偶极场扰动与冷却效应对同步运动的影响

在同步加速器特别是冷却存储环中，偶极场扰动和冷却效应将会对粒子的Betatron振荡和同步振荡产生影响。 叙述了偶极场扰动对粒子同步运动的影响与高频相位调制等效， 重点研究了偶极场扰动与冷却效应同时存在的情况对粒子的同步运动产生的影响。 在经典力学框架内把粒子的同步运动方程化为广义的摆方程， 然后利用Melnikov方法对系统的稳定性进行了分析， 讨论了系统进入Smale马蹄混沌的物理意义，并导出了系统稳定的临界条件。根据稳定性判据， 给出了系统稳定性所需要的偶极场扰动的高频相位调制幅度和冷却系数的限制条件。 结果表明， 系统的稳定性与它的参数有关， 只需适当调节这些参数， 混沌便可原则上控制或避免。 The Betatron oscillation and the synchrotron oscillation for the particles are effected by the dipole field perturbation and the cooling effect. Both effects are considered in the paper and the synchrotron motion equation of the particle in the synchroton is reduced to the general pendulum equation in the classical mechanics frame. The stabilities of the system caused by dipole field perturbation and cooling are analyzed by using Melnikov method. The thresholds entered a Smale horseshoe chaos are derived in detail and the stability conditions for the system caused by dipole field perturbation and cooling are dicussed. The results show that the critical condition or the stability thresholds are related to the system parameters. The chaos or an instability can be avoided or controlled in principle by regulating some parameters of the system.

Effect on Synchrotron Motion Caused by Dipole Field Perturbation and Cooling

The Betatron oscillation and the synchrotron oscillation for the particles are effected by the dipole field perturbation and the cooling effect. Both effects are considered in the paper and the synchrotron motion equation of the particle in the synchroton is reduced to the general pendulum equation in the classical mechanics frame. The stabilities of the system caused by dipole field perturbation and cooling are analyzed by using Melnikov method. The thresholds entered a Smale horseshoe chaos are derived in detail and the stability conditions for the system caused by dipole field perturbation and cooling are dicussed. The results show that the critical condition or the stability thresholds are related to the system parameters. The chaos or an instability can be avoided or controlled in principle by regulating some parameters of the system.