Hybrid resonance of Maxwell's equations in slab geometry

TL;DR

This paper mathematically analyzes hybrid resonance in Maxwell's equations within slab geometry, revealing the singular nature of solutions and their implications for plasma heating.

Contribution

It constructs and analyzes a mathematical solution for hybrid resonance using the limit absorption principle, highlighting the solution's singular structure.

Findings

Limit solution includes a Dirac mass and principal value component.

Singularities are directly related to plasma heating efficiency.

Provides a rigorous mathematical framework for hybrid resonance analysis.

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.