A model is presented that describes the excitation of density perturbations and parallel electric fields by standing shear Alfv¿n waves on dipole fields in Earth's magnetosphere. The model includes the effects of electron inertia and gyro-kinetic dispersion, accounting for field-aligned variations of the electron and ion temperatures and the ambient plasma density. In a model dipole magnetosphere, it is found that dispersion and nonlinearity determine the depth, spatial structure, and temporal evolution of large-amplitude density fluctuations near to the polar ionospheres. The characteristics of magnetospheric density cavities and their relationship to auroral luminosity, or field-aligned currents, is discussed in the context of recent satellite and ground based observations. ¿ 1999 American Geophysical Union