Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods

LI Jin-Hai; LU Jian-Qin

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]	ZHANG Zhuo , YANG Guo-Jun , . Lie algebraic analysis and simulation of high-current pulsed beam transport in a solenoidal lens. Chinese Physics C, 2010, 34(1): 134-137. doi: 10.1088/1674-1137/34/1/025
[2]	ZHANG Zhuo , . Lie algebraic analysis for the nonlinear transport of intense bunched beam in electrostatic quadrupoles. Chinese Physics C, 2008, 32(3): 209-214. doi: 10.1088/1674-1137/32/3/010
[3]	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.
[4]	HU Ji-Feng , HE Kang-Lin , ZHANG Zi-Ping , BIAN Jian-Ming , CAO Guo-Fu , DENG Zi-Yan , HE Miao , HUANG Bin , JI Xiao-Bin , LI Gang , LI Hai-Bo , LI Wei-Dong , LIU Chun- , , , . Correlation Analysis in Time-of-Flight Calibration of BESⅢ. Chinese Physics C, 2007, 31(10): 893-899.
[5]	HUANG Gui-Rong , GAO Hui , LIU Gong-Fa , lshang , WANG Jin-Xiang , FENG Lan-Lin . Analysis on the arc Phenomenon of RF Circulator. Chinese Physics C, 2005, 29(12): 1200-1204.
[6]	LI Jin-Hai , LU Jian-Qin . Nonlinear Analysis for the Wein Filter with Lie Algebraic Method. Chinese Physics C, 2004, 28(9): 998-1001.
[7]	XIAO Xiang-Hui , LIU Peng . Theoretical Analysis for Energy Resolution of Johann Monochromator. Chinese Physics C, 2003, 27(1): 83-88.
[8]	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.
[9]	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.
[10]	TAO Xiao-Ping . Analysis of Discharging Noise of Line-Type Pulse Modulator. Chinese Physics C, 2002, 26(6): 639-644.
[11]	LV Jian-Qin . Third Order Lie Map for the Sextupole Magnets. Chinese Physics C, 2001, 25(4): 354-358.
[12]	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.
[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]	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.
[15]	Ni Zhixiang . Nonlinear Spectrum-Generating Algebra for the Symmetrical Pöschl-Teller Potential. Chinese Physics C, 1999, 23(3): 289-297.
[16]	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.
[17]	ZHU Yong-Sheng , ZHANG Liang-Sheng , GAO Wen-Xiu , ZHANG Ying-Ping , ZHAO Ping-De , ZHANG Jia-Wen , LI Fang , CHEN Le-Jun , XU Zhi-Qing . THE COSMIC RAY DATA ANALYSIS OF μ-COUNTER ARRAY IN BES. Chinese Physics C, 1990, 14(2): 102-109.
[18]	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.
[19]	Wei Kai-yu . THE PARAMETERS AND ELECTRICAL TOLERANCE ANALYSIS FOR THE SINGLE BUNCHER SYSTEMS. Chinese Physics C, 1980, 4(6): 706-714.
[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(2647)
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.