设计了一种X波段过模高效率相对论返波管（RBWO），主要结构包括双谐振腔反射器、7周期梯形慢波结构与提取腔。该器件慢波结构的过模比为2.6，电子束与结构波TM01模的近π模相互作用，在慢波结构区域束波作用产生的TM01模表面波主要转化为TM02模的体波，其输出微波的模式主要为TM02模，占比为81%，其余为TM01模。提出一种过模条件下谐振腔反射器的设计思路，结合模式匹配法，优化得到了一种双谐振腔反射器结构，其对TM01模与TM02模的反射系数均大于0.99，可实现过模条件下RBWO慢波结构与二极管区的良好隔离；同时双谐振腔反射器两个谐振腔中的纵向电场可以对电子束进行充分的预调制，将促进慢波结构区域的束波作用，有利于提升效率。通过在慢波结构后端加入提取腔，进一步提升了转换效率。PIC仿真中,在二极管电压900 kV，电流14.3 kA，得到了6.6 GW的输出功率，转换效率约51%。

A high efficient X-band over-mode relativistic backward wave oscillator (RBWO) is studied in this paper, which is composed of a dual-cavity reflector, a 7-periods trapezoid SWS and extraction cavity. The ratio of D to λ of the generator is 2.6, and the electron beam interacts with the TM01 near π mode of the structure wave. In the SWS region the TM01 mode surface wave mainly transfers to the TM02 mode body wave, the primary mode of the output microwave is TM02 mode with the proportion 81%, and the remainder is TM01 mode. A method to design the resonant reflector under over-mode condition is proposed, a dual-cylindrical cavity reflector is optimized by using the mode-matching method, and the reflection coefficients for the TM01 and TM02 mode are larger than 0.99, hence the well insulation between the SWS and the diode is achieved. Simultaneously, the longitudinal electric field of the resonant reflector could pre-modulate the electron beam sufficiently, which would promote the beam-wave interaction in the SWS. Furthermore, the transfer coefficient is increased by loading the extraction cavity after the SWS. Simulation results indicate that microwave output power of 6.6 GW is achieved, the diode voltage is 900 kV and beam current is 14.3 kA, and the transfer efficiency is 51%.