Focusing properties of discrete RF quadrupoles

Zhi-Hui Li; Zhi-Jun Wang

doi:10.1088/1674-1137/41/8/087001

Chinese Physics C> 2017, Vol. 41> Issue(8) : 087001 DOI: 10.1088/1674-1137/41/8/087001

Focusing properties of discrete RF quadrupoles

Zhi-Hui Li ^1,, ,
Zhi-Jun Wang ²

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

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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 2^nd 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 1^st 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.
- RF quadrupole ,
- transform matrix ,
- focusing parameter ,
- iterative integration ,
- hybrid RFQ

References

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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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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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

Received Date: 2017-02-01

Available Online: 2017-08-05

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 2^nd 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 1^st 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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