Focusing properties of discrete RF quadrupoles

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Zhi-Hui Li and Zhi-Jun Wang. Focusing properties of discrete RF quadrupoles[J]. Chinese Physics C, 2017, 41(8): 087001. doi: 10.1088/1674-1137/41/8/087001
Zhi-Hui Li and Zhi-Jun Wang. Focusing properties of discrete RF quadrupoles[J]. Chinese Physics C, 2017, 41(8): 087001.  doi: 10.1088/1674-1137/41/8/087001 shu
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Received: 2017-02-01
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    Supported by National Natural Science Foundation of China (11375122,11511140277) and Strategic Priority Research Program of the Chinese Academy of Sciences (XDA03020705)

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Focusing properties of discrete RF quadrupoles

    Corresponding author: Zhi-Hui Li,
  • 1.  The Key Laboratory of Radiation Physics and Technology of Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610065, China
  • 2.  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
Fund Project:  Supported by National Natural Science Foundation of China (11375122,11511140277) and Strategic Priority Research Program of the Chinese Academy of Sciences (XDA03020705)

Abstract: The particle motion equation for a Radio Frequency (RF) quadrupole is derived. The motion equation shows that the general transform matrix of a RF quadrupole with length less than or equal to 0.5β λ (β is the relativistic velocity of particles and λ is wavelength of radio frequency electromagnetic field) can describe the particle motion in an arbitrarily long RF quadrupole. By iterative integration, the general transform matrix of a discrete RF quadrupole is derived from the motion equation. The transform matrix is in form of a power series of focusing parameter B. It shows that for length less than β λ, the series up to the 2nd order of B agrees well with the direct integration results for B up to 30, while for length less than 0.5βλ, the series up to 1st order is already a good approximation of the real solution for B less than 30. The formula of the transform matrix can be integrated into linac or beam line design code to deal with the focusing of discrete RF quadrupoles.

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