It is shown that polar cap arcs of typical electron energy ≤1 keV can be produced by the downward acceleration of polar rain electrons by parallel potential drops on open field lines. The formation of these arcs is the result of current response to meso-scale velocity shear structures in the ionospheric convection that is not matched at the magnetosphere. The theory predicts the formation of a pair of meso-scale field-aligned currents (one upward and one downward) for each ionospheric shear structure. The theory does not require a bifurcated magnetic configuration for each polar cap arc; hence, it can account for the frequently encountered multiple polar cap arcs without cutting up the magnetosphere into a large number of open and closed magnetic field regions. ¿ American Geophysical Union 1989