A two-dimensional particle code used to simulate the propagation of inertial Alfv¿n waves down auroral field lines. The simulation domain is 20,000 km parallel to the magnetic field and some tens of kilometers perpendicular to the field. Electrons are tied to the magnetic field. Effects of a variable magnetic field and magnetic mirror force are included. A spatially narrow Alfv¿n pulse is launched by application of a variable potential with peak amplitude of 100 V at the top of the simulation domain. If the thickness of the pulse is less than the electron inertial length, the pulse tends to broaden as it propagates down the field line. The result is a parallel electric field considerably smaller than might be expected, assuming a wave whose perpendicular wavelength maps along magnetic field lines. In this model the strongest interaction between the electrons and the Alfv¿n wave occurs in the 3000 to 7000 km altitude range with an energy gain of the order 100 eV. The downward acceleration was strongest when the applied excitation consisted of a moving positive pulse followed by a negative pulse. Strongest upward acceleration was seen when the polarity was reversed. When the magnitude of the driving potential was doubled, there appeared to be some acceleration in the 9000 to 18,000 km altitude range and acceleration of some particles to 1.5 keV.