Lie algebraic analysis for the nonlinear transport of intense bunched beam in electrostatic quadrupoles

ZHANG Zhuo

doi:10.1088/1674-1137/32/3/010

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2024年10月30日

Chinese Physics C> 2008, Vol. 32> Issue(3) : 209-214 DOI: 10.1088/1674-1137/32/3/010

Lie algebraic analysis for the nonlinear transport of intense bunched beam in electrostatic quadrupoles

ZHANG Zhuo ^, ,

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Abstract：
In this paper, the nonlinear transport of intense bunched beams in electrostatic quadrupoles is analyzed using the Lie algebraic method, and the results are briefly presented of the linear matrix approximation and the second order correction of particle trajectory in the state space. Beam having K-V distribution and Gaussian distribution approximation are respectively considered. A brief discussion is also given of the total effects of the quadrupole and the space charge forces on the evolution of the beam envelope.

References

[1]

. Dragt A J. Physics of High Energy Particle Accelerators.In: Carrigan R A et al. AIP Conference Proceedings No.87. New York: Am. Inst. Phys., 1987. 1472. Goldstein H. Classical Mechanics. 2nd ed. Massachusetts:Addison-Wesley, 1980. 3783. Takayama K. Lettere al Nuovo Cimento, 1982, 34(7): 1904. LI Jin-Hai. Lie Algebraic Analysis and Program Design for the Nonlinear Transport of Beam in Accelerators. Peking University: Thesis for a Doctor's Degree, 2005 (in Chinese)

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ZHANG Zhuo and Lie algebraic analysis for the nonlinear transport of intense bunched beam in electrostatic quadrupoles[J]. Chinese Physics C, 2008, 32(3): 209-214. doi: 10.1088/1674-1137/32/3/010

ZHANG Zhuo and Lie algebraic analysis for the nonlinear transport of intense bunched beam in electrostatic quadrupoles[J]. Chinese Physics C, 2008, 32(3): 209-214. doi: 10.1088/1674-1137/32/3/010 shu

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Received: 2007-02-25
Revised: 2007-05-14

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Lie algebraic analysis for the nonlinear transport of intense bunched beam in electrostatic quadrupoles

ZHANG Zhuo ^,

Corresponding author: ZHANG Zhuo,

Received Date: 2007-02-25
Accepted Date: 2007-05-14
Available Online: 2008-03-05

Abstract:

In this paper, the nonlinear transport of intense bunched beams in electrostatic quadrupoles is analyzed using the Lie algebraic method, and the results are briefly presented of the linear matrix approximation and the second order correction of particle trajectory in the state space. Beam having K-V distribution and Gaussian distribution approximation are respectively considered. A brief discussion is also given of the total effects of the quadrupole and the space charge forces on the evolution of the beam envelope.