Third Order Lie Map for the Solenoidal Lenses

LV Jian-Qin

Chinese Physics C> 2002, Vol. 26> Issue(2) : 186-191

Third Order Lie Map for the Solenoidal Lenses

LV Jian-Qin ^,

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

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Abstract：
Solenoidal lenses are usually used to focus charged particle beams moving in inductive accelerators,electron linear accelerators,proton linear accelerators,low energy beam transport systems as well as some cathode ray tubes. To understand the nonlinear optical properties of solenoidal lenses,Lie algebraic methods are used in the analysis of particle trajectories in this kind of lenses,and the results of third order approximation are obtained. Because of the existence of fringing fields,one should divide the fringing field into several small segments,and apply the Lie map to each of the segments.

References

[1]	. Goldstein H. Classical Mechanics, 2nd ed. Massachusetts: Addison-Wesley, 1980. 378—418 2. Dragt A J, Finn J M. Lie Series and Invariant Functions for Analytic Symplectic Maps. J Math Phys., 1976, 17(12): 2215

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LV Jian-Qin. Third Order Lie Map for the Solenoidal Lenses[J]. Chinese Physics C, 2002, 26(2): 186-191.

LV Jian-Qin. Third Order Lie Map for the Solenoidal Lenses[J]. Chinese Physics C, 2002, 26(2): 186-191. shu

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Received: 2001-01-15
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

Third Order Lie Map for the Solenoidal Lenses

LV Jian-Qin ^,

Corresponding author: LV Jian-Qin,

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

Received Date: 2001-01-15
Accepted Date: 1900-01-01
Available Online: 2002-02-05

Abstract: Solenoidal lenses are usually used to focus charged particle beams moving in inductive accelerators,electron linear accelerators,proton linear accelerators,low energy beam transport systems as well as some cathode ray tubes. To understand the nonlinear optical properties of solenoidal lenses,Lie algebraic methods are used in the analysis of particle trajectories in this kind of lenses,and the results of third order approximation are obtained. Because of the existence of fringing fields,one should divide the fringing field into several small segments,and apply the Lie map to each of the segments.