Observations from the FAST satellite are used to create a model for dispersive Alfv¿n waves above the auroral oval. Using this model, it is shown how these waves may accelerate ionospheric ions transverse to the geomagnetic field and cause ion outflow. The model waves grow from ionospheric conductivity variations due to auroral electron precipitation and resonate in the cavity between the ionosphere and the peak in the Alfv¿n speed that occurs at altitudes of ~1 Earth radius (Re). By tracing ions in the model wave field, it is demonstrated that for transverse wave amplitudes (E$perp$) satisfying E$perp$/Bo Ωi/k$perp$ the ion motion may become stochastic allowing acceleration to energies exceeding that prescribed by λ$perp$. The transversely accelerated ions in both the coherent and stochastic cases flow upward from the ionosphere under the influence of the mirror force to altitudes of 1 Earth radii over timescales as small as a few seconds to minutes with energies in the keV range. Ions accelerated by these means may account for the intense outflowing ion fluxes observed in Alfv¿n waves above the auroral oval.