The propagation, growth and absorption of electromagnetic ion cyclotron waves in the Pc 1 frequency range is investigated using the HOTRAY ray tracing program for a realistic distribution of thermal plasma (H+, He+ and O+) that is assumed to be in diffusive equilibrium inside the plasmasphere and collisionless in the low-density region outside the plasmapause. Free energy for L- mode wave growth is provided by a bi-Maxwellian distribution of energetic H+ and O+ with a temperature and density modelled on satellite observations. Solutions to the hot plasma dispersion relation show that inside the plasmasphere the spatial growth rates are small whereas they increase outside the plasmapause with increasing L shell. Ray tracing shows that inside the plasmasphere guided L-mode waves only grow during one crossing of the magnetic equator and only achieve small path-integrated wave gain (≤2 e-foldings). At the plasmapause the density gradient enables guided mode waves to grow during several equatorial crossings and the net path-integrated gain is much larger (≂8.7 e-foldings). For the largest observed ring current densities of 4¿106 m-3 at L=4 the gain is above the critical level (10 e-foldings) for amplification to observable levels. Just outside the plasmapause the waves only grow during the first equatorial crossing and the gain is smaller. In the absence of nonconvective instabilities the path-integrated amplification of the guided mode tends to increase the L shell and reaches the critical level for observable waves only in the outer magnetosphere (L≥7). Unguided L-mode waves have very small wave gain. For L≥7 the plasma beta becomes large (&bgr;⊥>1) and should lead to the onset of nonconvective instabilities. However, we suggest that inhomogeneities in the medium and quasi-linear scattering will prevent absolute instabilities from occurring and that in reality the waves are propagating with very low group velocities. We suggest that the waves observed by Anderson et al. (1990, 1992a, b) beyond L=7 near local noon are influenced by the enhanced wave gain due to these very low group velocity waves. ¿ American Geophysical Union 1993