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利用微扰展开法导出了变参数Ｓｍｉｔｈ－Ｐｕｒｃｅｌｌ型自由电子激光小信号增益表达式，其增益谱函数因子在形式上与变参数Ｗｉｇｇｌｅｒ情况的表达式相同。在此基础上讨论了光栅常数均匀变化时的小信号增益。结果表明：当电子入射速度低于系统初始谐振速度的某一范围时，有较高的小信号增益；在保证一定的饱和抽取效率情况下，为了提高小信号增益，应适当地选取光栅的空间频率变化率。
The small-signal gain of Smith-Purcell free-electron laser with varying parameters is deduced by the perturbation expansion method. The gain spectrum function factor is the same in form as Wiggler’s variable parameter. On this basis, we discuss the small signal gain when the grating constant changes uniformly. The results show that when the electron incident velocity is lower than a certain range of the initial resonance speed of the system, the small signal gain is high. In order to improve the gain of small signal under certain saturation extraction efficiency, the grating space should be properly chosen Rate of change of frequency.