提出了一种工作在TM₅₁-2π模式的Ka波段同轴多间隙谐振腔，使用CST本征模求解器研究了此结构的电场分布特性，并分析了基于外侧全通的耦合方式下该结构的冷腔模式特性。在此基础上，通过结合空间电荷波理论和CST三维粒子仿真分析，研究了在多电子注激励下同轴多间隙腔高次模式的起振特性，并分析了此种结构的模式稳定性与注-波互作用特性。研究结果表明：对于工作在Ka波段的TM₅₁-2π模式同轴多间隙腔，采取结构外侧全耦合的方式具有较高的模式稳定性；在此结构中，多电子注不仅会均匀激励起工作模式，也可能非均匀激励起竞争模式；不同于工作在基模的扩展互作用速调管，此种结构的速调管电场极值是分别建立的，因此激励电子注可放置在不同相位的电场极值处；在保持电子注电压、总电流不变的情况下，采取更多电子注的激励方式，需要更小的聚焦磁场。

This paper proposes a Ka-band coaxial multi-gap cavity operating in the TM₅₁-2π mode. The CST eigenmode solver is used to study the characteristics of the electric field distribution, and the mode characteristics of this cavity have been analyzed based on the all-pass coupling structure at the outer radius. By combining space-charge wave theory and 3-D particle-in-cell (PIC) simulation analysis, this paper studies the start-oscillation characteristics of the high-order mode coaxial multi-gap cavity using the multi-beam excitation method. And it analyzes the mode stability and beam-wave interaction characteristics of the coaxial multi-gap cavity operating in the high-order mode. The results show that the coaxial multi-gap cavity operating in the TM₅₁-2π mode adopting the coupling method at the outer radius possesses high mode stability. In this structure, multiple beams can not only uniformly inspire the operating mode but also non-uniformly inspire the competition mode. Different from the multi-beam extended-interaction klystron (EIK) operating in the fundamental mode, the high-order mode EIK with this structure establishes the gap voltages separately. Therefore, the peak electric fields with different phases can interact with the beams respectively. While keeping the same total beam current and beam voltage, the operating method driven by more beams requires a smaller focusing magnetic field.