<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>

Foi projetado, construído e instalado um sistema bolométrico para a análise das descargas de plasma do TCABR. Este sistema possibilita a observação da coluna de plasma através de cordas caracterizadas por diferentes direções e ângulos. Os bolômetros utilizados são fotodiodos especiais, acondicionados em câmeras dotadas de colimadores para observação do plasma. A faixa espectral da sensibilidade dos fotodiôdos abrange desde o visível até a região de raios-X moles, energia de fótons desde 7 eV até 6.000 eV. Para este diagnóstico, foi construída uma eletrônica específica para amplificação dos sinais bolométricos. A resolução temporal do diagnóstico é de 3 ms devido a interferência gerada pelo tokamak. Com este sistema, foi obtido pela primeira vez no TCABR, o perfil da potência emitida pela coluna de plasma, sendo este o principal resultado deste trabalho. Para isto, foi desenvolvido um programa destinado a inverter os dados bolométricos utilizando como princípio o método de Abel. Uma série de descargas ôhmicas ( 0,9 X \"10 POT.19\" < ne < 2,0 X 10 POT.19\" \"m POT.3\" e 67 < \"I IND.p\" < 100 kA) foram estudadas com o diagnóstico. Obteve-se para o volume da coluna uma fração Prad/Poh não maior que 30%, valor semelhante ao obtido para o tokamak TCA. Observou-se também diferenças acentuadas para o perfil de potência emitido por descargas com baixos e altos valores da corrente de plasma. Estas diferenças são atribuídas principalmente ao aumento da temperatura eletrônica. A concentração de impurezas metálicas foi calculada no eixo da coluna, obtendo-se valores entre 0,9-1,2 X \"10 POT.17\" \"m POT.-3\" / In this work, a bolometric diagnostic system was projected, built and installed in the TCABR tokamak, in order to measure the total power radiation loss from the plasma. The system allows plasma observation through 27 lines of sight with different directions and angles. The detector used was a silicon p-n junction photodiode array, for applications in the vacuum ultraviolet and the soft x-ray (XUV, energy range 7 eV to 6 keV) spectral region. An electronic system for amplification of the bolometer signal was also projected and built. This system was projected taking into account the strong electromagnetic noise due to the tokamak operation. Using this bolometric system, the shape of the emitted power was obtained for the first time in the TCABR, and this is the main result of this work. To deal with the bolometric data, we developed a program based on the Abel inversion. A serie of ohmic discharges were studied with this diagnostic. The value of the Prad/Poh obtained for this serie was below 30%, in agreement with the old TCA data. The shape for discharges with high and low plasma current were also analyzed. We find a big difference in the two cases, showing the effect of electron temperature change. The metallic impurity density on axis were calculated using the value of Prad(0) experimentally obtained. For the serie of discharges analyzed, this value remained between 0,9-1,2 X \"10 POT.17\" \"m POT.-3\"

Neste trabalho foi realizado um estudo do transporte de partículas em um plasma, confinado em um campo magnético uniforme, devido às ondas eletrostáticas de deriva. O modelo adotado consiste em descrever o movimento do centro de guia de uma partícula no campo magnético perpendicular a um campo elétrico radial perturbado pelas ondas de deriva. Usamos uma descrição Hamiltoniana para o movimento dos centros de guia. A velocidade de deriva produzida pelo campo elétrico radial é representada pela parte integrável da Hamiltoniana e a esta foram adicionadas perturbações periódicas representando as flutuações do campo elétrico associadas às ondas de deriva. Assim, obtemos órbitas caóticas que determinam o transporte radial das partículas. Apresentamos, para várias condições de equilíbrio, a variação do transporte radial de partículas com a amplitude da perturbação. Utilizamos dados experimentais, sobre a turbulência eletrostática no tokamak TBR-1, para verificar a validade do modelo e a importância das ondas de deriva no transporte radial das partículas. Comparamos os valores do coeficiente de difusão experimental com os do modelo e obtivemos os resultados com a mesma ordem de grandeza. / In this work we have studied the transport of particles in a magnetically confined plasma, due to electrostatic drift waves. The adopted model describes the trajectory of the guiding center of a particle in a uniform magnetic field perpendicular to a radial electric field perturbed by drift waves. We have used the Hamiltonian description for the guiding center trajectory. The drift produced by the radial electric field is represented by the integrable part of the Hamiltonian, while the other part contains periodic perturbations representing the fluctuations of the electric field associated to the drift waves. In this way we obtain chaotic orbits that determine the particles radial transport. For several balance conditions, we present the variation of the radial transport of particles with the amplitude of the perturbation. V/e have used the experimental data of the electrostatic turbulence measured in TBR-1 tokamak to verify, the validity of the model and the importance of the drift waves in the particles radial transport. We have also compared the values of the experimental diffusion coefficient with those provided by using the model, obtaining results with the same order of magnitude.

