The fine structure of dispersive Alfv¿n wave resonance layers extending along magnetic field lines from northern to southern auroral ionospheres is investigated using a magnetically incompressible, linear, two-fluid model. The model includes effects of finite electron inertia (at low altitude) and finite electron pressure (at high altitude). Plasma parameters are chosen so that refraction by the parallel inhomogeneity causes the dispersive Alfv¿n wave to become trapped in the resonance layer. The parallel and perpendicular structure of these nonradiative, dispersive resonance layers is computed for the first four odd harmonics. A significant enhancement of the perpendicular and parallel components of the electric field near the ionosphere is found. The instantaneous potential drop along the magnetic field is sufficient to accelerate electrons up to several keV. The thickness of field line resonance layers in the ionosphere is estimated to be less than 5 km. The results suggest that dispersive resonance layers produce subkilometer-scale, multiple, discrete auroral arcs. ¿ American Geophysical Union 1996