中国物理B ›› 2004, Vol. 13 ›› Issue (10): 1665-1668.doi: 10.1088/1009-1963/13/10/015

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Lie algebraic analysis for the nonlinear transportof intense pulsed beams in electrostatics lenses

吕建钦, 李金海   

  1. Institute of Heavy Ion Physics, Peking University, Beijing 100871, China
  • 收稿日期:2004-02-25 修回日期:2004-05-31 出版日期:2004-10-20 发布日期:2005-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10075005).

Lie algebraic analysis for the nonlinear transportof intense pulsed beams in electrostatics lenses

Lü Jian-Qin (吕建钦), Li Jin-Hai (李金海)   

  1. Institute of Heavy Ion Physics, Peking University, Beijing 100871, China
  • Received:2004-02-25 Revised:2004-05-31 Online:2004-10-20 Published:2005-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10075005).

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摘要： The Lie algebraic method is applied to the analysis of the nonlinear transport of an intense pulsed beam in cylindrically symmetrical electrostatic lenses, and particle orbits in a six-dimensional phase space (x, p_x, y, p_y, τ, p_τ) are obtained in the second order approximation. They can also be acquired in the third or higher order approximation if needed. In the analysis, we divide the electrostatic lenses into several segments. Each segment is considered as a uniform accelerating field, and each dividing point is treated as a thin lens. The particle distribution in a three-dimensional ellipsoid is of Gaussian type.

关键词: electrostatic lenses, intense pulsed beams, Gauss distribution, Lie map, nonlinear

Abstract: The Lie algebraic method is applied to the analysis of the nonlinear transport of an intense pulsed beam in cylindrically symmetrical electrostatic lenses, and particle orbits in a six-dimensional phase space ($x, p_x, y, p_y, \tau, p_{\tau}$) are obtained in the second order approximation. They can also be acquired in the third or higher order approximation if needed. In the analysis, we divide the electrostatic lenses into several segments. Each segment is considered as a uniform accelerating field, and each dividing point is treated as a thin lens. The particle distribution in a three-dimensional ellipsoid is of Gaussian type.

Key words: electrostatic lenses, intense pulsed beams, Gauss distribution, Lie map, nonlinear

中图分类号:  (Electrostatic lenses, septa)

  • 41.85.Ne
02.10.Ud (Linear algebra)