Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods

LI Jin-Hai; LU Jian-Qin

Chinese Physics C> 2005, Vol. 29> Issue(7) : 695-699

Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods

LI Jin-Hai ^, ,
LU Jian-Qin

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

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Abstract：
With the Lie algebraic methods, the charged particle trajectories in electrostatic analyzers are analyzed,and the third order solutions obtained. In this paper, we briefly describe the Lie algebraic methods and the procedures of calculating the nonlinear orbits. The procedures are: first, set up the Hamiltonian; then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees; next, calculate the Lie map associating to the Hamiltonian; finally, apply the Lie map on the particle initial coordinates in the phase space, and obtain the particle nonlinear trajectories of the first order,the second order, and the third order approximations respectively. Higher orders solutions could be obtained if needed.

References

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. Dragt A J, Lecture Notes on Nonlinear Orbit Dynamics. In: Physics ofHigh Energy Part icle Accelerators. Carrigan R A et al. ed AIP Confer..ence Proceedings No. 87. New York: Am. Inst. Phys. , 19872. Dragt A J,Finn J M. J.Math. Physics, 1976, 17: 2215 - 22273. Dragt A J,Forest E. J. Math. Physics, 1983, 24 (12) : 2734 - 27444. L#220; Jian-Qin. Nucl. Instrum. Methods, 1995, A355: 253

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LI Jin-Hai and LU Jian-Qin. Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods[J]. Chinese Physics C, 2005, 29(7): 695-699.

LI Jin-Hai and LU Jian-Qin. Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods[J]. Chinese Physics C, 2005, 29(7): 695-699. shu

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Received: 2004-10-22
Revised: 1900-01-01

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Nonlinear Analysis for the Electrostatic Analyzers With Lie Algebraic Methods

LI Jin-Hai ^,
LU Jian-Qin

Corresponding author: LI Jin-Hai,

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

Received Date: 2004-10-22
Accepted Date: 1900-01-01
Available Online: 2005-07-05

Abstract: With the Lie algebraic methods, the charged particle trajectories in electrostatic analyzers are analyzed,and the third order solutions obtained. In this paper, we briefly describe the Lie algebraic methods and the procedures of calculating the nonlinear orbits. The procedures are: first, set up the Hamiltonian; then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees; next, calculate the Lie map associating to the Hamiltonian; finally, apply the Lie map on the particle initial coordinates in the phase space, and obtain the particle nonlinear trajectories of the first order,the second order, and the third order approximations respectively. Higher orders solutions could be obtained if needed.