We study the interaction of a plasma cloud, jetting across the geomagnetic field with the surrounding ionosphere. The cloud is assumed of finite extension in the direction normal to both the direction of motion and the magnetic field, while the ionosphere is considered a collisional anisotropic magnetized plasma. It is shown that two main mechanisms contribute to the cloud's braking: momentum exchange with the ionosphere via Alfv¿n waves and momentum dissipation due to resistive currents. Due to the finite size of the cloud a differential braking of the different transverse harmonics of the Alfv¿n wave appears when the momentum exchange mechanism is dominant. The result is a sharpening of the cloud's velocity field. ¿ American Geophysical Union 1988