Neste trabalho foi realizado um estudo do transporte de partículas em um plasma, confinado em um campo magnético uniforme, devido às ondas eletrostáticas de deriva. O modelo adotado consiste em descrever o movimento do centro de guia de uma partícula no campo magnético perpendicular a um campo elétrico radial perturbado pelas ondas de deriva. Usamos uma descrição Hamiltoniana para o movimento dos centros de guia. A velocidade de deriva produzida pelo campo elétrico radial é representada pela parte integrável da Hamiltoniana e a esta foram adicionadas perturbações periódicas representando as flutuações do campo elétrico associadas às ondas de deriva. Assim, obtemos órbitas caóticas que determinam o transporte radial das partículas. Apresentamos, para várias condições de equilíbrio, a variação do transporte radial de partículas com a amplitude da perturbação. Utilizamos dados experimentais, sobre a turbulência eletrostática no tokamak TBR-1, para verificar a validade do modelo e a importância das ondas de deriva no transporte radial das partículas. Comparamos os valores do coeficiente de difusão experimental com os do modelo e obtivemos os resultados com a mesma ordem de grandeza. / In this work we have studied the transport of particles in a magnetically confined plasma, due to electrostatic drift waves. The adopted model describes the trajectory of the guiding center of a particle in a uniform magnetic field perpendicular to a radial electric field perturbed by drift waves. We have used the Hamiltonian description for the guiding center trajectory. The drift produced by the radial electric field is represented by the integrable part of the Hamiltonian, while the other part contains periodic perturbations representing the fluctuations of the electric field associated to the drift waves. In this way we obtain chaotic orbits that determine the particles radial transport. For several balance conditions, we present the variation of the radial transport of particles with the amplitude of the perturbation. V/e have used the experimental data of the electrostatic turbulence measured in TBR-1 tokamak to verify, the validity of the model and the importance of the drift waves in the particles radial transport. We have also compared the values of the experimental diffusion coefficient with those provided by using the model, obtaining results with the same order of magnitude.

Foi projetado, construído e instalado um sistema bolométrico para a análise das descargas de plasma do TCABR. Este sistema possibilita a observação da coluna de plasma através de cordas caracterizadas por diferentes direções e ângulos. Os bolômetros utilizados são fotodiodos especiais, acondicionados em câmeras dotadas de colimadores para observação do plasma. A faixa espectral da sensibilidade dos fotodiôdos abrange desde o visível até a região de raios-X moles, energia de fótons desde 7 eV até 6.000 eV. Para este diagnóstico, foi construída uma eletrônica específica para amplificação dos sinais bolométricos. A resolução temporal do diagnóstico é de 3 ms devido a interferência gerada pelo tokamak. Com este sistema, foi obtido pela primeira vez no TCABR, o perfil da potência emitida pela coluna de plasma, sendo este o principal resultado deste trabalho. Para isto, foi desenvolvido um programa destinado a inverter os dados bolométricos utilizando como princípio o método de Abel. Uma série de descargas ôhmicas ( 0,9 X \"10 POT.19\" < ne < 2,0 X 10 POT.19\" \"m POT.3\" e 67 < \"I IND.p\" < 100 kA) foram estudadas com o diagnóstico. Obteve-se para o volume da coluna uma fração Prad/Poh não maior que 30%, valor semelhante ao obtido para o tokamak TCA. Observou-se também diferenças acentuadas para o perfil de potência emitido por descargas com baixos e altos valores da corrente de plasma. Estas diferenças são atribuídas principalmente ao aumento da temperatura eletrônica. A concentração de impurezas metálicas foi calculada no eixo da coluna, obtendo-se valores entre 0,9-1,2 X \"10 POT.17\" \"m POT.-3\" / In this work, a bolometric diagnostic system was projected, built and installed in the TCABR tokamak, in order to measure the total power radiation loss from the plasma. The system allows plasma observation through 27 lines of sight with different directions and angles. The detector used was a silicon p-n junction photodiode array, for applications in the vacuum ultraviolet and the soft x-ray (XUV, energy range 7 eV to 6 keV) spectral region. An electronic system for amplification of the bolometer signal was also projected and built. This system was projected taking into account the strong electromagnetic noise due to the tokamak operation. Using this bolometric system, the shape of the emitted power was obtained for the first time in the TCABR, and this is the main result of this work. To deal with the bolometric data, we developed a program based on the Abel inversion. A serie of ohmic discharges were studied with this diagnostic. The value of the Prad/Poh obtained for this serie was below 30%, in agreement with the old TCA data. The shape for discharges with high and low plasma current were also analyzed. We find a big difference in the two cases, showing the effect of electron temperature change. The metallic impurity density on axis were calculated using the value of Prad(0) experimentally obtained. For the serie of discharges analyzed, this value remained between 0,9-1,2 X \"10 POT.17\" \"m POT.-3\"

