[pt] Este estudo apresenta um método computacional para modelar campos eletromagnéticos em guias de onda retangulares curvados com seção transversal uniforme, usando o método variacional de Rayleigh-Ritz. Potenciais aplicações desta pesquisa em engenharia incluem o projeto de alimentadores para antenas, conversores de modais na faixa de micro-ondas, filtros, entre outros. Embora vários modelos tenham sido propostos para resolver este problema, as técnicas numéricas convencionais baseadas em elementos finitos, diferenças finitas e volumes finitos requerem altos custos computacionais. Para superar esses problemas, foi desenvolvida uma formulação variacional para resolver as equações de Maxwell em um sistema de coordenadas toroidal local, por meio de um novo funcional introduzido neste trabalho. O funcional foi adaptado para domínios uniformemente curvados com seção transversal arbitrária, e investigações analíticas foram conduzidas para confirmar suas características estacionárias. O formalismo Rayleigh-Ritz foi utilizado para converter o funcional em um problema equivalente de autovalores e autovetores, usando uma expansão em harmônicas retangulares de um guia de onda reto como funções de base para modelar um guia de onda retangular curvo. Um algoritmo numérico foi desenvolvido em Matlab para validar nosso modelo, e os resultados foram comparados com soluções perturbacionais e numéricas de referência, demonstrando alta precisão e menor custo computacional. / [en] This study presents a computational method for modeling electromagnetic fields in curved rectangular waveguides with uniform cross-section, using the variational Rayleigh-Ritz method. The potential applications of this research in engineering include the design of feeders for antennas, microwave mode converter devices, filters, among others. While various models have been proposed to solve this problem, conventional numerical techniques based on finite elements, finite differences, and finite volumes require high computational costs. To overcome these issues, a variational formulation for solving Maxwell s equations in a local toroidal coordinate system was developed via a novel functional introduced in this work. The functional was adapted to handle uniformly bend domains with arbitrary cross-section, and analytical investigations were conducted to confirm its stationary characteristics. The Rayleigh-Ritz formalism was employed to convert the functional into an equivalent problem of eigenvalues and eigenvectors using an expansion in terms of rectangular harmonics of a straight waveguide as basis functions for modeling a bend rectangular waveguide. A numerical algorithm was developed in Matlab to validate our model, and the results were compared against reference perturbational and numerical solutions, demonstrating high accuracy and lower computational costs.

Wave energy converters of point absorber type have been developed and constructed. Full scale experiments have been carried out at sea and electricity has been successfully delivered. Linear permanent magnet generators together with a subsea substation and buoys of various geometric shapes have been investigated theoretically and experimentally. The design has in large extent an electronic approach, keeping the mechanical part of it as simple as possible, due to the long life span and reliability of electric components. Because of the nature of a linear generator, the internal translator with permanent magnets has a limited stroke length which will be reached when the buoy is exposed to large wave heights. Internal springs at the top and bottom of the generator prevent the translator from hitting the generator hull. Inertial forces due to the mass and velocity of the translator and the buoy and its heave added mass compresses the spring. The added mass is a rather large part of the total moving mass. Simulations of a converter with a vertical cylindrical buoy and with a toroidal buoy were conducted, as well as real sea experiments with converters with cylindrical buoys of two different sizes and a toroidal buoy. The overloads are likely to affect the design and service life of the generator, the buoy and the wire which interconnects them. Buoy shapes with as much excitation force as possible and as little heave added mass as possible were sought. A toroidal buoy caused less overloads on the generator at sea states with short wave periods and relatively large wave height, but for sea states with very long wave periods or extremely high waves, the magnitude of the overloads was mainly determined by the maximum displacement of the buoy. Snap loads on the interconnecting wire, as the slack wire tensed up after a very deep wave trough, were found to be greater but of the same order of magnitude as forces during the rest of the wave cycle. During a 4 day period at various wave conditions, two converters with cylindrical buoys proved efficiency between 11.1 % and 24.4 %. The larger buoy had 78 % larger water plane area than the other buoy which resulted in 11 % more power production. Short wave period was beneficial for the power production. Infinite frequency heave added mass was measured for a cylindrical buoy at real sea and found to be greater than the linearly calculated theoretical added mass.

