Third Order Lie Map for the Solenoidal Lenses

LV Jian-Qin

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《中国物理C》（英文）编辑部

2024年10月30日

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

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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

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[11]	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.
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[13]	HU Nai-Xiong , XIMEN Ji-Ye . The Beam Optics of Electric Multipole Lens. Chinese Physics C, 1991, 15(3): 193-199.
[14]	SUN Chang-Pu . ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS. Chinese Physics C, 1990, 14(9): 788-795.
[15]	TU Chuan-Shi . REALIZATION OF THE EMBEDDING OF LIESUBAL GEBRA IN THE CASE OF INTERACTING BOSON MODEL. Chinese Physics C, 1987, 11(5): 634-643.
[16]	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.
[17]	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.
[18]	LIU YU-CHENG , SHI CAI-TU , CHAO WEI . EFFECTIVE LENGTH MEASUREMENT OF PULSED QUADRUPOLE LENSE. Chinese Physics C, 1982, 6(4): 499-502.
[19]	HAN QI-ZHI , SONG XING-CHANG , LI GEN-DAO , SUN HONG-ZHOU . IRREDUCIBLE REPRESENTATIONS OF THE GRADED LIE ALGEBRA SU(m/n). Chinese Physics C, 1981, 5(5): 546-553.
[20]	YUE ZONG-WU , TANG JU-FEI . THE TEST OF SLAC METHOD USING LEE MODEL. Chinese Physics C, 1979, 3(3): 285-296.

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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

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

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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.