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The design of a 400-GHz gyrotron operating at the third cyclotron harmonic is presented. The gyrotron is designed to operate at the TE6!4-mode, which allows one to produce about 1 kW of output power with the density of ohmic losses acceptable for continuous operation. The dependence of performance characteristics on various gyrotron parameters (beam voltage, current, pitch-ratio, and velocity spread) is analyzed. It is shown that the desired mode is significantly distinct from competing modes. Special attention is given to the effect of imperfections in resonator fabrication on gyrotron performance. It is found that to keep the gyrotron performance close to the designed data obtained for an ideal resonator shape, the resonator should be fabricated with tolerance of about 1 mum. In view of the recent experimental data, such fabrication seems feasible. Therefore, the development of 1 kW, continuous-wave gyrotrons operating at the third harmonic in this frequency range looks possible.