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Hybrid resonance of Maxwell’s equations in slab geometry. (English) Zbl 1296.35182
Authors’ abstract: Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell’s equations with smooth coefficients, where the dielectric tensor is a non-diagonal Hermitian matrix. The main part of this work is dedicated to the construction and analysis of a mathematical solution of the hybrid resonance with the limit absorption principle. We prove that the limit solution is singular: it consists of a Dirac mass at the origin plus a principal value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.

MSC:
35Q61 Maxwell equations
82D10 Statistical mechanics of plasmas
35Q82 PDEs in connection with statistical mechanics
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