Hybrid resonance of Maxwell's equations in slab geometry

作者：Despres Bruno; Imbert Gerard Lise Marie^*; Weder Ricardo

来源：Journal de Mathematiques Pures et Appliquees, 2014, 101(5): 623-659.

DOI：10.1016/j:matpur.2013.10.001

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

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.

• 出版日期2014-5