Particles coupling between horizontal and vertical oscillations in CSRm

Particles coupling might lead to the loss of particles in some condition. This paper described that the rotation of the main magnets and the existence of the solenoid were the reasons of the particles coupling between horizontal and vertical oscillations and that the particles would be unstable when working at sum resonance and the existence of the solenoid contributed more to the particles coupling than the rotation of the main magnets. Using the typical parameters of HIRFL-CSRm system, the particles would be stable when CSRm worked at given working point which was nearly difference resonance.