Geodesic
Electromagnetic wave propagation and absorption in magnetised plasmas: variational formulations and domain decomposition
Back, Aurore1 ; Hattori, Takashi1  ; Labrunie, Simon1  ; Roche, Jean-Rodolphe1  ; Bertrand, Pierre2
1 Universitéde Lorraine, CNRS, Institut Elie Cartan de Lorraine, UMR 7502, 54506 Vandœuvre-lès-Nancy, France
2 Université de Lorraine, CNRS, Institut Jean Lamour, UMR 7198, 54011 Nancy, France
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1239-1260

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We consider a model for the propagation and absorption of electromagnetic waves (in the time-harmonic regime) in a magnetised plasma. We present a rigorous derivation of the model and several boundary conditions modelling wave injection into the plasma. Then we propose several variational formulations, mixed and non-mixed, and prove their well-posedness thanks to a theorem by Sébelin et al. Finally, we propose a non-overlapping domain decomposition framework, show its well-posedness and equivalence with the one-domain formulation. These results appear strongly linked to the spectral properties of the plasma dielectric tensor.

Reçu le :
DOI : 10.1051/m2an/2015009
Classification : 35J57, 35Q60, 65N55
Keywords: Magnetised plasma, Maxwell’s equations, domain decomposition

Back, Aurore 1 ; Hattori, Takashi 1 ; Labrunie, Simon 1 ; Roche, Jean-Rodolphe 1 ; Bertrand, Pierre 2

1 Universitéde Lorraine, CNRS, Institut Elie Cartan de Lorraine, UMR 7502, 54506 Vandœuvre-lès-Nancy, France
2 Université de Lorraine, CNRS, Institut Jean Lamour, UMR 7198, 54011 Nancy, France 
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     author = {Back, Aurore and Hattori, Takashi and Labrunie, Simon and Roche, Jean-Rodolphe and Bertrand, Pierre},
     title = {Electromagnetic wave propagation and absorption in magnetised plasmas: variational formulations and domain decomposition},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1239--1260},
     publisher = {EDP-Sciences},
     volume = {49},
     number = {5},
     year = {2015},
     doi = {10.1051/m2an/2015009},
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     zbl = {1328.35227},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015009/}
}
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Back, Aurore; Hattori, Takashi; Labrunie, Simon; Roche, Jean-Rodolphe; Bertrand, Pierre. Electromagnetic wave propagation and absorption in magnetised plasmas: variational formulations and domain decomposition. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1239-1260. doi: 10.1051/m2an/2015009

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