Nonlinear phase shift factors and particle dynamical behavior in the vicinity of transition energy

WU Muying LI Hongtao CHEN Shaowen LIU Minxia CHEN Guihua LUO Shiyu

doi:10.11889/j.0253-3219.2013.hjs.36.050204

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Nonlinear phase shift factors and particle dynamical behavior in the vicinity of transition energy

更新时间：2021-03-05

- Nonlinear phase shift factors and particle dynamical behavior in the vicinity of transition energy
- NUCLEAR TECHNIQUES Vol. 36, Issue 5, Article number: 050204(2013)
- 作者机构：
  
  东莞理工学院电子工程学院
- 作者简介：
- 基金信息：
  
  东莞市科技计划项目(200910814032)资助
- DOI：10.11889/j.0253-3219.2013.hjs.36.050204
  CLC： O32
- Published：01 May 2013
- 稿件说明：
移动端阅览
[1]吴木营,李洪涛,陈少文,刘敏霞,陈桂华,罗诗裕.非线性相移因子与渡越能量附近粒子的动力学行为[J].核技术,2013,36(05):41-45.

WU Muying LI Hongtao CHEN Shaowen LIU Minxia CHEN Guihua LUO Shiyu. Nonlinear phase shift factors and particle dynamical behavior in the vicinity of transition energy[J]. Nuclear techniques, 2013, 36(5): 050204
[1]吴木营,李洪涛,陈少文,刘敏霞,陈桂华,罗诗裕.非线性相移因子与渡越能量附近粒子的动力学行为[J].核技术,2013,36(05):41-45. DOI： 10.11889/j.0253-3219.2013.hjs.36.050204.

WU Muying LI Hongtao CHEN Shaowen LIU Minxia CHEN Guihua LUO Shiyu. Nonlinear phase shift factors and particle dynamical behavior in the vicinity of transition energy[J]. Nuclear techniques, 2013, 36(5): 050204 DOI： 10.11889/j.0253-3219.2013.hjs.36.050204.

摘要

束流穿越渡越能量后动量分散增加

束流品质退化。在经典力学框架内和小振幅近似下

考虑到相移因子的二阶非线性、射频噪声和辐射衰减的影响

把同步加速器的粒子同步运动方程化为具有阻尼项、受迫项的二阶非线性微分方程。对系统的相平面特征和振幅响应进行了数值分析;用摄动法讨论了系统的稳定性及1/3共振线附近粒子的运动行为:分析了系统的跳跃现象和系统的临界条件。结果表明

零次相移因子越大和三阶非线性越小系统越稳定。

Abstract

Background:After crossing the transition energy

the momentum dispersion of the beam increases

and its quality is degraded.Purpose:Considering the 2-order nonlinearity of the phase slip factor

the RF noise and the synchrotron radiation damping

the synchrotron motion equation of the particle in the synchrotron is reduced to the 3-order nonlinear differential equation with a damping term and a forced term in the classical mechanics frame and small amplitude approximation.Methods:Analysed the phase plane properties and the amplitude response of the system by the numerical method;discussed the stability and the motion behavior of the particle in the vicinity of the 1/3 resonance by the perturbed method.Results:Derived the jumping phenomena and the critical condition for the system.Conclusions:The greater zero-order phase shift factor and the smaller the third-order nonlienearity

the more stable the system becomes.

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