Instability of laminar magnetospheric convection with respect to the strongly anisotropic Alfven waves which are of small scale in the horizontal plane is examined. The waves prove to be trapped in the ionospheric Alfven resonator, bounded from below by the ionospheric E layer and from above by a zone of rapidly increasing Alfven velocity at altitudes of up to ~104 km. The finite-amplitude Alfven waves dissipate within a layer of anomalous resistance formed near the upper wall of the resonator. As a result, a high-energy particle source appears in the upper ionosphere. Further evolution results in the transition of laminar convection turbulent flow conditions and in the formation of a turbulent Alfven boundary layer in the polar ionosphere at altitudes from 102 to 104 km. The energy status of the turbulent Alfven boundary layer is calculated. It has been shown that the accelerated-electron energy flux density can reach ~100 ergs cm-2 s-1. ¿American Geophysical Union 1991