摘要
从系统的扰动Hamiltonian出发,在经典力学框架内小振幅近似下,把粒子的纵向运动方程化为Mathieu方程,指出了由于扰动的存在,准等时同步加速器出现了一系列新的共振线。用摄动法导出了一阶不稳定区的边界曲线和禁带宽度;指出了当粒子穿越禁带后的振幅与同步加速器的两个不稳定点相位相等时,系统处于临界状态;并由此导出了高频电压调制振幅的临界值。
In the classical mechanics frame and small amplitude approximation,the longitudinal motion equation of the particle was reduced to the Mathieu equation based on the perturbed Hamiltonian.It was pointed out that there is a series of new resonance lines in quasi-isochronous synchrotron by the perturbation.The boundary curve and the stop width for order instability zone one were derived by the method of perturbabtion.Also it was pointed that the system is at the critical point when the phase becomes equal to the phase of the instable point for the synchrotron after it crossed the stop band,and the critical condition of the high frequency voltage modulation was derived.
出处
《原子核物理评论》
CAS
CSCD
北大核心
2011年第2期191-194,共4页
Nuclear Physics Review
基金
国家自然科学基金资助项目(10947140)
广东省自然科学基金资助项目(10451170003004948)
东莞市科技计划项目(2008108101002
200910814047)~~
