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高频电压调制对同步运动的影响

刘慧杰 罗诗裕# 邵明珠

刘慧杰, 罗诗裕#, 邵明珠. 高频电压调制对同步运动的影响[J]. 原子核物理评论, 2011, 28(2): 191-194. doi: 10.11804/NuclPhysRev.28.02.191
引用本文: 刘慧杰, 罗诗裕#, 邵明珠. 高频电压调制对同步运动的影响[J]. 原子核物理评论, 2011, 28(2): 191-194. doi: 10.11804/NuclPhysRev.28.02.191
LIU Hui-jie, LUO Shi-yu#, SHAO Ming-zhu. Effect on Synchrotron Motion by Modulation of High Frequency Voltag[J]. Nuclear Physics Review, 2011, 28(2): 191-194. doi: 10.11804/NuclPhysRev.28.02.191
Citation: LIU Hui-jie, LUO Shi-yu#, SHAO Ming-zhu. Effect on Synchrotron Motion by Modulation of High Frequency Voltag[J]. Nuclear Physics Review, 2011, 28(2): 191-194. doi: 10.11804/NuclPhysRev.28.02.191

高频电压调制对同步运动的影响

doi: 10.11804/NuclPhysRev.28.02.191

Effect on Synchrotron Motion by Modulation of High Frequency Voltag

  • 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.
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出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  1900-01-01
  • 刊出日期:  2011-06-20

高频电压调制对同步运动的影响

doi: 10.11804/NuclPhysRev.28.02.191

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.

English Abstract

刘慧杰, 罗诗裕#, 邵明珠. 高频电压调制对同步运动的影响[J]. 原子核物理评论, 2011, 28(2): 191-194. doi: 10.11804/NuclPhysRev.28.02.191
引用本文: 刘慧杰, 罗诗裕#, 邵明珠. 高频电压调制对同步运动的影响[J]. 原子核物理评论, 2011, 28(2): 191-194. doi: 10.11804/NuclPhysRev.28.02.191
LIU Hui-jie, LUO Shi-yu#, SHAO Ming-zhu. Effect on Synchrotron Motion by Modulation of High Frequency Voltag[J]. Nuclear Physics Review, 2011, 28(2): 191-194. doi: 10.11804/NuclPhysRev.28.02.191
Citation: LIU Hui-jie, LUO Shi-yu#, SHAO Ming-zhu. Effect on Synchrotron Motion by Modulation of High Frequency Voltag[J]. Nuclear Physics Review, 2011, 28(2): 191-194. doi: 10.11804/NuclPhysRev.28.02.191

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