Exact analytical solutions for the quasistationary electromagnetic fields in the presence of conducting objects require the field solutions both internal and external to the conductors. Such solutions are limited for certain canonically shaped objects but are useful in testing the accuracy of various approximate models and numerical methods developed to solve complex problems related to real world conducting objects and in calibrating instruments designed to measure various field quantities. Theoretical investigations of quasistationary electromagnetic fields also aid in improving the understanding of the physical phenomena of electromagnetic induction. This thesis presents rigorous analytical expressions derived as benchmark solutions for the quasistationary field quantities both inside and outside, Joule losses and the electromagnetic forces acting upon a conducting spheroid placed in the proximity of a non-uniform field produced by current-carrying turns. These expressions are used to generate numerous numerical results of specified accuracy and selected results are presented in a normalized form for extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis and the position of the inducing turns relative to the spheroids. They are intended to constitute reference data to be employed for comprehensive comparisons of results from approximate numerical methods or from boundary impedance models used for real world conductors. Approximate boundary conditions such as the simpler perfect electric conductor model or the Leontovich surface impedance boundary condition model can be used to obtain approximate solutions by only analyzing the field external to the conducting object. The range of validity of these impedance boundary condition models for the analysis of axisymmetric eddy-current problems is thoroughly investigated. While the simpler PEC model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained using the surface impedance boundary condition model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis when calculating electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis when calculating Joule losses.

Exact analytical solutions for the quasistationary electromagnetic fields in the presence of conducting objects require the field solutions both internal and external to the conductors. Such solutions are limited for certain canonically shaped objects but are useful in testing the accuracy of various approximate models and numerical methods developed to solve complex problems related to real world conducting objects and in calibrating instruments designed to measure various field quantities. Theoretical investigations of quasistationary electromagnetic fields also aid in improving the understanding of the physical phenomena of electromagnetic induction. This thesis presents rigorous analytical expressions derived as benchmark solutions for the quasistationary field quantities both inside and outside, Joule losses and the electromagnetic forces acting upon a conducting spheroid placed in the proximity of a non-uniform field produced by current-carrying turns. These expressions are used to generate numerous numerical results of specified accuracy and selected results are presented in a normalized form for extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis and the position of the inducing turns relative to the spheroids. They are intended to constitute reference data to be employed for comprehensive comparisons of results from approximate numerical methods or from boundary impedance models used for real world conductors. Approximate boundary conditions such as the simpler perfect electric conductor model or the Leontovich surface impedance boundary condition model can be used to obtain approximate solutions by only analyzing the field external to the conducting object. The range of validity of these impedance boundary condition models for the analysis of axisymmetric eddy-current problems is thoroughly investigated. While the simpler PEC model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained using the surface impedance boundary condition model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis when calculating electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis when calculating Joule losses.

Le procédé de refusion sous laitier électroconducteur (Electro Slag Remelting ou ESR) est aujourd’hui largement utilisé pour la production d’alliages métalliques à haute valeur ajoutée, comme les aciers spéciaux ou les superalliages base nickel. La modélisation mathématique et la simulation numérique du procédé ESR présentent un grand intérêt puisque les études expérimentales sur installations industrielles sont coûteuses et souvent difficiles à mettre en oeuvre. Ainsi, afin d’améliorer la compréhension et la maîtrise de la conduite d’une refusion, un modèle prédictif a été développé dans le cadre de cette étude. Il décrit les transferts couplés de chaleur et de quantité de mouvement lors de la croissance et de la solidification d’un lingot, en géométrie axisymétrique. La résolution des équations est basée sur une approche de type volumes finis. Le modèle tient compte de l’effet Joule dans le laitier résistif, des forces électromagnétiques et de la turbulence éventuelle de l’écoulement des phases liquides. La zone pâteuse est traitée comme un milieu poreux. Le modèle permet notamment de prédire la formation de la peau de laitier solide qui entoure le laitier et le lingot. Par ailleurs, il offre l’avantage de simuler le comportement du lingot et du laitier après la coupure finale du courant.Le développement s’est accompagné d’une importante étape de validation. Quatre refusions à l’échelle industrielle ont ainsi été réalisées à l’aciérie des Ancizes (Aubert&Duval). Les observations expérimentales ont ensuite été confrontées aux résultats du calcul. La comparaison a montré que le modèle peut être utilisé afin de prédire le comportement du procédé, à condition d’accorder une attention particulière à l’estimation des propriétés thermophysiques du métal, et surtout du laitier. Enfin, afin d’illustrer l’utilisation du modèle comme support à la compréhension du procédé, nous avons étudié l’influence de la variation de paramètres opératoires tels que la profondeur d’immersion de l’électrode, le taux de remplissage ou la pression de l’eau de refroidissement. / Electro Slag Remelting (ESR) is widely used for the production of high-value-added alloys such as special steels or nickel-based superalloys. Because of high trial costs and complexity of the process, trial-and-error based approaches are not well suitable for fundamental studies and optimization of the process.Consequently, a transient-state numerical model which accounts for electromagnetic phenomena and coupled heat and momentum transfers in an axisymmetrical geometry has been developed. The model simulates the continuous growth of the electroslag remelted ingot through a mesh-splitting method. In addition, solidification of the metal and slag is modelled by an enthalpy-based technique. A turbulence model is implemented to compute the motion of liquid phases (slag and metal), while the mushy zone is described as a porous medium whose permeability varies with the liquid fraction, thus enabling an accurate calculation of solid/liquid interaction. The coupled partial differential equations are solved using a finite-volume technique.Computed results are compared to experimental observation of 4 industrial remelted ingots fully dedicated to the model validation step. Pool depth and shape are particularly investigated in order to validate the model. Comparison shows that the model can be used as a predictive tool to analyse the process behavior. Nevertheless, it is necessary to pay a particular attention to the estimation of the thermophysical properties of metal and especially slag.These results provide valuable information about the process performance and influence of operating parameters. In this way, we present some examples of model use as a support to analyse the influence of operating parameters. We have studied the variation of electrode immersion depth, fill ratio and water pressure in the cooling circuit.

La plasmonique vise à utiliser des nanostructures métalliques très petites devant la longueur d’onde pour manipuler la lumière. Les structures métalliques sont particulières parce qu’elles contiennent un plasma d’électrons libres qui conditionne complètement leur réponse optique. Notamment, lorsque la lumière se propage à proximité des métaux, sous forme de mode guidés comme les plasmons et les gap-palsmons, elle est souvent lente, présentant une vitesse de groupe faible. Dans ce travail, nous présentons une analyse physique qui permet de comprendre cette faible vitesse en considérant le fait que l’énergie se déplace à l’opposé de la lumière dans les métaux. Nous montrons que la vitesse de groupe est égale à la vitesse de l’énergie pour ces modes guidés, et proposons la notion de ralentissement plasmonique. Finalement, nous étudions comment cette « trainée plasmonique » rend une structure aussi simple qu’un coupleur à prisme sensible à la répulsion entre les électrons du plasma. / The field of plasmonics aims at manipulating light using deeply subwavelength nanostructures. Such structures present a peculiar optical response because of the free electron plasma they contain. Actually, when light propagates in the vicinity of metals, usually under the form of a guided mode, it presents a low group velocity. Such modes, like plasmons and gap-plasmons, are said to be slow. In this work we present a general physical analysis of this phenomenon by studying how the energy propagates in metals in a direction that is opposite to the propagation direction of the mode. We show that the group velocity and the energy velocity are the same, and finally introduce the concept of plasmonic drag. Finally, we study how slow guided modes make structures as simple as prism couplers sensitive to the repulsion between electrons inside the plasma.