[en] Using a variational technique, a set of coupled model equations for the mode-conversion process near the ion-cyclotron frequency is derived. The system is truncated to first order in Larmor radius but includes the effects of explicit gradients and a poloidal field. From the equations a conservation rule is extracted which ensures conservation of total energy and provides an explicit expression for the wave damping in differential form. The equations are integrated numerically for the standard cases of fast waves incident from either the low- or high-field sides of the mode-conversion layer. The scaling of the damping processes is discussed and implications for current rf-heating experiments on the Princeton Large Torus are drawn