Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles

LI Jin-Hai; LI Chao-Long; LU 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> 2003, Vol. 27> Issue(7) : 645-648

Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles

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

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Abstract：
With Lie algebraic methods, we analysed the nonlinear transport of particle motions in electrostatic quadrupoles up to third order. The procedures are: first, set up the Hamiltonian for the electrostatic quadrupoles, then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees, finally, calculate the particle's nonlinear trajectories up to third order. Higher orders could be obtained if necessary.

References

[1]	. Dragt A J.Physics of High Energy Particle Accelerators,AIP Conference Proceedings No.87,edited by R.A.Carrigan et al.Am.Inst.Phys.,New York,19872. Dragt A J,Finn J M.J .Math.Physics,1976,17:2215 3 Dragt A J,Forest E.J.Math.Physics,1983,24(12):2734

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LI Jin-Hai, LI Chao-Long and LU Jian-Qin. Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles[J]. Chinese Physics C, 2003, 27(7): 645-648.

LI Jin-Hai, LI Chao-Long and LU Jian-Qin. Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles[J]. Chinese Physics C, 2003, 27(7): 645-648. shu

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Received: 2002-11-11
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles

Corresponding author: LU Jian-Qin,

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

Received Date: 2002-11-11
Accepted Date: 1900-01-01
Available Online: 2003-07-05

Abstract: With Lie algebraic methods, we analysed the nonlinear transport of particle motions in electrostatic quadrupoles up to third order. The procedures are: first, set up the Hamiltonian for the electrostatic quadrupoles, then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees, finally, calculate the particle's nonlinear trajectories up to third order. Higher orders could be obtained if necessary.