理论推导了电磁波在半无限长直波导和均匀慢波结构交界面上的反射系数表达式，得到反射系数模值和相位随电磁波的纵向相移常数和慢波结构末端相位的变化关系。运用传输线理论以及反射系数的理论计算结果，得到了有限长慢波结构的纵向谐振条件，可以分析各种情况下有限长慢波结构的纵向谐振特性。计算了一种有限长慢波结构的纵向谐振频率，理论预测与数值仿真结果基本一致。对于一种非均匀慢波结构的数值计算结果表明，其纵向谐振模式对应的频率、场分布与相应的均匀慢波结构接近，因此仍可根据提出的纵向谐振条件对非均匀慢波结构进行分析。

The O-type Cerenkov devices usually use a section of finite-length slow wave structure (SWS) as the core region of beam-wave interaction, the longitudinal resonances occur when the electromagnetic wave is reflected at the terminal of SWS and affect the beam-wave interaction of the device, and as a result investigating the high-frequency characteristics of finite-length slow-wave structure is important for the designing of O-type Cerenkov devices’ structure. Using the field-matching method, the expression for the reflection coefficient of electromagnetic wave reflected at the intersection face of straight waveguide and SWS was derived, and the relationships between the reflection coefficient and the longitudinal wave number and SWS terminal phase were acquired. Then using the transmission line theory and the calculation results of reflection coefficient, the longitudinal resonant condition in finite-length SWS was brought forward, and using this method we analyzed the longitudinal resonances in finite-length SWS. We calculated the longitudinal resonant frequencies of a section of finite-length SWS. Theoretical and simulation results were close to each other. The resonant frequencies of a type of nonuniform SWS cold cavity were simulated; the frequencies and field distribution of the resonant mode in nonuniform SWS were close to the relevant uniform SWS. Consequently the longitudinal resonant condition could also be used for the analysis of nonuniform SWS with finite length.