[en] A series of recent papers has established the idea that even a small amount of hydrogen impurity at fundamental resonance in a deuterium plasma modifies entirely the damping mechanism of the fast magnetosonic wave (FMW). The FMW energy is linearly mode-converted into a slow electrostatic mode (EW) in the ion-ion hybrid resonance layer. The overall damping of the FMW eigen modes can be calculted without knowing the fate of the EW. Obviously, the evaluation of the heating performance requires to know the trajectory and damping of the EW which contain the information on the localisation and heating rate of the various plasma species. Perkins has presented preliminary solutions to this problem. In a Tokamak geometry, he showed the paramount importance of the effects of the finite temperature and the poloidal field component normal to the mode conversion layer. In this paper we consider again the same problem but we include the damping effects of the minority species and the integration of the deposited power in each species along the wave trajectory. Moreover we find necessary to solve the wave equation for an arbitrary magnitude of the damping decrement