Electromagnetic wave propagation and absorption in magnetised plasmas: variational formulations and domain decomposition

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 S\'ebelin 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

On multiple eigenvalues for Aharonov-Bohm operators in planar domains

We study multiple eigenvalues of a magnetic Aharonov-Bohm operator with Dirichlet boundary conditions in a planar domain. In particular, we study the structure of the set of the couples position of the pole-circulation which keep fixed the multiplicity of a double eigenvalue of the operator with the pole at the origin and half-integer circulation. We provide sufficient conditions for which this set is made of an isolated point. The result confirms and validates a lot of numerical simulations available in preexisting literature.Comment: 33 pages, 4 figure