This paper treats the double and multiple beam TWA and BWO from a unified coupled-mode point of view. Coupled mode and characteristic equations for completely separated and completely intermingled double beam TWA and BWO are first derived. Ash’s results are extended to cases with distributed loss. Theoretical starting current of such a BWO compares satisfactorily with the experimental values. The gain of a completely separated double beam TWA
as well as the beam separation effects
is discussed. Finally the starting current and gain respectively of a multiple beam TWA and BWO are treated as an extension of the double beam case.