The parallel electric fields associated with inertial Alfvén waves are investigated using a self-consistent drift-kinetic simulation code. The simulation code allows for non-linear effects and we show that when the wave energy is large in comparison to the plasma thermal energy, the amplitude and form of the parallel electric field can evolve significantly as the wave propagates throughout the plasma. In this paper, we discuss the effects of grid resolution on the amplitude of the parallel electric field and show that the integral of positive parallel electric field with respect to time is a more useful measure of the downward electric field force available for electron acceleration than the maximum of the parallel electric field. Although the parallel electric field theoretically maximises when the product of perpendicular wavenumber (k⊥) and electron skin depth (δe) is equal to one, the amount of resonant electron acceleration maximises for k⊥ δe > 1, since the electron acceleration mechanism is sensitive to the local phase velocity of the wave. We determine the phase velocity of the idealised pulses studied by our simulation code and show that it is well approximated by the solutions of the linear dispersion relation. Our results suggest that electron acceleration occurs mainly for k⊥ δe > 1, which in turn implies very short perpendicular scale lengths for waves in the auroral acceleration region.