Mathieu方程的不稳定区及其晶体摆动场辐射的稳定性

Unstable Region of Mathieu Equation and Stability for Crystalline Undulator Radiation

摘要:

从势和场的观点出发, 在经典力学框架内和线性近似下, 把粒子的运动方程化为Mathieu方程。利用多尺度方法求出了系统的周期解以及相应的过渡曲线, 并讨论了系统的稳定性。结果表明, 系统的稳定性与弯晶曲率有关, 曲率越大稳定性越差。这就是说, 试图利用晶体摆动场辐射作为短波长相干光源时, 系统稳定性必须充分考虑。

Abstract:

Looking for new sources, especially coherent light source with short-wavelength has aroused close attention. From the views of potential and field , the motion equations of particles is reduced into Mathieu equation in the framework of classical mechanics and linear approximation. The periodic solution and corresponding transition curve are calculated by using method of multiple scales, the stability of the system is discussed. The results show that the system stability related to curvature of bend crystal, the curvature the greater, stability of the system worse. This means that system stability must be fully considered when people tries to use a crystalline undulator radiation as coherent light source with short-wavelength.