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Méthodes déterministes de résolution des équations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen

Abstract : Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energy electrons and the existing electromagnetic waves.

This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is choosen in order to obtain the proper velocity resolution.

We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv computations of Weibel and whistler instabilities with one or two electrons species.
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https://tel.archives-ouvertes.fr/tel-00146258
Contributor : Solène Le Bourdiec <>
Submitted on : Monday, May 14, 2007 - 2:47:56 PM
Last modification on : Friday, April 10, 2020 - 2:10:25 AM
Long-term archiving on: : Friday, November 25, 2016 - 3:51:47 PM

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Solène Le Bourdiec. Méthodes déterministes de résolution des équations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen. Modélisation et simulation. Ecole Centrale Paris, 2007. Français. ⟨tel-00146258⟩

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