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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.

35Q61 Maxwell equations
82D10 Statistical mechanics of plasmas
35Q82 PDEs in connection with statistical mechanics
Full Text: DOI arXiv
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