变参数Smith－Purcell型自由电子激光的小信号增益公式

Formula for the Small Signal Gain of the Variable Parameter Smith-Purcell Effect FEL

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。

Using a disturbance develop method, we have obtained the formula for the small signal gain (S. S. G.) of the variable parameter Smith-Purcell effect FEL and show that the gain spectrum function factor takes the same form as the variable parameter Wiggler.On the basis of this formuls, the S.S.G. for linerly varying of grating space frequency is discussed. The resultS show that when the speed of the injected electron is within a range,lower than the initial resonance speed,a higher S.S.G. can be attained,and that in order to enhance S.S.G.for a given saturation efficiency, the changing rate of grating space frequency should be chosen properly.