<p>The magnetospheric cusps are two funnel-like regions of Earth's magnetosphere where solar wind plasma can have direct access to the ionosphere. The cusps are very dynamic regions where wave-particle interactions continuously take place and redistribute energy among different particle populations. In this thesis, both low and high frequency plasma waves in the cusp have been studied in detail using data from the Cluster spacecraft mission. The waves were studied with respect to frequency, Poynting flux and polarization. Wavelengths have also been estimated using multi-spacecraft techniques. At low frequencies, kinetic Alfvén waves and nonpotential ion cyclotron waves are identified and at high frequencies, electron cyclotron waves, whistler waves, upper-hybrid and RX-waves are observed. A common generation mechanism called the shell-instability is proposed for several of the wave modes present in the cusp, both at low and high frequencies. </p><p>The plasma in the cusp is shown to be strongly inhomogeneous. In an inhomogeneous low-frequency magnetoplasma, kinetic Alfvén waves couple to drift-waves. Such drift-kinetic Alfvén waves have long been believed to nonlinearly self-interact and form coherent structures in the form of drift-kinetic Alfvén vortices. In this thesis the first unambiguous direct measurements confirming the existence of such vortices in a turbulent space plasma are presented. Some of the crucial parameters such as the vortex radius are determined. </p><p>Plasma theory is electrodynamics applied to a large collection of charged particles. In this thesis a new way of looking at the fundamental Maxwell tensor is presented. A covariant spectral density tensor containing information on electromagnetic waves is formed. This tensor is then decomposed into irreducible components by using the spinor formalism for an arbitrary metric. The obtained fundamental tensors are shown to correspond both to well known tensors in Maxwell's theory, as well as several physically interesting new tensors.</p>

Capteurs et dispositifs électroniques des magnétomètres dédiés à l'étude des ondes dans les plasmas spatiaux.

Un enjeu majeur de l'industrie aéronautique de demain est de concevoir et développer un avion " plus " électrique. En effet, sur un avion de ligne, les principaux systèmes utilisent des types d'énergies différents tels que l'énergie hydraulique ou pneumatique. La tendance actuelle est à la conversion de ces systèmes à l'énergie électrique car elle présente de nombreux avantages et permettrait des économies de masse, d'énergie, et de coûts de maintenance. Avec l'augmentation croissante des systèmes électriques dans l'avion se posent par conséquent des problèmes d'interférences et de compatibilité électromagnétique entre ces différents dispositifs. Par ailleurs ces systèmes électriques sont soumis à des conditions de travail très sévères, notamment des températures extrêmes. Dans le cadre du projet FEMINA (Filtrage Electromagnétiques et Matériaux pour l'INtégration en Aéronautique), l'objectif de notre équipe était d'étudier un filtre électrique soumis à des conditions de températures extrêmes. Ce filtre composé d'éléments passifs (condensateurs et inductances) est destiné à éliminer les interférences provoquées par le convertisseur électrique placé à proximité de la source d'énergie et de chaleur (le propulseur). Dans le cadre de mes travaux de thèse, je me suis intéressé plus particulièrement à l'effet de la température sur le comportement des inductances au travers des matériaux magnétiques qui les composent. J'ai ainsi déterminé les matériaux magnétiques que j'estimais capable de remplir leur rôle de filtrage en hautes températures, puis j'ai élaboré un modèle de comportement magnétique dynamique, tenant compte de l'effet de peau et de l'effet de la température et enfin j'ai testé ce nouveau modèle en l'incluant dans un simulateur circuit, afin de modéliser un filtre de mode commun répondant au cahier des charges de nos partenaires industriels.

