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The design parameters of a 120-GHz gyromonotron capable of output powers in excess of 1 MW are determined. A nonlinear model of the interaction between the beam and RF field is used in which the efficiency is a function of only three normalized variables. By expressing the technological constraints in terms of these variables, permissible design parameters yielding high-efficiency operation can be calculated. Constraints that are considered include ohmic heating of the walls, voltage depression of the beam, reduced coupling between the beam and RF field due to beam thickness, and efficiency degradation due to space-charge forces within the beam. An analysis of the trade-offs between current and voltage at the 1-MW level indicates that lower-order modes can be utilized at lower voltages, but the constraints based on current limitations are difficult to satisfy. An 80-kV 29-A design is presented that achieves a total efficiency of 44 percent. The primary uncertainty of these designs is the severity of competition due to parasitic modes. However, a number of isolated asymmetric modes appear capable of single-mode emission at 1 MW based on present experimental results. Multimegawatt operation is also considered. It is shown that powers exceeding 20 MW are possible if single-mode operation can be achieved in very-high-order modes. The methodology presented in this paper is general and can be easily adapted to other frequencies and output powers.