关键词: 
参数X射线辐射 /
相平面 /
弯晶 /
摆方程 /
Jacobian椭圆函数

摘要: 寻找新光源， 特别是企图利用PXR作为激光光源引起了人们广泛关注。 要成功获得相干（衍射）的PXR光源， 粒子的运动必须是稳定的。 但是由于晶体弯曲，系统可能变得不稳定， 从而对PXR的反射、 衍射、 聚焦和谱分布均会产生直接影响。 在经典力学框架内和偶极近似下， 引入正弦平方势， 把粒子在弯晶中的运动方程化为具有常数力矩的摆方程。 利用Jacobian椭圆函数和椭圆积分分析了系统的相平面特征。 结果表明， 系统的稳定性与弯晶“曲率”Q有关， 当条件0≤Q<1满足时， 系统是稳定的。 An exploration of a new light source by PXR as Laser gived rise to extensive attention. The particle motion must be stable in order to obtain coherent PXR source. But, an instability of system is possible due to the effect of bent crystal， thus the reflection, the diffraction, the focus and the spectral distribution of PXR will be effected.In the classical mechanics frame and dipole approximation the particle motion equation in bent crystal is reduced to the pendulum equation with a constant momentum by the sinesquared potential.The phase planar properties are analysed by means of Jacobian elliptic function and the elliptic integral. It shows that the stability of the system is related to the curvature Q of the bent crystal. When the condition 0≤Q<1 is satisfied, the system is stable。