Les modes de déchirement sont connus pour détériorer le confinement et limiter les performances dans les machines de fusion. Plusieurs études sur les modes de déchirements ont été menées, en incluant un degré croissant de complexité dans le modèle physique afin de mieux comprendre les observations expérimentales. Une de ces extensions est l'introduction d'une description du plasma comme un fluide à deux espèces, ions et électrons, dont les dynamiques sont fortement différentes. Un autre mécanisme physique connu pour être important est la courbure du champ magnétique non perturbé. Dans cette thèse, nous étudions les questions de la stabilité linéaire et de l'évolution non linéaire des îlots magnétiques, en présence de la courbure des lignes de champ et de la rotation diamagnétique, avec le code MHD non linéaire XTOR-2F, qui inclut le transport anisotrope de chaleur et les effets géométriques. Cette analyse est appliquée à une décharge entièrement non-inductive de Tore Supra. Ce mode d'opération est crucial pour démontrer la possibilité d'un fonctionnement continu sur un réacteur de type tokamak. Dans cette thèse, la possibilité d'une stabilisation complète des modes de déchirement par la rotation diamagnétique, en présence de la courbure toroidale des lignes de champ magnétique, est démontrée. Dans le domaine linéairement stable, le mode est métastable: le niveau de saturation dépend de la taille de l'îlot initial. Dans le domaine non linéaire, la saturation de l'îlot est fortement réduite par la rotation diamagnétique et par le nombre de Lundquist. La question de l'extrapolation des résultats obtenus vers la future generation de machines de fusion est également abordée / Tearing modes are known to deteriorate the confinement and limit plasma performance in fusion devices. Various studies of this mode have been performed lately including an increasing level of complexity in the physical description which is required for understanding of experimental observations. One of such extensions is the introduction of diamagnetic rotation into the system. Another physical mechanisms known to be important for tearing mode dynamics is the curvature of unperturbed magnetic field lines and neoclassical physics. In this thesis we investigate the issues of linear stability of the tearing modes in a presence of both curvature and diamagnetic rotation using the non linear full-MHD toroidal code XTOR-2F, which includes anisotropic heat transport, diamagnetic and geometrical effects. This analysis is applied to one of the fully non-inductive discharges on Tore-Supra. Such experiments are crucially important to demonstrate reactor scale steady state operation for the tokamak. In this thesis, the possibility of full linear stabilization of the tearing modes by diamagnetic rotation in the presence of toroidal curvature is shown. In the linearly stable domain, the mode is metastable: saturation level depends on the seed island size. In the non linear regime, the saturation of n=1, m=2 mode is found to be strongly reduced by diamagnetic rotation and by Lundquist number. The question of extrapolation of the obtained results towards future generation of fusion devices is also addressed. In particular, for ITER size machines, the toroidal curvature is expected to be more important due to higher performance factor β.

The profile of the poloidal velocity in the edge region of tokamak plasmas has been identified as playing a major role in the confinement of particles and energy. It has been suggested that a strongly sheared poloidal flow can reduce particle and energy losses by the stabilization of unstable modes and decorrelation of turbulence the edge region of the plasma. A Gundestrup probe, a Mach probe array, is used to measure both the parallel and perpendicular flow velocities in the Saskatchewan Torus-Modified (STOR-M) tokamak during several discharge conditions. It is observed that during Ohmic discharges there is no velocity shear and the direction of the parallel flow is independent of the direction of the toroidal magnetic field. During H-mode induced by a turbulent heating current pulse, a region of strong velocity shear develops in the plasma edge and an edge transport barrier develops. This results in a short period of improved particle and energy confinement with reduced fluctuation amplitudes. During electrode biasing experiments, a stainless steel biasing electrode is inserted into the plasma up to r = 82 mm and biased to +500 V relative to the vacuum chamber. It is observed that the particle confinement improves during the biasing phase while the energy confinement is degraded. A region of weak shear in the poloidal flow is observed in the plasma scrapeoff layer (SOL). The results from STOR-M are compared with results from data taken in the Czech Academy of Sciences Torus (CASTOR) tokamak during both Ohmic discharges and discharges with electrode biasing.

