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In order to alleviate the problem of achieving large powers beyond 10 kW at frequencies as high as 220 GHz, a two-stage, two-sheet-beam relativistic TWT (SBRTWT) was proposed. For one-stage SBRTWT, there exists instability phenomenon as the effect of electron noise will become large enough compared with the small input power. To avoid the effect, the gain of the first-stage tube was decreased, and its output power was employed to drive the second-stage tube. A large-width branch-guide energy coupler was proposed, analyzed and designed, which can solve the difficult problem to couple the amplified microwave from a wide waveguide to another wide waveguide. A two-beam SBRTWT of 70 kW output with a gain of 28.5 dB was predicted. The findings establish that the two-stage configuration provides larger output powers than the single-stage configuration of SBRTWT and call for further research in two-stage SBRTWT. [ABSTRACT FROM PUBLISHER]