Chinese Physics C > 2002, Vol. 26 > Issue(4): 402-408

Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map

LV Jian-Qin^,

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

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Abstract：
Lie algebraic method is used in the analysis of nonlinear transport for the relativistic charged particles in cylindrical symmetrical electrostatic fields, and particle orbits of third order approximation in the six dimensional phase space (x, x′, y, y′, τ, p-τ) are obtained. In the analysis, we take the electrostatic accelerating tube as an example, and divide the electrostatic accelerating tube into three elements: entrance thin lens, uniform accelerating field and exit thin lens, on which Lie map is applied, and the solutions through third order of particle orbits are obtained finally. This method can also be used for the electrostatic lenses.

References

[1]

Septier A. Focusing of Charged Particles. New York: Academic Press, 1967. Vol. 11, 2972 LU lian-Qin. LEADS: A Graphical Display Computer Program for Linear and Electrostatic Accelerator Beam Dynamics Simulation, Nucl. Instrum. Methods Sec., 1995, A355: 253-2573 Coldstein H. Classical Mechanics 2nd ed., Addition-Wesley, Reading, Massachusetts, 19804 Dragt A J. AIP Conf. Proc., 1982, 87: 1475 Dragt A J, Finn J M. J. Math. Phys., 1979, 20: 2649

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LV Jian-Qin. Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map[J]. Chinese Physics C, 2002, 26(4): 402-408.

LV Jian-Qin. Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map[J]. Chinese Physics C, 2002, 26(4): 402-408. shu

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Received: 2001-05-29
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

Nonlinear Optics of the Electrostatic Accelerator Tubes-Third Order Lie Map

LV Jian-Qin^,

Corresponding author:LV Jian-Qin,

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

Received Date:2001-05-29
Accepted Date:1900-01-01
Available Online:2002-04-05

Abstract:Lie algebraic method is used in the analysis of nonlinear transport for the relativistic charged particles in cylindrical symmetrical electrostatic fields, and particle orbits of third order approximation in the six dimensional phase space (x, x′, y, y′, τ, p-τ) are obtained. In the analysis, we take the electrostatic accelerating tube as an example, and divide the electrostatic accelerating tube into three elements: entrance thin lens, uniform accelerating field and exit thin lens, on which Lie map is applied, and the solutions through third order of particle orbits are obtained finally. This method can also be used for the electrostatic lenses.