N度对称径向扇回旋加速器的动力学稳定性及系统的相平面特征
Dynamic Stability and Phase Planar Property for Radial Sector Cyclotrons with N-Folded Symmetry
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摘要: 本文导出了N度对称径向扇回旋加速器中粒子的非线性运动方程,并用数值方法分析了N=4,5,6,8,10等情况下粒子的自由振荡频率及vx=4/3共振线前后系统的相平面特征.讨论了系统的动力学稳定性和非线性效应,并同文献[1]进行了比较,结果表明,当不考虑系统的非线性特征时,二者完全一致.Abstract: The particle nonlinear motion equation for a radial sector cyclotron with N-folded symmetry was derived. The betalron oscillations frequency with N=4. 5, 6, 8, 10 and the phase planar properlies before and after vx=4/3 resonance with N=4, f=0.578 were analyzed, by using numerical method. The dynamic stabililies and nonlinear properties were discussed, the result compared with those of ref. [1] shows that both are consistent when nonlinear terms are neglected.
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[1] Gordon,M.M.,Ann.Phys.,50,3(1968),571. [2] 罗诗裕,共振线附近粒子运动的非线性行为,力学学报,1 (1979). [3] 罗诗裕,粒子穿越vx=4/3共振线的动力学特征,力学学报(1980),213. [4] 罗诗裕,马丢方程的一阶不稳定区及其在回旋加速器中的应用,应用数学和力学,3,4 (1982).555. [5] Luo Shi-yu,Liu Zheng-rong,Li Ji-bin and Shao Ming-zhu,Effect on a high frequency voltage distribution to a particle motion stability,Acta Mathematica Scientia,3,3(1983),285. [6] Stratton,J.A.,Electromagnetic Theory,(1941),49. [7] Kolomenski,A.A.,CERN Symposium,1(1965),265. [8] Servranckx,R.,Particle Accelerators,6,2(1975),83． -
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