A linear theory for a rectangular waveguide cyclotron maser with a sheet electron beam is developed by using the Laplace transformation approach. This theory can be applied to any TEmn rectangular waveguide mode. The corresponding equations for the TMmn mode in the rectangular waveguide are also derived as a useful reference. Especially, the effect from the coupling between degenerate modes, which is induced by the nonideal rectangular waveguide walls, on the dispersion relation is considered in order to provide a more accurate model for the real devices. Through numerical calculations, the linear growth rate, launching loss, and spontaneous oscillations (caused by the absolute instability and backward wave oscillation) of this new structure can be analyzed in detail. It is worthwhile to point out that the operation at higher power levels of the rectangular waveguide sheet beam system is possible.
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