with a maximum error of 7%.</p><p dir="ltr">These mathematical techniques form a set of powerful tools that extend prior studies by yielding exact and approximate SCLC in numerous nonplanar and multidimensional diode geometries, thereby not requiring expensive and time-consuming PIC simulations. While more experiments are required to benchmark the validity of these calculations, these results may ultimately prove useful by providing a rapid first-principles approach to determine SCLC for many geometries that can be used to assess the validity of PIC simulations and facilitate multiphysics simulations.</p>

Thesis (Ph.D.)--Mechanical Engineering, Georgia Institute of Technology, 2008. / Committee Co-Chair: Minami Yoda, Co-Advisor; Committee Co-Chair: Said I. Abdel-Khalik; Committee Member: Donald R. Webster; Committee Member: Narayanan M. Komerath; Committee Member: S. Mostafa Ghiaasiaan; Committee Member: Yogendra Joshi

<p dir="ltr">This dissertation reports experiments and simulations of micro-/nanoscale electrical breakdown, connects them to the microscale breakdown theories, relates them to field emission and space-charge-limited conditions, and demonstrates the modification of the approach to microwave fields. It provides the first comprehensive experimental assessment of the transitions between electron emission and gas breakdown mechanisms at microscale and nanoscale and extension of semi-empirical laws for ionization process in DC and microwave. These findings will be valuable in developing theories to predict electron emission and gas breakdown mechanisms, which provides guidance for nanoscale device design.</p>

<p dir="ltr"> Conventional RF switching technologies struggle to simultaneously achieve high-power handling, low loss, high isolation, broadband operation, quick reconfiguration, high linearity, and low cost, which are desirable for many applications, including communications, radar, and sensors. Moreover, they require electrical bias networks, which degrade performance and, in many cases, inhibit wideband applications, including DC operation. On the other hand, plasma (photoconductive) switches use an optical bias to generate free charge carriers. Recently these switches have begun to not only rival conventional technologies in terms of performance metrics such as switching speeds and loss but have exceeded what is possible in terms of power handling. This work details the strides made in placing solid-state plasma technologies at the forefront of advanced, high-power switching applications including a novel high-power tuner and an absorptive/reflective SPnT switch. In various form factors, SSP has achieved analog control of loss as low as 0.09 dB and isolation as high as 54 dB, linearity of 68.8 dBm (IP3), 110 GHz instantaneous bandwidth, including DC, switching speeds as low as 3.5 us, 100+ W power handling, and 30+ W hot switching. In addition, comprehensive physics modeling has been developed to enable seamless design validation before fabrication commences. This thesis discusses the achievements and design considerations for creating optimized plasma switches and proposes a path for future applications.</p>

