Using the WKB approximation, we analyze the phase and energy structure of damped Alfv¿n wave structures in a magnetospheric field configuration. In the WKB limit the real part of the eigenfrequency is determined by the field line length while the damping rate is determined by the ionospheric conductivity. Expressions are worked linking the damping decrement to the ionospheric damping, and it is shown that the damping effect of each ionosphere adds linearly to the damping decrement. We end with a critique of the use of the WKB solution for Alfv¿nic wave structures and indicate where such solutions may be unreliable. ¿ 2001 American Geophysical Union