We investigate the possibility of measuring and using the phase delay of radio frequency transmissions in the amateur satellite band as a method to determine the distribution of currents systems in the ionosphere. The amateur satellite transmissions at 7MHz, 14M Hz, and 144M Hz are low enough for Faraday rotation to cause a significant phase delay on the propagating signals in addition to the phase delay produced by the total electron content (TEC) in the ionosphere. The ionosphere in the E and F regions is modeled as an equivalent thin planar shell of collision free cold plasma 100 km in thickness located in an altitude range of 100 � 200 km. The earth's magnetic field is superposed with a weaker magnetic field due to a narrow Gaussian strip of current representing an ionospheric electrojet. The prole of the current system is obtained by numerically optimizing the Appleton-Hartree dispersion relation for rays of simulated radio frequency (RF) signals that propagate through the ionosphere shell. The optimization procedure is performed with a differential evolution algorithm. From the optimization procedure, we obtain the ionosphere total electron content (TEC) and the strength, prole, and orientation of the ionospheric current system.

We investigate the possibility of measuring and using the phase delay of radio frequency transmissions in the amateur satellite band as a method to determine the distribution of currents systems in the ionosphere. The amateur satellite transmissions at 7MHz, 14M Hz, and 144M Hz are low enough for Faraday rotation to cause a significant phase delay on the propagating signals in addition to the phase delay produced by the total electron content (TEC) in the ionosphere. The ionosphere in the E and F regions is modeled as an equivalent thin planar shell of collision free cold plasma 100 km in thickness located in an altitude range of 100 􀀀 200 km. The earth's magnetic field is superposed with a weaker magnetic field due to a narrow Gaussian strip of current representing an ionospheric electrojet. The prole of the current system is obtained by numerically optimizing the Appleton-Hartree dispersion relation for rays of simulated radio frequency (RF) signals that propagate through the ionosphere shell. The optimization procedure is performed with a differential evolution algorithm. From the optimization procedure, we obtain the ionosphere total electron content (TEC) and the strength, prole, and orientation of the ionospheric current system.

Cette thèse décrit comment les ondes électromagnétiques se propagent dans les plasmas magnétisés, lorsque les fréquences sollicitées sont proches de la fréquence électron cyclotron. Elle porte sur l’analyse mathématique des variétés caractéristiques qui sont associées à des systèmes de type Vlasov-Maxwell relativiste avec paramètres rapides.La première partie s’intéresse aux plasmas froids des magnétosphères planétaires. On explique comment obtenir les relations de dispersion dans le cas d’un dipôle magnétique. Cela conduit à l’étude détaillée de certaines variétés algébriques de l’espace cotangent : les cônes et les sphères dits ordinaires et extraordinaires. La description géométrique de ces cônes et de ces sphères donne accès à une classification complète des ondes électromagnétiques susceptibles de se propager. Diverses applications sont proposées, concernant l’équation eikonale et l’absence de propagation en mode parallèle, ou encore concernant la structure des ondes dites en mode siffleur.La seconde partie porte sur la modélisation des plasmas chauds, typiquement ceux qui sont mis en jeu dans les tokamaks. On prouve dans un contexte réaliste que la propagation des ondes électromagnétiques s’effectue au travers d’un tenseur dielectrique. Ce tenseur est obtenu via une analyse fine des résonances cinétiques qui sont issues des interactions entre les particules (Vlasov) et les ondes (Maxwell). Il s’exprime comme une somme infinie d’intégrales singulières, faisant intervenir l’opérateur de Hilbert. Le sens mathématique de la formule donnant accès à ce tenseur est rigoureusement justifié. / This thesis describes how electromagnetic waves propagate in magnetized plasmas, when the frequencies are in a range around the electron cyclotron frequency. It focuses on the mathematical analysis of the characteristic varieties which are associated with relativistic Vlasov-Maxwell systems involving fast parameters. The first part is concerned with cold plasmas issued from planetary magnetospheres. We explain how to obtain the dispersion relations in the case where the magnetic field is given by a dipole model. This leads to the detailed study of some algebraic varieties from the cotangent space: the so-called ordinary and extraordinary cones and spheres. The geometrical description of these cones and spheres gives access to a complete classification of the electromagnetic waves which can propagate. Various applications are proposed, concerning the eikonal equation and the absence of purely parallel propagation, or concerning the structure of whistler waves. The second part focuses on the modelling of hot plasmas, typically like those involved in tokamaks. We prove in a realistic context that the propagation of electromagnetic waves is governed by some dielectric tensor. This tensor is obtain via some careful analysis of the kinetic resonances, which are issued from the interactions between the particles (Vlasov) and the waves (Maxwell). It can be expressed as an infinite sum of singular integrals, involving the Hilbert transform. The mathematical meaning of the formula defining this tensor is rigorously justified.