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A new slow-wave circuit structure for traveling-wave tubes consists of a ridged rectangular waveguide with a series of transverse slots in the broad wall opposite the ridge. This structure can be fabricated easily in sizes small enough for use at millimeter wavelengths if the slotted wall is prepared either by winding a grid or by photo-etching the slots in a thin metal sheet. Demountable traveling-wave tubes were constructed in which an electron beam was coupled to space-harmonics of waves traveling on such a circuit. Using a circuit whose slotted wall was fabricated by the photo-etching technique, forward-wave interaction and backward-wave oscillations were obtained in a wavelength band centered at 5.4 mm. With structures whose slotted walls were prepared by grid winding, backward-wave oscillators were made which performed in wavelength bands centered at 5.1 mm and at 3.6 mm.