The formation, temporal behavior, and spatial structure of field line resonance (FLR) layers formed by shear Alfv¿n waves standing along auroral magnetic field lines between the ionospheres are investigated when the layer develops transverse structure on the scale of the ion Larmour radius. Using a new numerical model including full ion Larmour radius correction in dipole magnetic geometry with realistic distributions of background plasma temperature and density, the following is shown: (1) Hot magnetospheric ions significantly retard the development of a parallel electric field in ion gyroscale dispersive Alfv¿n waves. (2) A fundamental FLR forming near L=7.5 can contract to a transverse scale size of several hundred of meters in the direction perpendicular to the geomagnetic field at ionospheric altitudes, with a parallel electric field sufficient to produce a kV potential drop along the resonance field line from the ionosphere up to ~4 RE altitude, in the region where the wave dispersion is due to the finite electron inertia. (3) A plasma density depletion in the lower auroral magnetosphere (≈2--5 RE geocentric distance) enables the formation of a nonradiative fundamental FLR. (4) Dispersive FLRs for the higher harmonics are more radiative at the equatorial magnetosphere than the fundamental mode. ¿ 1998 American Geophysical Union