Hybrid resonance of Maxwell's equations in slab geometry

Bruno Després, Lise Marie Imbert-Gérard, Ricardo Weder

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)623-659
Number of pages37
JournalJournal des Mathematiques Pures et Appliquees
Issue number5
StatePublished - May 2014
Externally publishedYes


  • Anisotropic dielectric tensor
  • Hybrid resonance
  • Limit absorption principle
  • Maxwell equations
  • Resonant heating

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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