在经典力学框架内和小振幅近似下,把准等时同步加速器中的粒子纵向运动方程化为具有阻尼项、受迫项的广义维尔斯特拉斯方程。在无扰动情况下,用维尔斯特拉斯函数分析了系统的相平面特征;在扰动情况下,用多尺度法讨论了系统的稳定性。结果表明,在相平面上,分支轨道是一条过不稳定点的同宿轨道,包围的区域呈＂鱼形＂或α形。系统的稳定性由＂鱼形＂区的面积决定,面积越大系统越稳定;结果还表明,系统除了ωm=1的主共振外,还存在ωm=2,1/2的超次谐共振,并找到了系统稳定性的临界条件。
In the classical mechanics frame and with small amplitude approximation,the longutudial motion equation of particles in quasi-isochronous syhchrotron is reduced to the general Weierstrass equation with a damping term and a forced term.In the non-perturbed case,the phase plane properties are analysed by using Weierstrass function;in the perturbed case,the stabilities are discussed in terms of the multi-scalar techniques.The results show that the separatrix orbit is a homoclinic orbit through the instable point in the phase plane,the surrounding area is the fish form or α-form.The stabilities are determined by the fish area,the large the area,the better the stability;also the results show that there are ωm=2,1/2 super-and sub-harmonics resonance except the main resonance ωm=1,the critical condition of an instability is found.
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