The operation of an electrodynamic tethered satellite system in the ionosphere in a steady state (constant current) mode is intimately connected with the electromagnetic plasma waves the system excites, since these waves carry the electrical currents that complete the tethered system/plasma circuit. The analysis reported here determines (within cold plasma theory) the ionospheric currents and associated wave impedance based on a tethered system current distribution that takes into account the ''dumbbell'' geometry of the system. The analysis is not restricted to terminating satellite dimensions that are much greater than the system's velocity divided by the ion cyclotron frequency, as has been the case in almost all previous studies of the problem. When this condition is not satisfied, the ''Alfv¿n wings'' (field line sheet currents) are found to be wider than the dimensions of the terminating satellite, a result of the wave nature of the phenomenon and restrictions on perpendicular wavelengths along the line-of-flight direction. Previously reported large wave impedances associated with an orbiting wire, which would limit tether currents to low values, are shown to be inapplicable to a more realistic model of the tethered system. The calculated wave impedance, which depends weakly on the system dimensions, is only a few ohms or less in low Earth orbit. ¿ American Geophysical Union 1988