寻找新光源,特别是短波长相干光源引起了人们的广泛注意,利用晶体摆动场辐射作为短波长相干光源是最有可能的方案之一,本文从势和场的观点出发,把周期弯晶产生的离心力视为离心势,将粒子运动方程化为Duffing型Mathieu方程,从能量观点出发讨论了系统的稳定性,用摄动法对共振线附近粒子的运动行为进行了分析;揭示了系统的跳跃现象和不稳定行为,结果表明,系统的稳定性与其参数有关,适当调节这些参数,系统的分叉和不稳定性原则上可以避免。 Finding new light sources, especially short-wavelength coherent light sources, has drawn people’s attention. It is one of the most possible solutions to use the radiation of crystal oscillating field as the short-wavelength coherent light source. In this paper, from the viewpoint of potential and field, Centrifugal force is regarded as the centrifugal force. The particle motion equation is transformed into the Duffing-type Mathieu equation. From the energy point of view, the stability of the system is discussed. The perturbation method is used to analyze the particle’s movement behavior in the vicinity of the resonance line. Phenomenon and unstable behavior. The results show that the stability of the system is related to its parameters. Adjusting these parameters properly, the bifurcation and instability of the system can be avoided in principle.