We present a two-dimensional numerical model for the formation of discrete auroral arcs. This model describes the evolution of shear Alfv¿n waves generated by a growing force near the equatorial plane, and the transition to electrostatic fields when the force becomes stationary. The parallel electric fields on auroral field lines may be regarded as shear Alfv¿n waves driven by a magnetospheric generator at zero frequency. In our collisionless model, precipitating auroral electrons are accelerated to an energy of 350 eV when the upward current is 3.1 &mgr;Am-2. We also find that the electrostatic potential drop is proportional to the square of the current density. ¿ 2000 American Geophysical Union