自由电子激光的小型化和实现激光短波长一直是自由电子激光领域的研究热点 ,而短周期、强场摇摆器是解决此问题的行之有效的途径。文章分析了利用等离子体尾波场作为自由电子激光摇摆器的机制 ,推得自由电子的自发辐射谱 ,利用麦迪定理和天线阵列理论求得了电子的受激辐射公式 ,得到小信号增益 The miniaturization of free electron laser and the realization of short wavelength of laser have always been the focus of research in the field of free electron laser. However, the short period and strong field wobbler are the effective ways to solve this problem. The paper analyzes the mechanism of using the plasma tail wave field as the free electron laser wobbler, deduces the spontaneous emission spectrum of the free electrons, and uses the Maddie theorem and the antenna array theory to derive the electron’s stimulated emission formula to obtain the small signal gain