<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>

Desenvolvemos urna teoria cinética para urna mistura de gases ionizados em presença de campos elétricos e magnéticos. As leis de Ohm, Fourier e Navier-Stokes são obtidas por dois métodos distintos que se baseiam na equação de Boltzmann. Verificamos que o emprego de teoremas de representação torna o método de Chapman-Enskog mais direto. Entretanto o método combinado mostrou-se extremamente simples, onde os coeficientes de transporte são determinados através da inversão de tensores de segunda e quarta ordens. Calculamos também a integral de colisão para as possíveis interações em gases ionizados tais como, entre partículas carregadas, partícula carregada e partícula neutra e entre partículas neutras. Como uma aplicação do método combinado, determinamos os coeficientes de condutividade elétrica, condutividade térmica, coeficiente termo-elétrico e o coeficiente de viscosidade cisalhante para um gás totalmente ionizado. Obtemos seus respectivos gráficos, considerando então um gás ionizado formado a partir do gás de hélio. / We develop a kinetic theory for ionized gases mixtures under the presence of electric and magnetic fields. The laws of Ohm, Fourier and Navier-Stokes are obtained by two different methods based on the Boltzmann equation. We verify that the use of representation theorems makes the Chapman-Enskog method more direct. However the combined method shows up as extremely simple where the transport coefficients are determined through inversion of second-order and fourth order tensors. We calculate also the collision integrals for possible interactions in ionized gases like: between charged particles, between charged particles and neutral particles and between neutral particles. As an application of the combined method, we determine the electrical and thermal conductivity coefficients, thermo-electric and shear viscosity coefficients for a completely ionized gas. We obtain their respective graphics considering an ionized gas of helium.

Desenvolvemos urna teoria cinética para urna mistura de gases ionizados em presença de campos elétricos e magnéticos. As leis de Ohm, Fourier e Navier-Stokes são obtidas por dois métodos distintos que se baseiam na equação de Boltzmann. Verificamos que o emprego de teoremas de representação torna o método de Chapman-Enskog mais direto. Entretanto o método combinado mostrou-se extremamente simples, onde os coeficientes de transporte são determinados através da inversão de tensores de segunda e quarta ordens. Calculamos também a integral de colisão para as possíveis interações em gases ionizados tais como, entre partículas carregadas, partícula carregada e partícula neutra e entre partículas neutras. Como uma aplicação do método combinado, determinamos os coeficientes de condutividade elétrica, condutividade térmica, coeficiente termo-elétrico e o coeficiente de viscosidade cisalhante para um gás totalmente ionizado. Obtemos seus respectivos gráficos, considerando então um gás ionizado formado a partir do gás de hélio. / We develop a kinetic theory for ionized gases mixtures under the presence of electric and magnetic fields. The laws of Ohm, Fourier and Navier-Stokes are obtained by two different methods based on the Boltzmann equation. We verify that the use of representation theorems makes the Chapman-Enskog method more direct. However the combined method shows up as extremely simple where the transport coefficients are determined through inversion of second-order and fourth order tensors. We calculate also the collision integrals for possible interactions in ionized gases like: between charged particles, between charged particles and neutral particles and between neutral particles. As an application of the combined method, we determine the electrical and thermal conductivity coefficients, thermo-electric and shear viscosity coefficients for a completely ionized gas. We obtain their respective graphics considering an ionized gas of helium.

<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>