Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles

  • With Lie algebraic methods, we analysed the nonlinear transport of particle motions in electrostatic quadrupoles up to third order. The procedures are: first, set up the Hamiltonian for the electrostatic quadrupoles, then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees, finally, calculate the particle's nonlinear trajectories up to third order. Higher orders could be obtained if necessary.
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  • [1] . Dragt A J.Physics of High Energy Particle Accelerators,AIP Conference Proceedings No.87,edited by R.A.Carrigan et al.Am.Inst.Phys.,New York,19872. Dragt A J,Finn J M.J .Math.Physics,1976,17:2215 3 Dragt A J,Forest E.J.Math.Physics,1983,24(12):2734
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LI Jin-Hai, LI Chao-Long and LU Jian-Qin. Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles[J]. Chinese Physics C, 2003, 27(7): 645-648.
LI Jin-Hai, LI Chao-Long and LU Jian-Qin. Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles[J]. Chinese Physics C, 2003, 27(7): 645-648. shu
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Received: 2002-11-11
Revised: 1900-01-01
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Lie Algebraic Analysis for the Nonlinear Transport in Electrostatic Quadrupoles

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

Abstract: With Lie algebraic methods, we analysed the nonlinear transport of particle motions in electrostatic quadrupoles up to third order. The procedures are: first, set up the Hamiltonian for the electrostatic quadrupoles, then expand the Hamiltonian into a sum of homogeneous polynomials of different degrees, finally, calculate the particle's nonlinear trajectories up to third order. Higher orders could be obtained if necessary.

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