Chinese Physics C > 2003, Vol. 27 > Issue(1): 76-82

Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses

Institute of Heavy Ion Physics,Peking University,Beijing 100871,China

Abstract
HTML
Reference
Related

PDF

Abstract：
The nonlinear transport of intense pulsed beams is analyzed with the Lie algebraic method in the case of K-V distribution , and the particle trajectories of second order approximation in the 6-D phase space (x,x′,y, y′, τ, pτ) are obtained. The beams could be axial-symmetrical or non-axial-symmetrical in the transverse direction. In the analysis, the effective fields of lens are divided into several small intervals. Each interval is treated as a uniform accelerating field and each dividing point is considered as a thin lens. Let the Lie map act on each uniform accelerating field and thin lens, the nonlinear particle trajectories can be obtained.

References

[1]	Goldstein H. Classical Mechanics. 2nd ed Reading, Massachusetts Addison-Wesley, 19802 L Jian-Qin. Nucl. Instrum. Methods, 1998, A416:229-235

[1]	MIAO Xi-Xi,LIU Lie. Preliminary Research of the Propagation of Annular IREBS in Coaxial Permanent Magnet Halbach Circuit. Chinese Physics C, 2008, 32(S1): 313-316.
[2]	LÜ Jian-Qin,ZHAO Xiao-Song,ZHANG Zhuo. Lie Map for the Intense dc Beam Transport in Solenoids. Chinese Physics C, 2008, 32(S1): 241-243.
[3]	XIA Lian-Sheng,LI Jin,ZHANG Huang,XIE Yu-Tong,JIANG Xiao-Guo,DAI Zhi-Yong,ZHANG Kai-Zhi,SHI Jin-Shui,DENG Jian-Jun,ZHANG Lin-Wen. Experimental Research on Double Pulsed Relativistic Electron Beams Emission from Velvet. Chinese Physics C, 2007, 31(7): 674-677.
[4]	MA Yan-Yun,PEI Shi-Lun,CAO Xing-Zhong,WANG Ping,WEI Cun-Feng,MA Chuang-Xing,ZHANG Zhi-Ming,WANG Shu-Hong,WANG Bao-Yi,WEI Long. Design of a Pulsed Low Energy Positron System Based on Beijing Intense Slow Positron Beam. Chinese Physics C, 2006, 30(2): 166-170.
[5]	YANG Guo-Jun,ZHANG Zhuo,CHEN Si-Fu,LIU Cheng-Jun,LIN Yu-Zheng. Time-Resolved Emittance Measurement of Intense Pulse Beams Using the Modified Three Gradient Method. Chinese Physics C, 2005, 29(2): 191-196.
[6]	LI Jin-Hai,LU Jian-Qin. Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods. Chinese Physics C, 2005, 29(7): 695-699.
[7]	LONG Ji-Dong,LIN Yu-Zheng,LUO Fei,GU Zhuo-Wei,SHI Jin-Shui. Destruction Study of Tantalum Target Impacted by 12MeV Electron Beam. Chinese Physics C, 2004, 28(5): 564-568.
[8]	LI Jin-Hai,LU Jian-Qin. Nonlinear Analysis for the Wein Filter with Lie Algebraic Method. Chinese Physics C, 2004, 28(9): 998-1001.
[9]	LI Yong-Jun,WANG Lin,FENG Guang-Yao,XU Hong-Liang,LI Wei-Min,LIU Zu-Ping. Study of Insertion Device's Influence on Nonlinear Beam Dynamics in Electron Storage Ring Using Lie Algebra. Chinese Physics C, 2003, 27(9): 819-823.
[10]	LU Jian-Qin,LI Jin-Hai,LI Chao-Long. Nonlinear Transport of the Intense Pulsed Gaussian Beams in Magnetic Quadrupoles. Chinese Physics C, 2003, 27(10): 926-931.
[11]	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.
[12]	LV Jian-Qin. Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map. Chinese Physics C, 2002, 26(4): 402-408.
[13]	NI Zhi-Xiang. Nonlinear Spectrum and Generating Algebra for Infinitely Deep Square Well Potential and New Coherent State. Chinese Physics C, 2001, 25(6): 487-493.
[14]	Ni Zhixiang. Nonlinear Spectrum-Generating Algebra for the Symmetrical Pöschl-Teller Potential. Chinese Physics C, 1999, 23(3): 289-297.
[15]	Jie Quanlin,Wang Shunjin,Wei Lianfu. Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure. Chinese Physics C, 1998, 22(2): 111-116.
[16]	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.
[17]	YU Qing-Chang. Transport of Charged Particle Beam in Nonlinear Periodic Field. Chinese Physics C, 1993, 17(4): 305-309.
[18]	YU Zu-Rong. Irreducible Representations of Quantum Lie Superalgebra SL_q(2/1). Chinese Physics C, 1992, 16(11): 1035-1042.
[19]	HU Yu-Min,LI Yi. NUMERICAL CALCULATION FOR ELECTROSTATIC DECELERATING LENS ENERGY ANALYZER. Chinese Physics C, 1989, 13(6): 490-493.
[20]	Yu Qing-chang. THEORY OF NONLINEAR SPACE-CHARGE EFFECTS OF LOW ENERGY INTENSE CHARGED PARTICLE BEAMS. Chinese Physics C, 1980, 4(5): 579-587.

Access

Get Citation

LV Jian-Qin, LI Chao-Long and LI Jin-Hai. Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses[J]. Chinese Physics C, 2003, 27(1): 76-82.

LV Jian-Qin, LI Chao-Long and LI Jin-Hai. Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses[J]. Chinese Physics C, 2003, 27(1): 76-82. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2002-04-17
Revised: 1900-01-01

Article Metric

Article Views(4155)
PDF Downloads(555)
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

Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses

Corresponding author:LV Jian-Qin,

Institute of Heavy Ion Physics,Peking University,Beijing 100871,China

Received Date:2002-04-17
Accepted Date:1900-01-01
Available Online:2003-01-05

Abstract:The nonlinear transport of intense pulsed beams is analyzed with the Lie algebraic method in the case of K-V distribution , and the particle trajectories of second order approximation in the 6-D phase space (x,x′,y, y′, τ, pτ) are obtained. The beams could be axial-symmetrical or non-axial-symmetrical in the transverse direction. In the analysis, the effective fields of lens are divided into several small intervals. Each interval is treated as a uniform accelerating field and each dividing point is considered as a thin lens. Let the Lie map act on each uniform accelerating field and thin lens, the nonlinear particle trajectories can be obtained.