Mathieu方程与4-度对称径向扇回旋加速器的动力学稳定性

Mathieu Equation and Dynamic Stabilities for Cyclotron with 4-folded Symmetry

在线性近似下,考虑到二次谐波梯度场的影响,把粒子的运动方程化为标准的Mathieu方程．数值分析表明,在参数δ-ε平面上,系统存在一系列稳定和不稳定区．指出了,当粒子穿越不稳定区(禁带)时,振幅将呈指数增长,从而导致系统不稳定．为了保证系统的稳定性,要求粒子尽量避免穿越或少穿越不稳定区,为加速器设计提供了理论分析．

Considering gradient field with 2nd hamoric disturbance, the motion equation of the particles is reduced to the Mathieu equation in the linear approximation. It shows that there exist a series of stability and instability zones in the parameters plane. It indicates that the system may change the instability, if the particle passes through the instability zone. The theoretic analysis is provided for the design of accelerators.