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Dynamique et stabilisation d’un plasma magnétique froid

Abstract : In this thesis, we consider a linearized Euler-Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. Two types of boundary conditions are considered: perfectly conducting on the whole boundary and Silver-Müller, homogeneous or not, on part of it. First, I establish the equations of the model and show its well-posedness by the theory of semigroups. Then, I am interested in the stabilization of the model. First, I carry out a study on the long- term asymptotic behavior of the solution. I show that it decreases towards zero under certain physically reasonable assumptions. I conclude that it converges to a non-zero stationary state in a larger energy space. This stationary state is linked to the topology properties of the domain, and is expressed as a function of the initial data. Secondly, I study the energy decay rate by using the frequency domain method. I establish a polynomial decay for both boundary conditions. I also prove a conditional exponential decay result in the homogeneous Silver-Müller case. In the perfectly conducting case, we show that the Euler-Maxwell system is not exponentially stable. We conclude by a result of convergence towards the time-harmonic regime in the presence of a harmonic forcing. Among the main difficulties encountered, the resolvent of the evolution operator is not compact and the internal absorption acts only on the fluid variables. No homogeneity assumption is made, and the topological and geometrical assumptions on the domain are minimal. These results appear strongly linked to the spectral properties of various matrices describing the anisotropy and other plasma properties. Finally, we extend those results to the case of a vacuum-plasma interface problem.
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Submitted on : Friday, March 25, 2022 - 3:24:49 PM
Last modification on : Wednesday, April 20, 2022 - 3:11:02 PM


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Ibtissem Zaafrani. Dynamique et stabilisation d’un plasma magnétique froid. Mathématiques [math]. Université de Lorraine; Université de Sousse (Tunisie), 2021. Français. ⟨NNT : 2021LORR0312⟩. ⟨tel-03620093⟩



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