周期场中片状束输运的分叉与混沌行为

The Bifurcation and Chaotic Behavior of Sheet Beam Transport in Periodic Field

摘要:

强流技术的基本问题之一是它的空间电荷和束流的稳定性。利用片状束在周期场中的聚焦和输运可将问题减至最小。引入非线性和运动阻尼, 在经典物理框架内, 把周期场中片状束的冷腔运动方程化为广义的Mathieu方程。利用Melnikov方法分析了系统的次谐分叉和 Smale 马蹄混沌; 并对系统的临界条件进行了讨论。结果表明, 系统稳定性与它的参数有关, 只需适当调节参数原则上可以保证系统的稳定性。

Abstract:

The stability of space charge and beam is one of basic problems for strong beam technology. The problem can be minimized by using sheet beam focus and transport in the periodic field. By introducting non linear and motion damping, the motion equations of the sheet beam in the cold cavity was reduced into generalized Mathieu equation in the framework of classical physics. The Smale horseshoe chaos and subharmonic bifurcations were analyzed by Melnikov method; and the critical conditions of the system were discussed. The results show that the stability of the system is related to its parameters, so only adjustmenting parameters can guarantee the system stability.