We consider the problem of computing the global response of a tokamak to RF-antenna driving, including conversion at the ion-hybrid resonance layer. The tokamak is modeled as a 2-D circular cavity (a poloidal cross-section). An antenna launches a family of magnetosonic (MS) rays. The amplitude and phase of the MS wave field are transported using eikonal techniques: the phase is transported using the standard phase integral, while the amplitude is calculated using the van Vleck formula which accounts for the convergence or divergence of neighboring rays. As each ray of this family crosses the ion-hybrid (IH) resonance it is partially transmitted, partially reflected and partially converted into an IH wave which remains confined to the resonance layer. This MS/IH conversion process is described by an S-matrix. The S-matrix can be evaluated using previously developed techniques. The transmitted and reflected MS rays now propagate from the resonance layer. They are globally confined and are reflected at the edge of the plasma. Hence, they will re-enter the resonance layer. At each resonance crossing new families of rays are created and some fraction of the MS wave energy and action is converted into the IH wave, eventually damping on the background plasma. The resulting field distribution in the cavity will be a superposition of this multitude of ray families. Fine-scale structure is observed to emerge due to caustic formation. We focus our attention on this iterated conversion to the IH wave and ask how the energy leakage affects the overall cavity response and the spatial distribution of energy absorbed as a function of frequency.