The magnetospheric cusps are two funnel-like regions of Earth's magnetosphere where solar wind plasma can have direct access to the ionosphere. The cusps are very dynamic regions where wave-particle interactions continuously take place and redistribute energy among different particle populations. In this thesis, both low and high frequency plasma waves in the cusp have been studied in detail using data from the Cluster spacecraft mission. The waves were studied with respect to frequency, Poynting flux and polarization. Wavelengths have also been estimated using multi-spacecraft techniques. At low frequencies, kinetic Alfvén waves and nonpotential ion cyclotron waves are identified and at high frequencies, electron cyclotron waves, whistler waves, upper-hybrid and RX-waves are observed. A common generation mechanism called the shell-instability is proposed for several of the wave modes present in the cusp, both at low and high frequencies. The plasma in the cusp is shown to be strongly inhomogeneous. In an inhomogeneous low-frequency magnetoplasma, kinetic Alfvén waves couple to drift-waves. Such drift-kinetic Alfvén waves have long been believed to nonlinearly self-interact and form coherent structures in the form of drift-kinetic Alfvén vortices. In this thesis the first unambiguous direct measurements confirming the existence of such vortices in a turbulent space plasma are presented. Some of the crucial parameters such as the vortex radius are determined. Plasma theory is electrodynamics applied to a large collection of charged particles. In this thesis a new way of looking at the fundamental Maxwell tensor is presented. A covariant spectral density tensor containing information on electromagnetic waves is formed. This tensor is then decomposed into irreducible components by using the spinor formalism for an arbitrary metric. The obtained fundamental tensors are shown to correspond both to well known tensors in Maxwell's theory, as well as several physically interesting new tensors.

Les métamatériaux à indice de réfraction négative ont attiré énormément l'attention ces dernières années surtout à cause de leurs propriétés électromagnétiques uniques. Ces matériaux sont des structures artificielles qui présentent des caractéristiques n'étant pas disponibles en matériaux naturels. Récemment, le développement technologique avec de nouvelles techniques de fabrication offrent un grand nombre de nouvelles application et développement de nouveaux matériaux. Il est possible d'obtenir un métamatériau en combinant des structures artificielles périodiquement. Les propriétés uniques du Split Ring Resonator (SRR), les Surfaces à Haute Impédance (HIS), les Surface Sélective en Fréquence (FSS) sont étudiées ainsi que les métamatériaux composés. Il a été démontré avec succès l'utilisation pratique de ces structures dans les circuits et les antennes. Il a été confirmé expérimentalement que les métamatériaux pourrait améliorer la performance des structures considérées dans cette thèse, pour des fréquences où la bande interdite électromagnétique se produit.

La récupération d'énergie vise à réaliser des dispositifs électromécaniques de taille centimétrique permettant d'alimenter des systèmes électroniques en puisant de manière opportuniste l'énergie du milieu environnant. Parmi les différentes sources disponibles (solaire, thermique etc.) les vibrations ambiantes sont susceptibles de fournir assez de puissance pour alimenter des microsystèmes autonomes tels que des noeuds de réseaux de capteurs communicants. L'enjeu consiste à concevoir des microgénérateurs effectuant la conversion de cette énergie mécanique ambiante en énergie électrique exploitable de manière optimale. Ces travaux de thèse proposent dans un premier temps un critère d'étude et de comparaison des performances des générateurs de types piézoélectriques ou électromagnétiques, à partir d'un modèle normalisé unifié. Dans un second temps, un circuit non linéaire d'extraction de l'énergie est étudié pour les générateurs électromagnétiques, et ses performances sont discutées en comparaison avec un circuit classique d'extraction de l'énergie. A partir de ces résultats, une nouvelle structure de générateur électromagnétique est conçue, optimisée puis validée expérimentalement

