谐振腔链色散关系及场分布的解析研究

从圆柱坐标系下的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，导出了整腔 结尾的谐振腔链内角向均匀TM模的色散关系及场分布的解析表达式.运用该解析法对实际器 件——四腔渡越管振荡器进行了求解，求得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符合. 关键词： 谐振腔链 色散关系 场分布 解析法

ANALYTIC RESEARCH ON THE DISPERSION RELATION AND FIELD DISTRIBUTION OF THE RESON ANT CAVITY CHAIN

Starting from homogeneous scalar Helmholtz's equations associated with Borgnis p otential 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 resonant cavity chain with full-cavity terminations are derived, by using boundary conditions for Borgnis potential function in conjunction with field matching conditions at the common interface between adjacent sub regions. The resonance frequency of the four-cavity transit-time tube oscillator calculated by this analytic method is compared with that measured in experiment s 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 simula ted by numerical code.