The complex ray theory of Budden & Terry (1971) has been used to study ion cyclotron whistlers in the topside ionosphere. A study of mode coupling processes by the use of ray tracing is impossible using standard real ray theory, but they can sometimes be handled by using complex rays and complex space. Losses by coupling have a similar effect to losses by collisional damping, and large coupling losses produce large complex lateral deviation in the ray path, which in turn requires the use of angles of incidence with an appreciable imaginary part to ensure that the ray path ends at a real point. The importance of understanding the branch points of the Booker quartic equation, and the Stokes phenomenon at these points is stressed. Results are presented for calculations in a model ionosphere, which agree quite well with experimental observations.
