An advantageous configuration for plasma heating with a relativistic beam utilizes an annular beam rotating about a guide magnetic field. The return current processes for such a configuration are considered. For the parameters expected to prevail in an experiment, the plasma response can be described as magnetic diffusion or critically damped magnetosonic waves, these being equivalent. Equations for the axial and angular return currents are derived and take the form of decoupled diffusion equations. The effects of pulse shape, boundary conditions, etc. are then treated. The drag force on the beam resulting from the interaction is greatly enhanced and leads to a stopping length reduction by the factor (1/2)(v∥/c)3as compared with nonrotating beams. The implications of these effects for a plasma heating application are discussed.