We analyze the Alfven wave signature left behind in the ionosphere by
orbiting insulated tethers operating as thrusters or generators with s
teady currents. Using a recent description of tether radiation to dete
rmine the far held, we show that, at their leading edges, the Alfven w
ings have an Airy function crosswise structure. The field amplitude fa
lls off weakly as the inverse cube root of the distance along the wave
front. The front itself, which carries a negligible fraction of the p
ower radiated as Alfven waves, broadens proportionally to the cube roo
t of that distance. We show that collisional decay becomes important a
t about 10(3) lan along the front. For tethers longer than about 2 km,
the top and bottom structures (''wings'') are fully disjoint.