Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses

LV Jian-Qin; LI Chao-Long; LI Jin-Hai

Chinese Physics C> 2003, Vol. 27> Issue(1) : 76-82

Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses

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

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Abstract：
The nonlinear transport of intense pulsed beams is analyzed with the Lie algebraic method in the case of K-V distribution , and the particle trajectories of second order approximation in the 6-D phase space (x,x′,y, y′, τ, pτ) are obtained. The beams could be axial-symmetrical or non-axial-symmetrical in the transverse direction. In the analysis, the effective fields of lens are divided into several small intervals. Each interval is treated as a uniform accelerating field and each dividing point is considered as a thin lens. Let the Lie map act on each uniform accelerating field and thin lens, the nonlinear particle trajectories can be obtained.

References

[1]	Goldstein H. Classical Mechanics. 2nd ed Reading, Massachusetts Addison-Wesley, 19802 L Jian-Qin. Nucl. Instrum. Methods, 1998, A416:229-235

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LV Jian-Qin, LI Chao-Long and LI Jin-Hai. Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses[J]. Chinese Physics C, 2003, 27(1): 76-82.

LV Jian-Qin, LI Chao-Long and LI Jin-Hai. Lie Algebraic Analysis for the Nonlinear Transport of Intense Pulsed Beams in Electrostatic Lenses[J]. Chinese Physics C, 2003, 27(1): 76-82. shu

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Received: 2002-04-17
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 of Intense Pulsed Beams in Electrostatic Lenses

Corresponding author: LV Jian-Qin,

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

Received Date: 2002-04-17
Accepted Date: 1900-01-01
Available Online: 2003-01-05

Abstract: The nonlinear transport of intense pulsed beams is analyzed with the Lie algebraic method in the case of K-V distribution , and the particle trajectories of second order approximation in the 6-D phase space (x,x′,y, y′, τ, pτ) are obtained. The beams could be axial-symmetrical or non-axial-symmetrical in the transverse direction. In the analysis, the effective fields of lens are divided into several small intervals. Each interval is treated as a uniform accelerating field and each dividing point is considered as a thin lens. Let the Lie map act on each uniform accelerating field and thin lens, the nonlinear particle trajectories can be obtained.