【摘要】 本文针对高频电压调制与冷却效应,讨论它们对同步运动稳定性的影响。在经典力学框架内和小振幅近似下,把粒子的同步运动方程化为具有参数激励的广义Duffing方程。用Melnikov方法分析了周期轨道的分叉性质和异宿轨道的混沌行为,导出了系统稳定的临界条件,并对其物理意义进行了讨论。结果表明,只需适当调节参数就可保证同步运动是稳定的。更多还原

【Abstract】 Stability of synchronized motion of the particle beams can be affected by high-frequency voltage disturbance and beam cooling.In this paper,using classical mechanics and small amplitude approximation,the particle motion equation is reduced to the generalized Duffing equation with the parametric excitation,while using the Melnikov method,the bifurcation nature of the periodic orbits and the chaotic behavior of the heteroclinic orbits are analyzed to derive the critical conditions for a stable system.The results show that stable synchronized motion of the particle beams can be achieved by adjusting the parameters.更多还原