Hybrid resonance of Maxwell's equations in slab geometry
Plasma Physics
2019-08-16 v2 Mathematical Physics
math.MP
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 is constituted of a Dirac mass at the origin plus a principle value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.
Keywords
Cite
@article{arxiv.1210.0779,
title = {Hybrid resonance of Maxwell's equations in slab geometry},
author = {Bruno Després and Lise-Marie Imbert-Gérard and Ricardo Weder},
journal= {arXiv preprint arXiv:1210.0779},
year = {2019}
}
Comments
This published version has been edited to improve the presentation of the results