高频调制与储存环中粒子纵向运动的稳定性

High-frequency Modulation and Stability of Particle Longitudinal Motion in Storage Rings

摘要:

考虑到运动阻尼、高频噪声和系统非线性等因素的影响, 把储存环的同步运动方程化为含有阻尼项、受迫项和高阶相移因子的非线性微分方程。用摄动法导出了系统的近似解, 并分析了系统在共振线附近的运动行为。揭示了系统跳跃现象和临界特征, 分析了系统的数学稳定性和物理稳定性。结果表明, 当三阶非线性相移因子小于零时, 系统可以实现三束储存。

Abstract:

Taking into account of the effects of such parameters as motion damping, high frequency noise and nonlinearity, the synchronization motion equation in the storage ring was reduced to nonlinear differential equation containing motion damping, forced term and higher order phase shift factor. By using perturbation method, the approximate solution of the system was derived and the motion behavior was analyzed in the vicinity of the resonance. The jumping phenomenon and critical characteristics of the system were revealed, and the mathematical stability and physical stability were analyzed. The results show that when the third order nonlinear phase shift factor is less than zero, the system can achieve three beam storage.