Resonant Magnetic Perturbation (RMP) fields produced by external control coils are considered a viable option for the suppression of Edge Localized Modes (ELMs) in present and future tokamaks. Repeated reversals of the toroidal phase of the I-coil magnetic field in RMP shot 147170 on DIII-D has generated uniquely different edge pedestal profiles, implying different edge transport phenomena. The causes, trends, and implications of RMP toroidal phase reversal on edge transport is analyzed by comparing various parameters at 0 and 60 degree toroidal phases, with an I-coil mode number of n=3. An analysis of diffusive and non-diffusive transport effects of these magnetic perturbations it the plasma edge pedestal for this RMP shot is characterized by interpreting the ion and electron heat diffusivities, angular momentum transport frequencies, ion diffusion coefficients, and pinch velocities for both phases.

The profile of the poloidal velocity in the edge region of tokamak plasmas has been identified as playing a major role in the confinement of particles and energy. It has been suggested that a strongly sheared poloidal flow can reduce particle and energy losses by the stabilization of unstable modes and decorrelation of turbulence the edge region of the plasma. A Gundestrup probe, a Mach probe array, is used to measure both the parallel and perpendicular flow velocities in the Saskatchewan Torus-Modified (STOR-M) tokamak during several discharge conditions. It is observed that during Ohmic discharges there is no velocity shear and the direction of the parallel flow is independent of the direction of the toroidal magnetic field. During H-mode induced by a turbulent heating current pulse, a region of strong velocity shear develops in the plasma edge and an edge transport barrier develops. This results in a short period of improved particle and energy confinement with reduced fluctuation amplitudes. During electrode biasing experiments, a stainless steel biasing electrode is inserted into the plasma up to r = 82 mm and biased to +500 V relative to the vacuum chamber. It is observed that the particle confinement improves during the biasing phase while the energy confinement is degraded. A region of weak shear in the poloidal flow is observed in the plasma scrapeoff layer (SOL). The results from STOR-M are compared with results from data taken in the Czech Academy of Sciences Torus (CASTOR) tokamak during both Ohmic discharges and discharges with electrode biasing.

Multilayered metallo-dielectric nanoparticles are increasingly considered in various applications to control the spatial and temporal behavior of electromagnetic fields. In particular, the surface mode excitation by photons or electrons in metal nanorings finds significant applications because of the implied field distribution and electromagnetic energy confinement. However, most solid nanorings that are multilayered and/or embedded in a medium have non-simply connected geometry resulting in surface modes which are not linearly independent. That is, unlike particle plasmon eigenmodes in other geometries, the amplitudes of the eigenmodes of tori exhibit a distinct forward and backward coupling. We investigate the surface modes of such toroidal nano-structures and obtain the canonical plasmon dispersion relations and resonance modes for arbitrarily layered nanorings. When seeking the nonretarded surface modes for a stratified solid torus, we obtain a three-term difference equation which plays an important role in obtaining the needed dispersion relations. The obtained dispersion relations are investigated in depth in terms of the involved matrix continued fractions and their convergence properties including their determinant forms for computing the plasmon eigenmodes. The numerical solutions of the dispersion relations in case of a solid ring are presented for comparison and the resonance frequencies for the first few dominant modes of a ring composed of plasmon supporting materials such as gold, silver, and aluminum are provided and compared to those for a silicon ring. The mode complementarity and hybridization in multilayered toroidal structures is discussed and different ring configurations are simulated in the quasistatic limit by selecting number of layers modeled by their local dielectric functions. A generalized Green’s function with derivation intricacies addressed for multilayer tori is obtained from which one may calculate and study the scattering behavior of any of the modes that may exist in the many layer system. In particular, the electric potential distribution corresponding to individual poloidal and toroidal modes in response to an arbitrarily polarized external field and the field of electrons is obtained. The results are applied to obtain the local density of states and decay rate of a dipole near the center of the torus. Finally, two new types of toroidal particles in the form of janus nanorings are introduced.

