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。%Searching for new light source, especially short wave-length coherence light source has attracted extensive attention. The using of the crystalline undulator radiation as a short wave-length coherence light source is most likely to be one of the options. From the viewpoints of potential and field, the centrifugal force generated by periodic bent crystal is regarded as centrifugal potential, the particle motion equation is reduced to Mathieu equation with Duffing-type, and from the energy viewpoint the stability of the system is discussed. The behaviors of particles in the vicinity of the resonance are analyzed by perturbation method; the jump phenomena and instable behavior are revealed. The results show that the stability of the system is related to its parameters, and only properly adjusting these parameters, the bifurcation and instability for the system can be avoided in principle.
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