Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods

LI Jin-Hai; LU Jian-Qin

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2005, Vol. 29> Issue(7) : 695-699

Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods

LI Jin-Hai ^, ,
LU Jian-Qin

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

Abstract
HTML
Reference
Related

PDF

Abstract：
With the Lie algebraic methods, the charged particle trajectories in electrostatic analyzers are analyzed,and the third order solutions obtained. In this paper, we briefly describe the Lie algebraic methods and the procedures of calculating the nonlinear orbits. The procedures are: first, set up the Hamiltonian; then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees; next, calculate the Lie map associating to the Hamiltonian; finally, apply the Lie map on the particle initial coordinates in the phase space, and obtain the particle nonlinear trajectories of the first order,the second order, and the third order approximations respectively. Higher orders solutions could be obtained if needed.

References

[1]

. Dragt A J, Lecture Notes on Nonlinear Orbit Dynamics. In: Physics ofHigh Energy Part icle Accelerators. Carrigan R A et al. ed AIP Confer..ence Proceedings No. 87. New York: Am. Inst. Phys. , 19872. Dragt A J,Finn J M. J.Math. Physics, 1976, 17: 2215 - 22273. Dragt A J,Forest E. J. Math. Physics, 1983, 24 (12) : 2734 - 27444. L#220; Jian-Qin. Nucl. Instrum. Methods, 1995, A355: 253

[1]	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.
[2]	LI Jin-Hai , LU Jian-Qin . Nonlinear Analysis for the Wein Filter with Lie Algebraic Method. Chinese Physics C, 2004, 28(9): 998-1001.
[3]	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.
[4]	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.
[5]	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.
[6]	LV Jian-Qin . Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map. Chinese Physics C, 2002, 26(4): 402-408.
[7]	LV Jian-Qin . Third Order Lie Map for the Sextupole Magnets. Chinese Physics C, 2001, 25(4): 354-358.
[8]	ZHANG Jing-Bo , HUO Lei , ZHANG Wei-Ning , LIU Yi-Ming . HBT Parameters for Au+Au Collisions at RHIC Energy. Chinese Physics C, 2001, 25(12): 1253-1257.
[9]	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.
[10]	XU JianMing . Nonlinear Effect in the Circular Mass Spectrometer. Chinese Physics C, 2000, 24(7): 667-675.
[11]	Chen Gang , Gao Yanmin , Liu Lianshou . Factorial Moment Analysis of High Energy Experimental Data With Non-integer Partitian Number. Chinese Physics C, 1999, 23(6): 552-560.
[12]	Chen Yinbao , Huang Zhibin . Nonlinear Space Charge Effects and Emittance Growth in Linac. Chinese Physics C, 1999, 23(12): 1231-1242.
[13]	Ni Zhixiang . Nonlinear Spectrum-Generating Algebra for the Symmetrical Pöschl-Teller Potential. Chinese Physics C, 1999, 23(3): 289-297.
[14]	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.
[15]	Zhuang Pengfei , Liu Lianshou . Linear Background and Nonlinear Effect in Relativistic Heavy Ion Collisions. Chinese Physics C, 1994, 18(2): 143-147.
[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 Zu-Rong . Irreducible Representations of Quantum Lie Superalgebra SL_q(2/1). Chinese Physics C, 1992, 16(11): 1035-1042.
[18]	GAO Xiao-Chun , WANG Yong , XU Jing-Bo , LI Wen-Zhu . THE STUDY OF TOPOLOGICAL TERMS OF THE NONLINEAR SIGMA MODEL. Chinese Physics C, 1989, 13(6): 526-529.
[19]	HU Yu-Min , LI Yi . NUMERICAL CALCULATION FOR ELECTROSTATIC DECELERATING LENS ENERGY ANALYZER. Chinese Physics C, 1989, 13(6): 490-493.
[20]	LI XIN-ZHOU , GU MING-GAO , YIN PENG-CHENG . NONLINEAR SUPERFIELDS AND QUARK CONFINEMENT. Chinese Physics C, 1979, 3(6): 716-722.

Access

Get Citation

LI Jin-Hai and LU Jian-Qin. Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods[J]. Chinese Physics C, 2005, 29(7): 695-699.

LI Jin-Hai and LU Jian-Qin. Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods[J]. Chinese Physics C, 2005, 29(7): 695-699. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2004-10-22
Revised: 1900-01-01

Article Metric

Article Views(2618)
PDF Downloads(541)
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

Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods

LI Jin-Hai ^,
LU Jian-Qin

Corresponding author: LI Jin-Hai,

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

Received Date: 2004-10-22
Accepted Date: 1900-01-01
Available Online: 2005-07-05

Abstract: With the Lie algebraic methods, the charged particle trajectories in electrostatic analyzers are analyzed,and the third order solutions obtained. In this paper, we briefly describe the Lie algebraic methods and the procedures of calculating the nonlinear orbits. The procedures are: first, set up the Hamiltonian; then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees; next, calculate the Lie map associating to the Hamiltonian; finally, apply the Lie map on the particle initial coordinates in the phase space, and obtain the particle nonlinear trajectories of the first order,the second order, and the third order approximations respectively. Higher orders solutions could be obtained if needed.