El Método de los Momentos (MoM) ha sido ampliamente utilizado en las últimas décadas para la discretización y la solución de las formulaciones de ecuación integral que aparecen en muchos problemas electromagnéticos de antenas y dispersión. Las más utilizadas de dichas formulaciones son la Ecuación Integral de Campo Eléctrico (EFIE), la Ecuación Integral de Campo Magnético (MFIE) y la Ecuación Integral de Campo Combinada (CFIE), que no es más que una combinación lineal de las dos anteriores.Las formulaciones MFIE y CFIE son válidas únicamente para objetos cerrados y necesitan tratar la integración de núcleos con singularidades de orden superior al de la EFIE. La falta de técnicas eficientes y precisas para el cálculo de dichas integrales singulares a llevado a imprecisiones en los resultados. Consecuentemente, su uso se ha visto restringido a propósitos puramente académicos, incluso cuando tienen una velocidad de convergencia muy superior cuando son resuelto iterativamente, debido a su excelente número de condicionamiento.En general, la principal desventaja del MoM es el alto coste de su construcción, almacenamiento y solución teniendo en cuenta que es inevitablemente un sistema denso, que crece con el tamaño eléctrico del objeto a analizar. Por tanto, un gran número de métodos han sido desarrollados para su compresión y solución. Sin embargo, muchos de ellos son absolutamente dependientes del núcleo de la ecuación integral, necesitando de una reformulación completa para cada núcleo, en caso de que sea posible.Esta tesis presenta nuevos enfoques o métodos para acelerar y incrementar la precisión de ecuaciones integrales discretizadas con el Método de los Momentos (MoM) en electromagnetismo computacional.En primer lugar, un nuevo método iterativo rápido, el Multilevel Adaptive Cross Approximation (MLACA), ha sido desarrollado para acelerar la solución del sistema lineal del MoM. En la búsqueda por un esquema de propósito general, el MLACA es un método independiente del núcleo de la ecuación integral y es puramente algebraico. Mejora simultáneamente la eficiencia y la compresión con respecto a su versión mono-nivel, el ACA, ya existente. Por tanto, representa una excelente alternativa para la solución del sistema del MoM de problemas electromagnéticos de gran escala.En segundo lugar, el Direct Evaluation Method, que ha provado ser la referencia principal en términos de eficiencia y precisión, es extendido para superar el cálculo del desafío que suponen las integrales hiper-singulares 4-D que aparecen en la formulación de Ecuación Integral de Campo Magnético (MFIE) así como en la de Ecuación Integral de Campo Combinada (CFIE). La máxima precisión asequible -precisión de máquina se obtiene en un tiempo más que razonable, sobrepasando a cualquier otra técnica existente en la bibliografía.En tercer lugar, las integrales hiper-singulares mencionadas anteriormente se convierten en casi-singulares cuando los elementos discretizados están muy próximo pero sin llegar a tocarse. Se muestra como las reglas de integración tradicionales tampoco convergen adecuadamente en este caso y se propone una posible solución, basada en reglas de integración más sofisticadas, como la Double Exponential y la Gauss-Laguerre.Finalmente, un esfuerzo en facilitar el uso de cualquier programa de simulación de antenas basado en el MoM ha llevado al desarrollo de un modelo matemático general de un puerto de excitación en el espacio discretizado. Con este nuevo modelo, ya no es necesaria la adaptación de los lados del mallado al puerto en cuestión. / The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in several electromagnetic antenna and scattering problems. The most utilized of these formulations are the Electric Field Integral Equation (EFIE), the Magnetic Field Integral Equation (MFIE) and the Combined Field Integral Equation (CFIE), which is a linear combination of the other two. The MFIE and CFIE formulations are only valid for closed objects and need to deal with the integration of singular kernels with singularities of higher order than the EFIE. The lack of efficient and accurate techniques for the computation of these singular integrals has led to inaccuracies in the results. Consequently, their use has been mainly restricted to academic purposes, even having a much better convergence rate when solved iteratively, due to their excellent conditioning number. In general, the main drawback of the MoM is the costly construction, storage and solution considering the unavoidable dense linear system, which grows with the electrical size of the object to analyze. Consequently, a wide range of fast methods have been developed for its compression and solution. Most of them, though, are absolutely dependent on the kernel of the integral equation, claiming for a complete re-formulation, if possible, for each new kernel. This thesis dissertation presents new approaches to accelerate or increase the accuracy of integral equations discretized by the Method of Moments (MoM) in computational electromagnetics. Firstly, a novel fast iterative solver, the Multilevel Adaptive Cross Approximation (MLACA), has been developed for accelerating the solution of the MoM linear system. In the quest for a general-purpose scheme, the MLACA is a method independent of the kernel of the integral equation and is purely algebraic. It improves both efficiency and compression rate with respect to the previously existing single-level version, the ACA. Therefore, it represents an excellent alternative for the solution of the MoM system of large-scale electromagnetic problems. Secondly, the direct evaluation method, which has proved to be the main reference in terms of efficiency and accuracy, is extended to overcome the computation of the challenging 4-D hyper-singular integrals arising in the Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE) formulations. The maximum affordable accuracy --machine precision-- is obtained in a more than reasonable computation time, surpassing any other existing technique in the literature. Thirdly, the aforementioned hyper-singular integrals become near-singular when the discretized elements are very closely placed but not touching. It is shown how traditional integration rules fail to converge also in this case, and a possible solution based on more sophisticated integration rules, like the Double Exponential and the Gauss-Laguerre, is proposed. Finally, an effort to facilitate the usability of any antenna simulation software based on the MoM has led to the development of a general mathematical model of an excitation port in the discretized space. With this new model, it is no longer necessary to adapt the mesh edges to the port.

