在人们寻找新光源,特别是短波长激光光源的探索中弯晶起到了十分重要的作用,参数X-射线辐射射和晶体摆动场辐射引起了人们极大注意。为了成功获得参数X-射线辐射和晶体摆动场辐射,系统必须是稳定的。分析了晶体弯曲、辐射衰减、晶格热振动、电子多重散射和相互作用的非线性等因素对系统稳定性的影响。在经典力学框架内和小振幅近似下,把粒子运动方程化为了具有阻尼项、受迫项和固定力矩的广义摆方程。用摄动法讨论系统在1/2和1/3超共振附近的运动行为,发现了共振曲线的后弯和跳跃现象。临界条件的分析表明,系统的稳定性与它的参数有关,适当调节系统参数,就可以保证系统是稳定的。 Bending crystals play an important role in the exploration of new light sources, especially for short-wavelength laser sources. Parameters X-ray radiation and crystal swing field radiation have drawn great attention. In order to successfully obtain the parameters of X-ray radiation and crystal swing field radiation, the system must be stable. The effects of crystal bending, radiation attenuation, lattice thermal vibration, electron multiple scattering and the nonlinearity of interaction on system stability are analyzed. In the framework of classical mechanics and small amplitude approximation, the particle motion equations are generalized pendulum equations with damping term, forced term and fixed moment. The perturbation method is used to discuss the motion of the system in the vicinity of 1/2 and 1/3 superresonance, and the phenomenon of backward bending and jumping of the resonance curve is found out. The analysis of critical conditions shows that the stability of the system is related to its parameters. By properly adjusting the system parameters, the stability of the system can be guaranteed.