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。 One of the basic problems with strong current technology is its space charge and beam stability. Focusing and transporting the sheet beam in the periodic field can minimize the problem. In the classical physics, the nonlinear cavity motion damping is introduced into the generalized Mathieu equation for the cold cavity motion of sheet beam in periodic field. The Melnikov method is used to analyze the sub-harmonic bifurcation and Smale horseshoe chaos. The critical conditions of the system are also discussed. The results show that the stability of the system is related to its parameters. In principle, the stability of the system can be ensured only by properly adjusting the parameters.