A Stable Formulation of Resonant Maxwell's Equations in Cold Plasma

Martin Campos Pinto (1, 2) , Anouk Nicolopoulos (1) , Bruno Després (1)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CNRS - Centre National de la Recherche Scientifique

We consider a boundary value problem (BVP) for a reduced system of time harmonic Maxwell equations in magnetized plasma. The dielectric tensor is strongly anisotropic and the system admits resonant solutions in the context of the limit absorption principle. In particular, in the vanishing viscosity limit the normal component of the electric field becomes infinite and non integrable at the resonant point, and the system becomes ill-posed. In this article we recast the problem in the framework of mixed variational problems and we propose a well-posed formulation that characterizes the singular limit solutions. A key tool is the method of manufactured solutions [7] to construct an integral variational characterization of the jump conditions at the resonance. The well posedness is demonstrated and basic numerical results illustrate the robustness of our approach.

Mots clés: Maxwell's equations; mixed variational formulations; finite elements; manufactured solutions; singular solutions; plasma heating; mode coupling; hybrid resonance

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Physique des plasmas [physics.plasm-ph]

Martin Campos Pinto, Anouk Nicolopoulos, Bruno Després. A Stable Formulation of Resonant Maxwell's Equations in Cold Plasma. Journal of Computational and Applied Mathematics, 2019, ⟨10.1016/j.cam.2019.05.007⟩. ⟨hal-01743546v3⟩