基于电子与光栅表面电势场相互作用的模型，用经典的单粒子理论研究了Smith-Purcell效应的辐射过程，得到了自发辐射谱。讨论了自发辐射与受激辐射之关系，即Madey定理在该类激光器中的对应形式。结果对于高能电子束同样适用。

On the basis of the model of the interaction between eletron and the surface electrostatic field of the grating,the radiation in Smith Purcell effect is studied by the classical theory of single particle,and the spontaneous radiation spectrum is derived.The relation of the spontaneous radiation and the stimulated radiation,which is Madey theorem in Smith Purcell effect FEL,is discussed.The results mentioned above are available for high energy eletron beam.