As Alfv¿n waves with finite extent perpendicular to the magnetic field propagate from the magnetosphere to the ionosphere, there is a region of parallel electric field in the ''wave front'' of the propagating wave. For short perpendicular wavelengths this parallel electric field can be large enough to accelerate electrons to auroral energies. This problem is solved for the case of uniform plasma density and background magnetic field. The parallel electric field solution is then applied to a background Maxwellian plasma to study the effects of the acceleration due to this field on the electron distribution function. Two effects are found: (1) the relatively modest acceleration of the bulk of the background electrons and (2) Fermi-like resonant acceleration of a small component of the electrons up to velocities of the order of twice the Alfv¿n speed. Although both effects always occur, the response of the background electrons is a sensitive function of the magnitude, wavelength, and timescale associated with the driving perpendicular electric field. In particular, the latter effect does not produce a significant signature for all conditions. However, for reasonable values of perpendicular electric field magnitude and scale size, and plasma parameters appropriate for auroral field lines at altitudes around 7000 km near where the Alfv¿n speed peaks, the effect can be significant. ¿ American Geophysical Union 1994