Keywords: 
• 同步运动 /
• 偶极场 /
• 冷却效应 /
• 混沌 /
• 稳定性

Abstract: The Betatron oscillation and the synchrotron oscillation for the particles are effeeted by the dipole field perturbation and the cooling effect. Both effects are considered in the paper and the synchrotron mo- tion 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.