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A closed microwave resonator is derived from the beam waveguide of rectangular symmetry. The resonator is essentially a metal box with one curved wall and approximate dimensions by by , where is the free-space wavelength. Each beam waveguide mode is shown to resonate at a distinct frequency. When apertures are cut in one wall of the resonator a line source antenna is formed. Since the and beam modes have field distributions which are, respectively, a Gaussian and the derivative of a Gaussian, the radiation patterns produced are of interest in monopulse radar and tracking. A 9 GHz resonator antenna was built, and its measured radiation patterns confirm the theory.