非谐激励与周期弯晶中粒子运动的混沌行为

Anharmonic Excitation and Chaotic Behaviours for Particle Motion in Periodic Bending Crystals

摘要:

利用Melnikov方法讨论了非谐激励系统的混沌行为,并在极限情况κ→0下,把非谐激励转化为谐波激励,而运动方程化为倒置摆方程。倒置摆方程描写了带电粒子在周期弯晶中翻越势垒的横向运动行为。结果表明:系统的稳定性与参数有关,适当调整参数就能保证系统是稳定的;即使保持参数不变,调整系统初始状态也可以使系统完成从无序向有序,或者从有序向无序转换。

Abstract:

The chaotic behavior of the system with anharmonic excitation is discussed by using the Melnikov method. In the limit case, the anharmonic excitation is transformed into the harmonic excitation, and the equation of motion is induced into the inverted pendulum equation. The inverted pendulum equation describes the transverse motion of a charged particle in a periodic bending crystal. The results show that the stability of the system is related to the parameters, and the system can be stabilized by adjusting the parameters properly. Even if the system parameters remain unchanged, adjusting the initial state of the system also allows the system to transit from unordered to ordered, or vice versa.