同步加速器的粒子纵向运动及系统的接受度

The Longitudinal Motion of Particles in Synchrotron and Acceptance of System

在经典力学框架内,把粒子的纵向运动方程化为具有固定力矩的摆方程。在无扰动情况下,用Jacobian椭圆函数解析地给出了系统的异宿轨道;在扰动情况下,找到了同宿轨道的的积分表达式。从接受度概念出发分析了系统的稳定性。结果表明,在无扰动情况下,系统的接受度最大;随着扰动的增加,接受度变小,当无量纲的扰动强度Q=1时,接受度为零,系统处于临界状态。再现了在转变能量以下(γ<γ(?)),同步相位0<ξ_s<π/2的经典结果。

In the classical mechanics frame the longutudial motion equation of the particle is reduced to the pendulum equation with a constant momentum.The heteroclinic orbit is expressed by Jacobian elliptic function for the non-pertubed system;the homoclinic orbit is expressed by an integral form for the pertubed system.The stabilities of the system is analysed by the concept of the acceptance.It is shown that the acceptance is maximum for the non pertubed system;the acceptance is decreased with increasing of the pertubation;the acceptance reduced to the zero if the pertubance Q=1,and the system is in the critical condition.The synchro-phase is in 0ξ_sπ/2 for the synchrotron with（γγ（？））,and the classical result is reproduced.