The vector finite element method has gained great attention since overcoming the deficiencies incurred by the scalar basis functions for the vector Helmholtz equation. Most implementations of vector FEM have been non-adaptive, where a mesh of the domain is generated entirely in advance and used with a constant degree polynomial basis to assign the degrees of freedom. To reduce the dependency on the users' expertise in analyzing problems with complicated boundary structures and material characteristics, and to speed up the FEM tool, the demand for adaptive FEM grows high. For efficient adaptive FEM, error estimators play an important role in assigning additional degrees of freedom. In this proposal study, hierarchical vector basis functions and four error estimators for p-refinement are investigated for electromagnetic applications.

This thesis presents a robust method for estimating the relaxations of a metallic object from its electromagnetic induction (EMI) response. The EMI response of a metallic object can be accurately modeled by a sum of real decaying exponentials. However, it is diffcult to obtain the model parameters from measurements when the number of exponentials in the sum is unknown or the terms are strongly correlated. Traditionally, the time constants and residues are estimated by nonlinear iterative search that often leads to unsatisfactory results. In this thesis, a constrained linear method of estimating the parameters is formulated by enumerating the relaxation parameter space and imposing a nonnegative constraint on the parameters. The resulting algorithm does not depend on a good initial guess to converge to a solution. Using tests on synthetic data and laboratory measurement of known targets the proposed method is shown to provide accurate and stable estimates of the model parameters.

Various error estimation and adaptive refinement techniques for the solution of electromagnetic integral equations were developed. Residual based error estimators and h-refinement implementations were done for the Method of Moments (MoM) solution of electromagnetic integral equations for a number of different problems. Due to high computational cost associated with the MoM, a cheaper solution technique known as the Locally-Corrected Nyström (LCN) method was explored. Several explicit and implicit techniques for error estimation in the LCN solution of electromagnetic integral equations were proposed and implemented for different geometries to successfully identify high-error regions. A simple p-refinement algorithm was developed and implemented for a number of prototype problems using the proposed estimators. Numerical error was found to significantly reduce in the high-error regions after the refinement. A simple computational cost analysis was also presented for the proposed error estimation schemes. Various cost-accuracy trade-offs and problem-specific limitations of different techniques for error estimation were discussed. Finally, a very important problem of slope-mismatch in the global error rates of the solution and the residual was identified. A few methods to compensate for that mismatch using scale factors based on matrix norms were developed.