Abstract: As the operating frequency band of traveling wave tubes continues to advance into the terahertz frequency band, the influence of the size co-transit effect is becoming more and more obvious, which is mainly manifested in the continuous reduction of the transverse size of the slow wave structure and the width of the electron beam channel, resulting in the improvement of the processing difficulty, the reduction of the operating current and the decrease of the coupling impedance, which seriously affects the performance of the traveling wave tubes. Over-mode traveling wave tubes operating in higher order mode can solve this problem effectively. In order to solve the problems of low-order mode competition and back-wave oscillation, an improved staggered double vane slow wave structure is proposed. This structure works in high-order TE₃₀ mode. Compared with the basic mode circuit operating in the same frequency band, the transverse size and channel height are extended by 3 times and 2 times, respectively. The results of mode analysis show that the new structure can effectively suppress back-wave oscillation and mode competition at relatively low operating voltage. Based on the new structure, a two-stage high frequency circuit is designed. PIC simulation shows that the power output of 103.5 W can be obtained at 217 GHz with a gain of 19.6 dB at 26 kV voltage and two 150 mA sheet-beams. The spectrum analysis results show that the operation is stable and no oscillation occurs. This work has guiding significance for the development of over-mode traveling wave tubes.