Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map

LV 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> 2002, Vol. 26> Issue(4) : 402-408

Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map

LV Jian-Qin ^,

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

Abstract
HTML
Reference
Related

PDF

Abstract：
Lie algebraic method is used in the analysis of nonlinear transport for the relativistic charged particles in cylindrical symmetrical electrostatic fields, and particle orbits of third order approximation in the six dimensional phase space (x, x′, y, y′, τ, p-τ) are obtained. In the analysis, we take the electrostatic accelerating tube as an example, and divide the electrostatic accelerating tube into three elements: entrance thin lens, uniform accelerating field and exit thin lens, on which Lie map is applied, and the solutions through third order of particle orbits are obtained finally. This method can also be used for the electrostatic lenses.

References

[1]

Septier A. Focusing of Charged Particles. New York: Academic Press, 1967. Vol. 11, 2972 LU lian-Qin. LEADS: A Graphical Display Computer Program for Linear and Electrostatic Accelerator Beam Dynamics Simulation, Nucl. Instrum. Methods Sec., 1995, A355: 253-2573 Coldstein H. Classical Mechanics 2nd ed., Addition-Wesley, Reading, Massachusetts, 19804 Dragt A J. AIP Conf. Proc., 1982, 87: 1475 Dragt A J, Finn J M. J. Math. Phys., 1979, 20: 2649

[1]	JIN Hua , ZHENG Ren-Rong , ZHU Shun-Quan , LI Jun-Qing . Chaotic Motion of Single Particle in the Potential of Nonaxial Octupole Deformation. Chinese Physics C, 2006, 30(2): 134-139.
[2]	LI Jin-Hai , LU Jian-Qin . Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods. Chinese Physics C, 2005, 29(7): 695-699.
[3]	LI Jin-Hai , LU Jian-Qin . Nonlinear Analysis for the Wein Filter with Lie Algebraic Method. Chinese Physics C, 2004, 28(9): 998-1001.
[4]	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.
[5]	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.
[6]	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.
[7]	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.
[8]	XU JianMing . Nonlinear Effect in the Circular Mass Spectrometer. Chinese Physics C, 2000, 24(7): 667-675.
[9]	Ni Zhixiang . Nonlinear Spectrum-Generating Algebra for the Symmetrical Pöschl-Teller Potential. Chinese Physics C, 1999, 23(3): 289-297.
[10]	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.
[11]	Li Junqing . Chaotic Motion of Classical Particles in Axially Symmetric Potentials with Octupole Deformation. Chinese Physics C, 1997, 21(9): 818-824.
[12]	Zeng Jinyan , Lei Yian , Wu Wenqing . Construction of Paired States in Axially Symmetric Deformed Nuclei. Chinese Physics C, 1995, 19(9): 834-839.
[13]	Zhuang Pengfei , Liu Lianshou . Linear Background and Nonlinear Effect in Relativistic Heavy Ion Collisions. Chinese Physics C, 1994, 18(2): 143-147.
[14]	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.
[15]	HAO San-Ru . The Hidden Symmetries and Their Algebraic Structure of the Static Axially Symmetric SDYM Fields. Chinese Physics C, 1993, 17(6): 538-543.
[16]	YU Qing-Chang . Transport of Charged Particle Beam in Nonlinear Periodic Field. Chinese Physics C, 1993, 17(4): 305-309.
[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 , XU Jing-Bo , YAN Ji-Jin , LI Wen-Zhu . Removability of the Topological Term in the O(3) Nonlinear σ-model. Chinese Physics C, 1991, 15(7): 591-597.
[19]	ZHUANG Pen-Fei , LIU Lian-Shou . TARGET MASS DEPENDENCE AND NON-LINEAR EFFECTS IN HIGH ENERGY HEAVY ION COLLISIONS. Chinese Physics C, 1990, 14(3): 240-246.
[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. Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map[J]. Chinese Physics C, 2002, 26(4): 402-408.

LV Jian-Qin. Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map[J]. Chinese Physics C, 2002, 26(4): 402-408. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2001-05-29
Revised: 1900-01-01

Article Metric

Article Views(2387)
PDF Downloads(492)
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 Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map

LV Jian-Qin ^,

Corresponding author: LV Jian-Qin,

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

Received Date: 2001-05-29
Accepted Date: 1900-01-01
Available Online: 2002-04-05

Abstract: Lie algebraic method is used in the analysis of nonlinear transport for the relativistic charged particles in cylindrical symmetrical electrostatic fields, and particle orbits of third order approximation in the six dimensional phase space (x, x′, y, y′, τ, p-τ) are obtained. In the analysis, we take the electrostatic accelerating tube as an example, and divide the electrostatic accelerating tube into three elements: entrance thin lens, uniform accelerating field and exit thin lens, on which Lie map is applied, and the solutions through third order of particle orbits are obtained finally. This method can also be used for the electrostatic lenses.