Mathieu方程与束流冷却对同步运动的影响  

Effects of Mathieu Equation and Beam Cooling on Synchrotron Motion

作　　者：罗晓华[1,2] 何为[2] 

机构地区：[1]重庆交通大学图书馆,重庆400074 [2]重庆大学电气工程学院,重庆400044

出　　处：《东莞理工学院学报》2012年第3期25-30,共6页Journal of Dongguan University of Technology

摘　　要：在经典力学框架内,考虑了束流冷却对同步运动的影响,在周期冷却情况下,把粒子的同步运动方程化为Mathieu方程。由于参数激励,系统呈现出了一系列稳定区和不稳定区(禁带);对可能存在的一阶不稳定区进行了讨论,用摄动法导出了它的边界曲线和禁带宽度,并讨论了粒子的禁带穿越和临界条件,导出了一次谐波振幅的临界值。This paper considered the effect on the synchrotron motion by the cooling effect;in the classical mechanics frame and the periodic cooling case, the synchrotron motion equation of the particle is reduced to the Mathieu equation. There is the series stable and instable zone in the system by the parameter activation. We discussed 1-order instable zone and its width of the stop band, studied crossing over the stop band and the critical condition in the system, and derived the critical value for 1-order harmonic amplitude.

关 键 词：同步运动 束流冷却 MATHIEU方程 稳定性 禁带穿越 

分 类 号：TL1[核科学技术—核能科学] TL5