Analytical Study of Dynamic Aperture for Storage Ring by Using Successive Linearization Method

YANG Jian-Cheng; XIA Jia-Wen; WU Jun-Xia; XIA Guo-Xing; LIU Wei; YIN Xue-Jun

Chinese Physics C> 2004, Vol. 28> Issue(1) : 82-87

Analytical Study of Dynamic Aperture for Storage Ring by Using Successive Linearization Method

Institute of Modern Physics,Chinese Academy of Sciences,Lanzhou 730000,China2 The Graduate School of Chinese Academy of Sciences,Beijing 100039,China

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Abstract：
The determination of dynamic aperture is a critical issue in circular accelerator. In this paper, we solved the equation of motion including non-linear forces by using successive linearization method and got a criterion for the determining of the dynamic aperture of the machine. Applying this criterion, a storage ring with FODO lattice has been studied. The results are agree well with the tracking results in a large range of linear turn(Q). The purpose is to improve our understanding of the mechanisms driving the particle motion in the presence of non-linear forces and got another mechanism driving instability of particle in storage ring-parametric resonance caused by “fluctuating transfer matrices” at small amplification.

References

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.Ropert A.Dynamic Aperture.In:CERN 90204.19902.Guignard G.Chromaticity:Nonlinear Aberration.In:CERN 87203.19873.Ando A.Particle Accelerators,1984,15:1774.Willeke F.Analytical Study of the Tevatron Nonlinear Dynamics.In:FN2422.FNAL.19845.Collins T.Distortion Function.In:Tech Note Fermilab284P114.19846.Forest E.Lie Algebraic Methods for Charged Particle Beams and LightOptics.Ph.D.Thesis.Univ.Maryland.19847.Courant E,Snyder H.Ann.Phys.(N.Y),1958,3:488.Hagel J.Analytic Calculation of the Off2Momentum Closed Orbit in Stor2age Rings with Insertions and Sextupoles.In: CERNPLEP2THP84218.19849.Guignard G,Hagel J.Particle Accelerators,1986,18:12910.Keil E.Single Particle Dynamics2Linear Machine Lattice.In:CERN 77213.Geneva:1977.2211.Christoph Iselin F.The Mad Program(Methodical Accelerator Design)12.Wiedemann H.Chromaticity Correction in Large Storage Rings.In:(SLAC) PEP20220.197613.Guignard G.First Order Chromatic Perturbation and Sextupole Strength.In:CERN ISR2THP82214.198214.GAO J.Nucl.Instrum.Meth.,2000,A451:545

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YANG Jian-Cheng, XIA Jia-Wen, WU Jun-Xia, XIA Guo-Xing, LIU Wei and YIN Xue-Jun. Analytical Study of Dynamic Aperture for Storage Ring by Using Successive Linearization Method[J]. Chinese Physics C, 2004, 28(1): 82-87.

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Received: 2003-02-20
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Analytical Study of Dynamic Aperture for Storage Ring by Using Successive Linearization Method

Corresponding author: YANG Jian-Cheng,

Institute of Modern Physics,Chinese Academy of Sciences,Lanzhou 730000,China2 The Graduate School of Chinese Academy of Sciences,Beijing 100039,China

Received Date: 2003-02-20
Accepted Date: 1900-01-01
Available Online: 2004-01-05

Abstract: The determination of dynamic aperture is a critical issue in circular accelerator. In this paper, we solved the equation of motion including non-linear forces by using successive linearization method and got a criterion for the determining of the dynamic aperture of the machine. Applying this criterion, a storage ring with FODO lattice has been studied. The results are agree well with the tracking results in a large range of linear turn(Q). The purpose is to improve our understanding of the mechanisms driving the particle motion in the presence of non-linear forces and got another mechanism driving instability of particle in storage ring-parametric resonance caused by “fluctuating transfer matrices” at small amplification.