倒置摆的有效势与晶体摆动场辐射的稳定性

Effective Potential Of Inverted Pendulum And Stability Of Crystalline Undulator Radiation

在经典力学框架内,把粒子的运动方程化为倒置摆方程。在线性近似下,分别用参数变易法和LP方法讨论了无阻尼情况下系统的一阶不稳定区。在非线性近似下,用有效势分析了系统的稳定性,并对普通摆和倒置摆进行了统一描述。结果表明,系统的稳定性与阻尼有关,阻尼越大稳定性越好;指出了普通摆描述的沟道粒子的运动行为,系统的平衡位置过支点垂直向下;倒置摆描述了带电粒子在周期弯晶中的准沟道行为,平衡状态过支点垂直向上。

In the framework of classical mechanics,the motion equations of particles in crystalline undulator was reduced to inverted pendulum equation.In linear approximation first order unstable region with undamping system was discussed respectively by the parameters variation methods and LP methods.In the non-linear approximation,the stability of the system was analyzed by using the effective potential,and the properties for the ordinary pendulum and the inverted pendulum were descripted uniformly.The results show that the systems stability is related to damping,and greater damping results in better stability.It pointed that ordinary pendulum describes the motion behavior of channeling particle,the equilibrium position of the system is vertically downwards over the pivot,inverted pendulum describes a quasi-channeling behavior of a charged particle in a crystalline undulator,and the equilibrium state is vertically upwards over the pivot.