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

We study the long-time asymptotic of the solutions to Maxwell's equation in the case of an 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. Després, L.M. Imbert-Gérard and R. Weder (2014) [15], 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.