A numerical study of the solution of X-Mode equations around the hybrid resonance*

The hybrid resonance is a physical phenomenon that appears for example in the heating of plasma, and as such is of scientific interest for the development of the ITER project. In this paper we focus on solutions of low regularity to Maxwell equations in magnetized plasmas. Our main purpose is three-fold. First, we aim at investigating the finite element approximation of the frequency-domain problem. Second, we would like to study the resonant solutions in the time domain, with the help of two different finite difference approximations. We finally compare the results with the ones obtained in the frequency domain, by numerical examination of the limiting absorption and limited amplitude principles