Analysis of Third Order Quadrupole Aberrations

  • The formulae of 3rd order quadrupole aberrations are derived with Lie-algebraic map. It is the field extension along the axis that dominates the aberrations. For fixed focal length, the aberrations are small if the quadrupole length is long enough or its aperture is large enough. When the length is comparable to the aperture, the quadrupole with soft edge carries relatively small aberrations.
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  • [1] . Courant E D, Snyder H S. Annals of Physi cs, 1958, 3: 1-482. Ruth R. Lecture Notes in Physics, 1985, 247: 37-633. Dragt A, Finn J. J. Math. Phys. , 1976, 17: 2215-22274. Dragt A. American Inst itut e of Physics Proceedings, 1982, 87: 147-3135. Baartman R. Intrinsic Third Order Aberrat ions in Electrostatic and Mag..netic Quadrupoles. PAC97, 1997, 1415-1417
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SONG Ming-Tao, YANG Xiao-Dong, YUAN You-Jin, YUAN Ping and ZHANG Wen-Zhi. Analysis of Third Order Quadrupole Aberrations[J]. Chinese Physics C, 2004, 28(7): 758-761.
SONG Ming-Tao, YANG Xiao-Dong, YUAN You-Jin, YUAN Ping and ZHANG Wen-Zhi. Analysis of Third Order Quadrupole Aberrations[J]. Chinese Physics C, 2004, 28(7): 758-761. shu
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Received: 2003-10-22
Revised: 1900-01-01
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Analysis of Third Order Quadrupole Aberrations

    Corresponding author: SONG Ming-Tao,
  • Institute of Modern Physics,Chinese Academy of Sciences,Lanzhou 730000,China

Abstract: The formulae of 3rd order quadrupole aberrations are derived with Lie-algebraic map. It is the field extension along the axis that dominates the aberrations. For fixed focal length, the aberrations are small if the quadrupole length is long enough or its aperture is large enough. When the length is comparable to the aperture, the quadrupole with soft edge carries relatively small aberrations.

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