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

Abstract
HTML
Reference
Related

PDF

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

[1]

. 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

[1]	X.Wu,D.Cole,M.Doleans,G.Machicoane,F.Marti,P.Miller,J.Stetson, M.Steiner,P.Zavodszky,Q.Zhao. Beam Dynamics Studies of ECR Injections for the Coupled Cyclotron Facility at NSCL. Chinese Physics C, 2007, 31(S1): 196-200.
[2]	YANG Jian-Jun,ZHANG Tian-Jue,AN Shi-Zhong,JIA Xian-Lu,LIN Yu-Zheng. A Two-Dimension Beam Dynamics Simulation Code Base on PIC Method. Chinese Physics C, 2007, 31(8): 769-773.
[3]	BAO Jing-Dong. Simulating Methods in Nuclear Reaction Dynamics. Chinese Physics C, 2006, 30(S2): 24-28.
[4]	LI Jin-Hai,LU Jian-Qin. Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods. Chinese Physics C, 2005, 29(7): 695-699.
[5]	XING Qing-Zi,LIN Yu-Zheng,FU Shi-Nian,FANG Shou-Xian. Study of Simultaneous Acceleration of Positive and Negative Ion Beams by Dynamic Simulation in RFQ. Chinese Physics C, 2004, 28(6): 659-663.
[6]	YANG Jian-Cheng,XIA Jia-Wen,WU Jun-Xia,XIA Guo-Xing,LIU Wei,YIN Xue-Jun. Analytical Study of Dynamic Aperture for Storage Ring by Using Successive Linearization Method. Chinese Physics C, 2004, 28(1): 82-87.
[7]	LI Jin-Hai,LU Jian-Qin. Nonlinear Analysis for the Wein Filter with Lie Algebraic Method. Chinese Physics C, 2004, 28(9): 998-1001.
[8]	LI Jin-Hai,LI Chao-Long,LU Jian-Qin. Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles. Chinese Physics C, 2003, 27(7): 645-648.
[9]	LV Jian-Qin,LI Chao-Long,LI Jin-Hai. Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses. Chinese Physics C, 2003, 27(1): 76-82.
[10]	LV Jian-Qin. Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map. Chinese Physics C, 2002, 26(4): 402-408.
[11]	HOU BoYu,FAN Heng,YANG WenLi,CAO JunPeng. Drinfeld Currents of Dynamical Elliptic Algebra A_q,p,π(gl_n). Chinese Physics C, 2000, 24(2): 98-105.
[12]	Luo Zihua,Wang Shuhong. Design and Study of Beam Dynamics for the BPL-RFQ. Chinese Physics C, 1995, 19(7): 658-666.
[13]	Wang Yanshen,Hou Boyu. The Poisson-Lie Structure of O(n) Non-Linear Sigma Model in Moving Frames. Chinese Physics C, 1994, 18(10): 892-901.
[14]	Zhao Zhentang,Lin Yuzheng,Wang Hongyuan. Beam Dynamics characteristic in 1/2+m Cell's Harmonic Microwave Cun. Chinese Physics C, 1994, 18(7): 664-672.
[15]	WANG Shu-Hong. RFQ's Beam Dynamics and RF Structure. Chinese Physics C, 1993, 17(4): 310-321.
[16]	YU Zu-Rong. Irreducible Representations of Quantum Lie Superalgebra SL_q(2/1). Chinese Physics C, 1992, 16(11): 1035-1042.
[17]	ZHANG Zhen-Hai,SONG Zhong-Heng. Dynamics Calculation in a L-band Travelling Wave Electron Linac. Chinese Physics C, 1991, 15(5): 391-398.
[18]	SONG Zhong-Heng,WANG Xiao-Min. THREE-DIMENSIONAL DYNAMIC CALCULATION OF CHARGE DISC WITH VARIABLE RADIUS OF ELECTRON LINAC. Chinese Physics C, 1990, 14(1): 16-23.
[19]	LUO Zi-Hua,WANG Shu-Hong. COMPUTATION RESEARCH ON THE BEAM TRANSVERSE MOTION FOR THE 35MeV BEIJING PROTON LINAC. Chinese Physics C, 1988, 12(6): 793-798.
[20]	WG SHU-HIUNG. BEAM DYNAMICS DESIGN STUDY FOR RFQ LINAC. Chinese Physics C, 1982, 6(4): 428-434.

Access

Get Citation

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.

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2002-11-04
Revised: 1900-01-01

Article Metric

Article Views(4674)
PDF Downloads(635)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者:陈斌, bchen63@163.com

1.
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.