We analyze the Alfv¿n wave signature left behind in the ionosphere by orbiting insulated tethers operating as thrusters or generators with steady currents. Using a recent description of tether radiation to determine the far field, we show that, at their leading edges, the Alfv¿n wings have an Airy function crosswise structure. The field amplitude falls off weakly as the inverse cube root of the distance along the wave front. The front itself, which carries a negligible fraction of the power radiated as Alfv¿n waves, broadens proportionally to the cube root of that distance. We show that collisional decay becomes important at about 103 km along the front. For tethers longer than about 2 km, the top and bottom structures (wings) are fully disjoint.¿ 1997 American Geophysical Union