Third Order Lie Map for the Solenoidal Lenses

  • 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.
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  • [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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Third Order Lie Map for the Solenoidal Lenses

    Corresponding author: LV Jian-Qin,
  • Institute of Heavy Ion Physics,Peking University, Beijing 100871, China

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.

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