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A high efficient relativistic backward wave oscillator with coaxial nonuniform slow-wave structures (SWSs) and depth-tunable extractor is presented. The physical mechanism to increase the power efficiency is investigated theoretically and experimentally. It is shown that the nonuniform SWSs, the guiding magnetic field distribution, and the coaxial extractor depth play key roles in the enhancement of the beam-wave power conversion efficiency. The experimental results show that a 1.609 GHz, 2.3 GW microwave can be generated when the diode voltage is 890 kV and the beam current is 7.7 kA. The corresponding power efficiency reaches 33.6%. [ABSTRACT FROM AUTHOR]