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The production of high-power microwave radiation from a large-orbit gyrotron in azimuthally periodic boundary systems is studied theoretically and experimentally. Linear growth rates are calculated for the 2Â¿ modes of magnetron-like vane resonator (VR) and hole- and-slot resonator (HASR) systems using a general growth-rate formalism. The experiment involves the interaction of a 2.3-MeV, 1-2-kA, 5-ns rotating electron layer with two different periodic structures. About 500 MW is produced in Ku band with a 20-slot VR system and about 300 MW is produced in X band with a 10-slot HASR system. The relative merits of both types of systems are discussed.