Impulsive changes in the solar wind can deposit energy into magnetospheric cavity modes. We discuss the coupling of cavity modes to the field line continuum, and show that the time scales for dissipative phase mixing and mode conversion to kinetic Alfv¿n waves in the magnetosphere are long compared with lifetimes of MHD wave events with periods that vary continuously with radial distance. Therefore the ultimate dissipative sink for cavity mode energy should be the ionosphere. For model magnetospheres in which all wave components have a complex field aligned wave number kz=kz0(1+i&kgr;) to simulate a Poynting flux into the ionosphere, we use simple arguments to show that the coupled cavity mode damping decrement is given approximately by &ggr;/&ohgr;0 =(&ggr;/&ohgr;0)c+(kz0/k)2&kgr;. Here (&ggr;/&ohgr;0)c is the damping via coupling to the field line continuum alone, and k is the total wave number magnitude. Detailed numerical calculations in a cylindrical magnetospheric model support this, although significant departures from the approximate expression can occur for small &kgr;. Following earlier work by other authors, we emphasize that complex kz may not simulate the appropriate boundary condition for the coupled cavity mode outside resonance regions. ¿ American Geophysical Union 1989