This thesis relates to the design and implementation of a Gysel power combiner consisting of two input ports. The design is implemented using discrete (lumped) components over the conventional transmission line architecture and operates at 100 MHz. Because of the high power requirements for the power combiner, special attention is given to the power handling capabilities of the lumped elements and the other components involved. Simulations of an S-parameter of Gysel power combiner are performed using the Advanced Design System (ADS) from Keysight Technologies. The final design of two-way Gysel power combiner using PCB toroidal inductor was implemented, simulated and optimized at centre frequency of 100 MHz. Satisfactory results were obtained in terms of Insertion loss, Return loss and Port Isolation.

A large aspect ratio leads to higher ion capacity in miniaturized ion trap mass spectrometers. The aspect ratio (AR) of an ion trap represents the ratio between an extended trapping dimension and the characteristic trapping dimension. In contrast to linear and rectilinear traps, changing the AR of a toroidal ion trap (TorIT) results in changes to the degree of curvature and shape of the trapping potential, and hence, on performance as a mass analyzer. SIMION simulations show that higher-order terms in the trapping potential vary strongly for small and moderate AR values (below ~10), with the effects asymptotically flattening for larger AR values. Because of the asymmetry in electrode geometry, the trapping center does not coincide with the geometric center of the trap, and this displacement also varies with AR. For instance, in the asymmetric TorIT, the saddle point in the trapping potential and the geometric trap center differ from +0.6 to -0.4 mm depending on AR. Ion secular frequencies also change with the AR. Whereas ions in the simplified TorIT have stable trajectories for any value of AR, ions in the asymmetric TorIT become unstable at large AR values. Variations in high-order terms, the trapping center, and secular frequencies with AR are a unique feature of toroidal traps, and require significant changes in trap design and operation as the aspect ratio is changed.

This dissertation presents advances in the development of planar electrode ion traps. An ion trap is a device that can be used in mass analysis applications. Electrode surfaces create an electric field profile that trap ionized molecules of an analyte. The electric fields can then be manipulated to mass-selectively eject ions out of the trap into a detector. The resulting data can be used to analyze molecular structure and composition of an unknown compound. Conventional ion traps require machined electrode surfaces to form the electric trapping field. This class of electrode presents significant obstacles when attempting to miniaturize ion traps to create portable mass spectrometers. Machined electrodes lose required precision in shape, smoothness, and alignment as trapping dimensions decrease. Simplified electrode geometries are essential to open the way to miniaturized ion traps. The planar electrode ion trap presents a simplified geometry that utilizes photolithography processes in its fabrication. Patterns of electrodes are patterned on a planar ceramic substrate. Electric fields generated by these patterns can be nearly identical to those of ideal ion traps. The microfabrication processes involve the challenge of patterning on ceramic, patterning on two sides of a substrate, and patterning on a substrate with high topographic features. Four successful designs of planar ion traps are presented in this work: the planar Paul, toroidal, coaxial, and linear ion trap. These four designs have different strengths and weaknesses. The planar Paul trap is simpler to design and operate, the toroidal has a larger ion storage volume and so can be a more sensitive instrument, and the coaxial trap is a hybrid planar Paul and toroidal trap. The linear trap combines the simplicity of the planar Paul trap with the increased storage capacity of the toroidal trap. This work presents how these four designs advance work in miniaturized ion traps. In addition, microfabrication techniques and trap performance for these designs are presented.