Measurements are presented of the edge wave magnetic fields generated by fast wave antennas in the TORTUS Tokamak. All measurements were made in a deuterium plasma and at frequencies in the range 2< omega / omega ci<4, where omega ci is the ion cyclotron frequency. High Q cavity modes were observed only for the m=+1 mode, although many other cavity modes were expected on the basis of cold plasma calculations. High m modes were also observed, not as cavity modes, but in the form of an evanescent beam guided along steady magnetic field lines in the plasma edge. The three-dimensional structure of the beam was determined using toroidal and poloidal arrays of magnetic probes. The existence of the beam is attributed to Alfven resonance conditions at the plasma edge.