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In this paper, I present simulations of a new buncher that can be used in a compact high-repetition-rate high-power microwave device. The bunching mechanism involves the growth of the II-mode of two coupled cavities traversed by a medium-power annular electron beam (200 keV, 1 kA). The cavities are simple pillboxes, and frequency tuning can be obtained by using plungers to vary the internal radius of the cavities. Since the magnetic field needed to ensure beam transport is small enough to be provided by permanent magnets, no external source is required.