Alfv¿n waves reflected by the ionosphere and by inhomogeneities in the Alfv¿n speed can develop an oscillating parallel electric field when electron inertial effects are included. These waves, which have wavelengths of the order of an Earth radius, can develop a coherent structure spanning distances of several Earth radii along geomagnetic field lines. This system has characteristic frequencies in the range of 1 Hz and can exhibit electric fields capable of accelerating electrons to several keV. These electric fields have the potential to accelerate electrons in several senses: via Landau resonance, bounce or transit time resonance as discussed by Andr¿ and Eliasson [1992> or through the effective potential drop which appears when the transit time of the electrons is much smaller than the wave period, so that the electric fields appear effectively static. A time-dependent model of wave propagation is developed which represents inertial Alfv¿n wave propagation along auroral field lines. The disturbance is modeled as it travels earthward, experiences partial reflections in regions of rapid variation, and finally reflects off a conducting ionosphere to continue propagating antiearthward. The wave experiences partial trapping by the ionospheric Alfv¿n resonator, which is the effective cavity formed between the ionosphere and the Alfv¿n speed peak discussed earlier by Polyakov and Rapoport [1981> and Trakhtengerts and Feldstein [1981, 1984, 1991> and later by Lysak [1991, 1993>. Results of the wave simulation and an accompanying test particle simulation are presented, which indicate that inertial Alfv¿n waves are a possible mechanism for generating electron conic distributions and field-aligned particle precipitation. The model incorporates conservation of energy by allowing electrons to affect the wave via Landau damping, which appears to enhance the effect of the interactions which heat electron populations. ¿ American Geophysical Union 1996