Abstract: The interaction between the free-electron and laser field has been considered; the longitudinal equation for an electron has been reduced to the pendulum equation, and the gain has been derived by using the energy conservation and the perturbed method.

Key words: channeling radiations, pendulum equation, gain

摘要： 考虑了电子同激光场的作用,把电子的纵向运动方程化为摆方程;并利用能量守恒和摄动法,导出了激光增益表达式。

关键词: 沟道辐射, 摆方程, 增益