Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations

TL;DR

This paper analyzes the long-time behavior of solutions to Maxwell's equations during upper-hybrid resonance in cold plasma, extending frequency domain results to the time domain to understand plasma heating and diagnostics.

Contribution

It extends recent frequency domain results to the time domain for Maxwell's equations in plasma, providing insights into plasma heating during upper-hybrid resonance.

Findings

Characterization of long-time asymptotics in plasma resonance.

Connection between singular solutions and plasma heating.

Implications for plasma diagnostics and heating methods.

Abstract

We study the long-time asymptotic of the solutions to Maxwell's equation in the case of a upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Despr\'es, L.M. Imbert-G\'erard and R. Weder, J. Math. Pures Appl. {\bf 101} ( 2014) 623-659, where the singular solutions to Maxwell's equations in the frequency domain were constructed by means of a limiting absorption principle and a formula for the heating of the plasma in the limit of vanishing collision frequency was obtained. Currently there is considerable interest in these problems, in particular, because upper-hybrid resonances are a possible scenario for the heating of plasmas, and since they can be a model for the diagnostics involving wave scattering in plasmas.