三腔渡越管振荡器高频结构的解析研究

 从圆柱坐标系下Borgnis位函数的齐次标量Helmholtz方程出发，引入慢波驻波概念及其场表达式，利用Borgnis位函数的边界条件及相邻子区公共界面上的场匹配条件，导出了三腔渡越管振荡器内角向均匀TM模的色散关系及场分布的解析表达式。运用该解析法求得三腔渡越管振荡器的谐振频率与实验中测得的微波频率一致，求得的场分布与数值法得到的场分布十分吻合。

ANALYTIC RESEARCH ON THE HIGH FREQUENCY STRUCTURE OF THE THREE-CAVITY TRANSIT-TIME TUBE OSCILLATOR

Starting from homogeneous scalar Helmholtz's equations associated with Borgnis potential function in a cylindrical coordinate system, and based on the standing wave concept of slow-wave introduced in the paper, the analytic expressions of the dispersion relation and field distribution for azimuthally symmetric transverse magnetic modes in the three-cavity transit-time tube oscillator are derived, by using boundary conditions for Borgnis potential function in conjunction with field matching conditions at the common interface between the adjacent subregions. The resonance frequency of the oscillator calculated by this analytic method is compared with that measured in experiments and it is found that they are in agreement quite well. The field distribution of the oscillator developed by this analytic method is agreeable to that simulated by numerical code.