A new model of the ionospheric Alfv¿n resonator (IAR) including the effect of wave frequency dispersion is presented. It is shown that the shear Alfv¿n waves in the IAR are coupled to the compressional mode through the boundary conditions at the ionosphere. This coupling results in the appearance of the Hall dispersion and subsequent shift of the IAR frequency spectrum. The excitation mechanism involving the IAR interaction with the magnetospheric convective flow is considered. It is shown that the Hall dispersion of the IAR eigenmode increases the growth rate of the feedback instability. However, for the observed values of ionospheric conductivity this effect is not very high. It is shown that the physical mechanism of the feedback instability is similar to the Čerenkov radiation in collisionless plasmas. The IAR eigenfrequencies and growth rates are evaluated for the case of exponential variation of the Alfv¿n velocity with altitude in the topside ionosphere. ¿ 2000 American Geophysical Union