参数激励与加速器系统的全局分叉性质

Parameter Excitation and Global Bifurcation in Beam Dynamics

考虑到二次谐波梯度场和三阶非线性的影响,把粒子的运动方程化为参数激励的非线性Mathieu方程,并用Melnikov方法计算了系统的全局分叉.结果表明,当参数满足一定条件时,系统将通过偶阶次谐分叉,进入Smale马蹄变换意义下的混沌状态.

Considering gradient field with the 2nd harmonic disturbance, the motion equation of the particles is reduced to the nonlinear Mathieu equation in the nonlinear approximation. A global bifurcation of a particle dynamics in the cyclotron is analyzed by using Melnicov method. It shows that the system will enter into chaos with Smale horse＇s by a bifurcation with the even-order harmonic.