Study of Insertion Device's Influence on Nonlinear Beam Dynamics in Electron Storage Ring Using Lie Algebra

LI Yong-Jun; WANG Lin; FENG Guang-Yao; XU Hong-Liang; LI Wei-Min; LIU Zu-Ping

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2003, Vol. 27> Issue(9) : 819-823

Study of Insertion Device's Influence on Nonlinear Beam Dynamics in Electron Storage Ring Using Lie Algebra

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China

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Abstract：
In designing the 3rd generation synchrotron radiation light source, many long, and dispersion free straight sections are left for installing undulators to produce coherent radiation. For the damping ring used as pre-injector of next generation linear collider, many wigglers are used to increase radiation damping rate. So it is important to understand those Insertion devices'(ID) influence on beam dynamics in design and optimization stage. This paper introduces the study of insertion device's influence on beam dynamics in electron storage ring using the symplectic Lie mapping. Firstly the Hamiltonian of charged particle's motion along ID axis is given, then two methods are adopted to analyse ID's influence on beam dynamics. One method is expanding Hamiltonian to 4th order Taylor series, then all kinds of multipole components (till to octupole) can be obtained; another is constructing a second order symmetrical, symplectic integrator using Lie map product by similar transformation directly. The simulation results show those two methods are consistent. The primary results of influence on beam dynamics of UD-1, a new undulator which will be installed in Hefei Light Source storage ring soon, are also given. The tune-shift and decrease of dynamic aperture caused by UD-1 can be found in simulation results.

References

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. L Jian-Qin.HEPNP ,2002,26(2):186—191(in Chinese)(吕建钦.高能物理与核物理,2002,26(2):186—191)2. WANG Pei-Wei et al.HEP NP ,1996,20(5):468—475(in Chinese)(王培玮等.高能物理与核物理,1996,20(5):468—475)3. Jackson J D .Classical Electrodynamics.3rd Ed.New York:John Wiley Sons Inc.19984. CourantE ,SnyderH .AnnalsofPhysics,2000,281:360—4085. Dragt.AIP Proc.87,Phys.High Energy Accel.,Fermilab,1981

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LI Yong-Jun, WANG Lin, FENG Guang-Yao, XU Hong-Liang, LI Wei-Min and LIU Zu-Ping. Study of Insertion Device's Influence on Nonlinear Beam Dynamics in Electron Storage Ring Using Lie Algebra[J]. Chinese Physics C, 2003, 27(9): 819-823.

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Received: 2002-11-04
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

Study of Insertion Device's Influence on Nonlinear Beam Dynamics in Electron Storage Ring Using Lie Algebra

Corresponding author: LI Yong-Jun,

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China

Received Date: 2002-11-04
Accepted Date: 1900-01-01
Available Online: 2003-09-05

Abstract: In designing the 3rd generation synchrotron radiation light source, many long, and dispersion free straight sections are left for installing undulators to produce coherent radiation. For the damping ring used as pre-injector of next generation linear collider, many wigglers are used to increase radiation damping rate. So it is important to understand those Insertion devices'(ID) influence on beam dynamics in design and optimization stage. This paper introduces the study of insertion device's influence on beam dynamics in electron storage ring using the symplectic Lie mapping. Firstly the Hamiltonian of charged particle's motion along ID axis is given, then two methods are adopted to analyse ID's influence on beam dynamics. One method is expanding Hamiltonian to 4th order Taylor series, then all kinds of multipole components (till to octupole) can be obtained; another is constructing a second order symmetrical, symplectic integrator using Lie map product by similar transformation directly. The simulation results show those two methods are consistent. The primary results of influence on beam dynamics of UD-1, a new undulator which will be installed in Hefei Light Source storage ring soon, are also given. The tune-shift and decrease of dynamic aperture caused by UD-1 can be found in simulation results.