考虑了当射频调制的超短脉冲电子束径向长度远小于辐射波长时,将其理想化为δ时间函数,提出了用波导本征模展开的方法来计算矩形波导中超短脉冲电子束的相干同步辐射及其频率特性。结果发现：①当谐振频率等于调制电子束微脉冲间隔的射频的整数倍时,辐射模式表现为“纯”的波导本征模。②波导效应使得超短脉冲电子束在两个频率处发生相干同步辐射,而且低频支的辐射功率高于高频立的。最后指出了波导自由电子激光器单横模运行的条件。

Idealizing the radio-frequency (RF) modulating ultrashort electron pulse as a δ time function, we analysize theoretica1ly the coherent synchrotron radiation emitted by the high bunched electron beam and its frequency properties in a reetangular waveguide. We find two new performances: (1 ) when the resonance frequency fs is just equal to integral times of radio frequency fRF which is applied to modulate electron beam, the coherent synchortron radiation field pattern appears "pure" waveguide eigenmode; (2) the coherent synchrotron radiation power at low resonance frequency is higher than that of at high resonance frequency. In addition, we predict the condition for single mode transverse operation in a waveguide FEL.