Inertial Alfvén waves propagating in regions of auroral electron acceleration are observed from the FAST (Fast Auroral Snapshot) spacecraft over its entire altitude range (350–4180 km). These electron skin depth sized field structures are dispersive and carry an electric field component parallel to the geomagnetic field leading to a variety of non-linear effects including the formation of magnetic field-aligned density cavities and electron acceleration. High resolution measurements show that the electron distribution inside the impulsive wave field envelope or density cavity consists of a cold ionospheric component and an accelerated and heated field-aligned component comprised of downgoing and reflected ionospheric and magnetosheath (solar wind like) electrons. In large amplitude examples the plasma within the wave may be dominated by the accelerated component and the depletion of plasma within the cavity approaches 100%. Comparison of the observed density depletion with the predictions of ponderomotive density cavity formation in association with electron heating shows good agreement. Furthermore, simulations show that most of the observed features of the accelerated component can be explained through Landau resonance of the cold ionospheric and magnetosheath electrons with the inertial Alfvén wave as it propagates through an altitude dependent density profile.