<p>  </p> <p>Electron emission plays a vital role in many modern technologies, from plasma medicine to heavy ion beams for fusion. An accurate theoretical model based upon the physics involved is critical to efficient operation of devices pushing the boundaries of complexity. The interactions between different electron emission mechanisms can severely alter device performance, especially when operating in extreme conditions. This dissertation studies electron emission from the perspectives of increasing geometric and physical mechanism complexities </p> <p>One half of this dissertation derives new relations for space-charge limited emission (SCLE) in non-planar geometries. SCLE is the maximum stable current that may be produced by electron emission before the electric field of the electrons themselves self-limits further emission. In planar devices, this is modeled by the well-established Child-Langmuir (CL) equation. The Langmuir-Blodgett (LB) equations remain the most commonly accepted theory for SCLE for cylindrical and spherical geometries after nearly a century; however, they suffer from being approximations based on a polynomial series expansion fit to a nonlinear differential equation. I derive exact, fully analytic equations for these geometries by using variational calculus to transform the differential equation into a new form that is fully and exactly solvable. This variational approach may be extended to any geometry and offers a full description of the electric field, velocity, and charge density profiles in the diode. </p> <p>SCLE is also an important mechanism for characterizing the operation of devices with an external magnetic field orthogonal to the electric field. This “crossed-field” problem decreases the limiting current as electrons travel longer, curved paths, effectively storing some charge in the gap (moving parallel to the emitter). At a critical magnetic field called the Hull cutoff, electron paths become so tightly curved that the circuit can no longer be completed, a condition called magnetic insulation. Crossed-field SCLE has been accurately modeled in planar devices by Lau and Christenson. Using the variational approach, I replicate their planar results and extend the calculation to cylindrical geometry, a common choice for magnetron devices. Further, I derive additional equations with simplified assumptions that, for the first time, provide an analytic description of experimental results below the Hull cutoff field. Following this I incorporate a series resistor: device resistance (or impedance) changes non-linearly with current and voltage, so I couple Ohm’s Law (OL) to all the models of crossed-field devices. For devices just below the Hull cutoff, I predict analytically and show in simulation novel bi-modal behavior, oscillating between magnetically insulated and non-insulated modes. With crossed-field device assessment, the variational calculus approach to space-charge may be used for numerous applications, including high power microwave sources, relativistic klystron devices, heavy ion beams, Hall thrusters, and plasma processing. </p> <p>The other half of this dissertation derives analytic theories to solve for emission current with three or more electron emission mechanisms simultaneously. In addition to the CL law, SCLE may also occur in neutral, non-vacuum diodes, modeled by the Mott-Gurney (MG) equation. These are the two limiting mechanisms I study; the other major modality of electron emission is direct electron production, the source of current in the device. Electrons are ejected when impelled by high temperature or electric field at the emission surface. These mechanisms are thermionic (or thermal) emission, modeled by the Richardson-Laue-Dushman (RLD) equation, and field emission, modeled by the Fowler-Nordheim (FN) equation, respectively. Additionally, just as I calculated the impedance of devices operating in a crossed-field configuration, all these models can be similarly coupled to OL. I derive models unifying FN, MG, and CL (with an extension linking OL, mentoring an undergraduate) and RLD, FN, and CL. These models are relevant for modern device design, especially as micro- and nano-scale devices seek to eliminate vacuum requirements and as space and military applications require higher temperature tolerances.</p> <p>While multi-physics models, like the ones described above, are important, the single-physics models (FN, RLD, MG, CL, OL) are still valid (and much easier to use) in their respective asymptotic limits. For example, a circuit behaves purely according to OL for very high resistances, according to MG for very high pressures, and so forth. Importantly, when devices operate in transition regions between these asymptotic limits, <em>none </em>of the asymptotic equations match the predictions of multi-physics models. Yet, intersections between the asymptotic equations are easily found, say for a certain set of voltage, gap distance, and pressure, CL=MG. Since both asymptotic equations give the same prediction, we may conclude that both must be inaccurate for those physical parameters! This gives rise to what I term “nexus theory:” solving two or more asymptotic equations simultaneously to rapidly and accurately predict sets of physical parameters at which multi-physics models (specifically, the physics leading to the “nexus point” parameters, points or curves at which nexus conditions are satisfied) are required for accurate device predictions. In fact, I show that multi-physics models are necessary within roughly one to two orders of magnitude from a nexus. In effect, nexus theory provides a simple, powerful tool to determine how complex a model is necessary for a particular device. Both nexus theory and multi-physics results in this dissertation have been successfully used to design devices to operate in specific transition regimes and identify the resulting device behavior.  </p>

<p dir="ltr">Understanding the acceleration of particles responsible for high-energy non-thermal phenomena in astrophysical jets is a ubiquitous pursuit. A possible culprit for non-thermal particle acceleration is turbulence. Specifically in this thesis, I investigate highly magne- tized or relativistic turbulence, where the magnetic energy to enthalpy ratio of the plasma is much greater than one, as a possible high-energy accelerator inside relativistic jets. I do this through three distinct projects. </p><p dir="ltr">My first project [1] (discussed in Section 3) was built upon a recent study of relativistic turbulence from [2], which found that a non-thermal particle equilibrium can be achieved when a plasma is heated via turbulence but allowed to cool radiatively. I extrapolated these results from PIC (Particle-in-Cell) simulations to larger scales and magnetizations, allowing me to encode key microphysical results of PIC simulations into a Fokker-Planck formalism. Combining these results with a single zone model for a blazar jet, I successfully define the underlying particle distribution with the global parameters of the emission region. To test this model, I fit data from 12 sources and successfully constrain key blazar parameters such as magnetization, bulk Lorentz factor, emission region size, and distance from the central engine. </p><p dir="ltr">My second project covers the development and testing of the open-source toolkit Tleco. This code base was used to evolve the Fokker-Planck equation and solve the resultant emission in my first project. Tleco offers efficient algorithms for evolving particle distributions and solving the resultant emission. It is meant to be user-friendly and easily customizable. </p><p dir="ltr">My third project attempts to enhance our understanding of coherent structures in relativistic turbulence. I employ intermittency analysis to establish a link between statistical fluctuations within the plasma and regions of high-energy dissipation. To achieve this, we used first-principle turbulent PIC simulations across a range of magnetizations and fluctuating magnetic field values. By utilizing the statistical fluctuations to determine the fractal dimension of the structures, I then examine their filling fraction and its dependence on magnetization and the fluctuating magnetic field.</p>