Ionospheric currents must close by means of field-aligned currents into the magnetosphere if they are not divergence free. Particle precipitation associated with the field-aligned current can change the ionospheric conductivity and therefore the current pattern, leading to a feedback process which can result in traveling enhancements of the ionospheric conductivity. These processes are studied by means of a two-dimensional model of magnetosphere-ionosphere coupling which includes enhancements in the Pedersen conductivity but assumes that the Hall current is divergence free. It is shown that under appropriate conditions this feedback instability can take place with the efficiency of the coupling dependent on the ratio of the height-integrated Pedersen conductivity to the effective admittance of Alfv¿n waves on the flux tube. Since the Alfv¿n admittance changes along the field line, internal reflections of Alfv¿n waves from gradients in this admittance can lead to the generation of pulsations of the current in the Pi 1 range, with the frequency being dependent on the ionospheric scale height.