Third Order Lie Map for the Sextupole Magnets

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> 2001, Vol. 25> Issue(4) : 354-358

Third Order Lie Map for the Sextupole Magnets

LV Jian-Qin ^,

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

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Abstract：
Sextupole magnets are usually used in beam analyzing systems with high resolving power, micro-beam systems and storage rings of high energy accelerators. It is well known that sextupoles are equivalent to the drift spaces under first order approximation. Therefore, this kind of optical elements is often used to correct the second order aberrations of beam optics systems. When it is necessary to calculate the third order aberrations of a system, or to correct the third order aberrations with octupole magnets, one should know the analytical expressions of the third order terms of sextupoles. In this paper, Lie algebraic methods were used in the analysis of relativistic particle trajectories in the sextupole magnets, and the solutions of third order approximation in the six dimensional phase spaces were obtained.

References

[1]	. Dragt A J. Lecture Notes on Nonlinear Orbit Dynamics, In: Carrigan R A etal. eds., Summer School on High Energy Particle Accelerators, Fermi National Accelerator Laboratory, 1981, NewYork: AIP87, 1982:147

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LV Jian-Qin. Third Order Lie Map for the Sextupole Magnets[J]. Chinese Physics C, 2001, 25(4): 354-358.

LV Jian-Qin. Third Order Lie Map for the Sextupole Magnets[J]. Chinese Physics C, 2001, 25(4): 354-358. shu

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Received: 2000-03-13
Revised: 1900-01-01

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Third Order Lie Map for the Sextupole Magnets

LV Jian-Qin ^,

Corresponding author: LV Jian-Qin,

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

Received Date: 2000-03-13
Accepted Date: 1900-01-01
Available Online: 2001-04-05

Abstract: Sextupole magnets are usually used in beam analyzing systems with high resolving power, micro-beam systems and storage rings of high energy accelerators. It is well known that sextupoles are equivalent to the drift spaces under first order approximation. Therefore, this kind of optical elements is often used to correct the second order aberrations of beam optics systems. When it is necessary to calculate the third order aberrations of a system, or to correct the third order aberrations with octupole magnets, one should know the analytical expressions of the third order terms of sextupoles. In this paper, Lie algebraic methods were used in the analysis of relativistic particle trajectories in the sextupole magnets, and the solutions of third order approximation in the six dimensional phase spaces were obtained.