Third Order Lie Map for the Solenoidal Lenses

LV Jian-Qin

Chinese Physics C> 2002, Vol. 26> Issue(2) : 186-191

Third Order Lie Map for the Solenoidal Lenses

LV Jian-Qin ^,

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

Abstract
HTML
Reference
Related

PDF

Abstract：
Solenoidal lenses are usually used to focus charged particle beams moving in inductive accelerators,electron linear accelerators,proton linear accelerators,low energy beam transport systems as well as some cathode ray tubes. To understand the nonlinear optical properties of solenoidal lenses,Lie algebraic methods are used in the analysis of particle trajectories in this kind of lenses,and the results of third order approximation are obtained. Because of the existence of fringing fields,one should divide the fringing field into several small segments,and apply the Lie map to each of the segments.

References

[1]	. Goldstein H. Classical Mechanics, 2nd ed. Massachusetts: Addison-Wesley, 1980. 378—418 2. Dragt A J, Finn J M. Lie Series and Invariant Functions for Analytic Symplectic Maps. J Math Phys., 1976, 17(12): 2215

[1]	LI Qing , MA Li-Zhen , HE Yuan , WU Wei , BIAN Wen-Long , YAO Qing-Gao . Optimization Design of Magnetic Field on Cold Yoke Superconducting Solenoid. Chinese Physics C, 2008, 32(S1): 49-52.
[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]	DONG Jing , XIE Yi-Gang , CHEN Yuan-Bo , LIU Qian , OUYANG Qun , XIE Wan , WEI Wei . Experimental Study of Triple-GEM' Performance and a Multi-channel Image. Chinese Physics C, 2007, 31(7): 664-668.
[4]	LAI Yong-Fang , LI Yu-Lan , LI Yuan-Jing , LI Jin , ZHENG Xiao-Cui , CAO Liang-Jun . Experimental Study on the Performance of Tri-GEM Gas Detector. Chinese Physics C, 2006, 30(8): 767-770.
[5]	LU Jian-Qin , LI Jin-Hai . Computer Codes for the Beam Optics Calculations —Third Order Approximation. Chinese Physics C, 2006, 30(S1): 25-27.
[6]	Zhou Xue-Mei , XIA Jia-Wen , YUAN You-Jin , WU Jun-Xia , YANG Jian-Cheng , LIU Yong , LIU Wei , Mao Li-Jun , ZHOU Jun . Coupling Effect of Solenoid in CSRm. Chinese Physics C, 2006, 30(5): 462-465.
[7]	SUN Tian-Xi , XIE Ya-Ning , LIU Zhi-Guo , LIU Tao , HU Tian-Dou , YANG Jun , CHU Xue-Lian , DING Xun-Liang . Application of Monolithic Polycapillary X-Ray Lens in Focusing of Synchrotron Radiation. Chinese Physics C, 2005, 29(S1): 137-139.
[8]	SONG Ming-Tao , YANG Xiao-Dong , YUAN You-Jin , YUAN Ping , ZHANG Wen-Zhi . Analysis of Third Order Quadrupole Aberrations. Chinese Physics C, 2004, 28(7): 758-761.
[9]	LV Jian-Qin . Third Order Lie Map for the Sextupole Magnets. Chinese Physics C, 2001, 25(4): 354-358.
[10]	GUO JianYou , RUAN TuNan , XU FuXin . Collective Motion of a pure Octupole Deformed System. Chinese Physics C, 2000, 24(12): 1194-1198.
[11]	Yu Qingchang , Guo Weiming . Focusing Properties of Radio-Frequency Quadrupole Lenses. Chinese Physics C, 1999, 23(3): 302-307.
[12]	Shen Qixing , Yu Hong , Zhang Lin . Study of the Boson Resonance Produced in the Three-Step Two-Body Decay Process of J/ψ. Chinese Physics C, 1995, 19(1): 16-26.
[13]	KUANG Le-Man , ZENG Gao-Jian . Super-coherent State Representation of Lie Superalgebra B(0,1). Chinese Physics C, 1993, 17(3): 215-221.
[14]	SHEN Qi-Xing , YU Hong . Spin and parity analysis for the three-step two-body hadronic decay processes of J/ψ. Chinese Physics C, 1992, 16(3): 219-228.
[15]	HU Nai-Xiong , XIMEN Ji-Ye . The Beam Optics of Electric Multipole Lens. Chinese Physics C, 1991, 15(3): 193-199.
[16]	HU Yu-Min , LI Yi . NUMERICAL CALCULATION FOR ELECTROSTATIC DECELERATING LENS ENERGY ANALYZER. Chinese Physics C, 1989, 13(6): 490-493.
[17]	WU Ji-Min , ZHAO Pei-Ying . THE ANALYTIC RESULTS FOR U₁ AND SU₂ AVERAGE PLAQUETTE TO THE THIRD ORDER APPROXIMATION IN THE CUMULANT EXPANSION. Chinese Physics C, 1986, 10(3): 297-307.
[18]	QIU Hong , CHEN Jian-Pu , XU Jian-Ming . STUDIES OF THE FOCUSING PROPERTIES OF A SPACE CHARGE LENS. Chinese Physics C, 1983, 7(5): 583-588.
[19]	LIU YU-CHENG , SHI CAI-TU , CHAO WEI . EFFECTIVE LENGTH MEASUREMENT OF PULSED QUADRUPOLE LENSE. Chinese Physics C, 1982, 6(4): 499-502.
[20]	YUE ZONG-WU , TANG JU-FEI . THE TEST OF SLAC METHOD USING LEE MODEL. Chinese Physics C, 1979, 3(3): 285-296.

Access

Get Citation

LV Jian-Qin. Third Order Lie Map for the Solenoidal Lenses[J]. Chinese Physics C, 2002, 26(2): 186-191.

LV Jian-Qin. Third Order Lie Map for the Solenoidal Lenses[J]. Chinese Physics C, 2002, 26(2): 186-191. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2001-01-15
Revised: 1900-01-01

Article Metric

Article Views(2930)
PDF Downloads(634)
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

Third Order Lie Map for the Solenoidal Lenses

LV Jian-Qin ^,

Corresponding author: LV Jian-Qin,

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

Received Date: 2001-01-15
Accepted Date: 1900-01-01
Available Online: 2002-02-05

Abstract: Solenoidal lenses are usually used to focus charged particle beams moving in inductive accelerators,electron linear accelerators,proton linear accelerators,low energy beam transport systems as well as some cathode ray tubes. To understand the nonlinear optical properties of solenoidal lenses,Lie algebraic methods are used in the analysis of particle trajectories in this kind of lenses,and the results of third order approximation are obtained. Because of the existence of fringing fields,one should divide the fringing field into several small segments,and apply the Lie map to each of the segments.