The exponential increase of the Alfv¿n speed in the topside ionosphere leads to the formation of a resonant cavity (Lysak, 1988) which has been termed the ionospheric Alfv¿n resonator by Trakhtengertz and Feldstein (1984). These authors primarily considered the situation where the ionospheric Pedersen conductivity is low, while Lysak (1988) considered the opposite limit of infinite ionospheric conductivity. These results have been extended to arbitrary ionospheric conductivity by performing a numerical solution of the cavity dispersion relation, which involves Bessel functions of complex argument and order. These results indicate that the damping of excitations of this resonant cavity is strongest when the ionospheric Pedersen and Alfv¿n conductivities are comparable and that growth is possible for incoming wave boundary conditions. The existence of this cavity leads to a modification of the Alfv¿n wave reflection coefficient at the ionosphere. While this reflection coefficient is independent of frequency at low frequencies, it exhibits structure due to the resonant cavity modes at frequencies around 0.1-1 Hz. These cavity modes can also be excited by feedback instabilities (Sato, 1978; Lysak, 1986), leading to growth rates which are enhanced over the case without the cavity. These waves have maximum growth at short wavelengths, particularly when the background Pedersen conductivity is large. The perturbations associated with these instabilities can lead to structuring of auroral currents during substorms, and may help explain the westward traveling surge. ¿1991 American Geophysical Union