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

Abstract
HTML
Reference
Related

PDF

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

[1]	U. Ratzinger, In Proceedings of the 1988 Linac Conference, (Virginia, USA, 1988) p. 185
[2]	P. N. Ostroumov, A. A. Kolomiets, S. Sharma et al, Nuclear Instruments and Methods in Physics Research A, 547:259-269 (2005)
[3]	Zhi-Jun Wang, Yuan He, A. A. Kolomiets et al, Chinese Physics C, 37(12):127001 (2013)
[4]	N. W. McLachlan, Theory and application of Mathieu functions, (Amen House, London E.C.4, Oxford University Press, 1951)
[5]	K. R. Crandal, R. H. Stokes, T. P. Wangler, In Proceedings of 1979 Linac Conference p205
[6]	T. P. Wangler, Principles of RF linear accelerators, (John wiley sons, Inc., New York, 1998) P189

[1]	Bao-Dong Sun , Yu-Bing Dong . ρ meson impact parameter distributions. Chinese Physics C, 2018, 42(6): 063104. doi: 10.1088/1674-1137/42/6/063104
[2]	Xiao-Jun Sun , Chun-Xing Chen , Ning Wang , Hou-Bing Zhou . Systematic description of nuclear electric quadrupole moments. Chinese Physics C, 2018, 42(12): 124105. doi: 10.1088/1674-1137/42/12/124105
[3]	Yu-Lian Zhang , Hui-Rong Qi , Bi-Tao Hu , Hai-Yun Wang , Qun Ou-Yang , Yuan-Bo Chen , Jian Zhang , Zhi-Wen Wen . A hybrid structure gaseous detector for ion backflow suppression. Chinese Physics C, 2017, 41(5): 056003. doi: 10.1088/1674-1137/41/5/056003
[4]	Qiu-Yue Li , Xiao-Xiang Wang , Yan Zuo , Yu Zhang , Feng Pan . Triaxial dynamics in the quadrupole-deformed rotor. Chinese Physics C, 2016, 40(1): 014101. doi: 10.1088/1674-1137/40/1/014101
[5]	Liang Zhang , Peng-Zhi Huang . ρ meson decays of heavy hybrid mesons. Chinese Physics C, 2016, 40(7): 073105. doi: 10.1088/1674-1137/40/7/073105
[6]	NIU Li-Bo , LI Yu-Lan , HUANG Meng , HE Bin , LI Yuan-Jing . Track reconstruction based on Hough-transform for nTPC. Chinese Physics C, 2014, 38(12): 126201. doi: 10.1088/1674-1137/38/12/126201
[7]	LIU Ren-Hong , QU Hua-Min , KANG Ling , ZHANG Jun-Song , WANG Hai-Jing . Modal analysis of AC quadrupole magnet system for CSNS/RCS. Chinese Physics C, 2013, 37(8): 087002. doi: 10.1088/1674-1137/37/8/087002
[8]	WEI Wei , CHEN Lei-Lei . Rotochemical heating in hybrid stars withmodified Urca reactions in operation. Chinese Physics C, 2012, 36(7): 601-604. doi: 10.1088/1674-1137/36/7/006
[9]	BAO Tmurbagan , LI Gen-Quan , WANG Zong-Chang , YANG Xing-Qiang , LIU Guang-Zhou . Influences of the bag constant on properties of hybrid stars. Chinese Physics C, 2011, 35(6): 539-542. doi: 10.1088/1674-1137/35/6/005
[10]	B. A. Soliman , M. M. Abdelrahman , A. G. Helal , F. W. Abdelsalam . Simulation of ion beam extraction and focusing system. Chinese Physics C, 2011, 35(1): 83-87. doi: 10.1088/1674-1137/35/1/017
[11]	ZHOU Quan-Feng , ZHU-Kun , LU Yuan-Rong , GAO Shu-Li , KANG Ming-Lei , YAN Xue-Qing , GUO Zhi-Yu , CHEN Jia-Er . Simulation and experiments of rf tuning of a 201.5 MHz four-rod RFQ cavity. Chinese Physics C, 2011, 35(11): 1042-1046. doi: 10.1088/1674-1137/35/11/012
[12]	PENG Yue-Mei , XU Gang . Analytical transfer matrix of a quadrupole fringe. Chinese Physics C, 2011, 35(11): 1047-1052. doi: 10.1088/1674-1137/35/11/013
[13]	KANG Miao , ZHOU Xia , WANG Xiao-Dong , HENG Yao-Fu . Influence of medium effects on the rotating hybrid stars. Chinese Physics C, 2010, 34(11): 1696-1699. doi: 10.1088/1674-1137/34/11/005
[14]	BAO Tmurbagan , LIU Guang-Zhou , ZHU Ming-Feng . Properties of hybrid stars in an extended MIT bag model. Chinese Physics C, 2009, 33(5): 340-344. doi: 10.1088/1674-1137/33/5/004
[15]	WANG Zhen-Tian , ZHANG Li , HUANG Zhi-Feng , KANG Ke-Jun , CHEN Zhi-Qiang , FANG Qiao-Guang , ZHU Pei-Ping . An ART iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging. Chinese Physics C, 2009, 33(11): 975-980. doi: 10.1088/1674-1137/33/11/009
[16]	NIE Yuan-Cun , LU Yuan-Rong , CHEN Jia-Er , YAN Xue-Qing , GUO Zhi-Yu , ZHU Kun , FANG Jia-Xun . Beam dynamics and RF design of trapezoidal IH-RFQ with low energy spread. Chinese Physics C, 2009, 33(S2): 105-108. doi: 10.1088/1674-1137/33/S2/027
[17]	SUN Zhi-Rui , PENG Jun , FU Shi-Nian . Matrix method for the solution of RF field perturbations due to local frequency shifts. Chinese Physics C, 2009, 33(9): 798-803. doi: 10.1088/1674-1137/33/9/018
[18]	ZHU Kun , GUO Zhi-Yu , FANG Jia-Xun , GAO Shu-Li , SONG Xiang-Xiang . The Simulation and Experiment Study of a 4 Rod RFQ RF Property. Chinese Physics C, 2005, 29(5): 512-516.
[19]	Chen Min , Hou Boyu , Shi Kangjie . Reflection Matrix of Z_n Belavin Model. Chinese Physics C, 1996, 20(S4): 325-331.
[20]	WANG Shu-Hong . RFQ's Beam Dynamics and RF Structure. Chinese Physics C, 1993, 17(4): 310-321.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2017-02-01

Fund

Supported by National Natural Science Foundation of China (11375122,11511140277) and Strategic Priority Research Program of the Chinese Academy of Sciences (XDA03020705)

Article Metric

Article Views(1478)
PDF Downloads(43)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

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.

HTML

Reference (6)

Focusing properties of discrete RF quadrupoles

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article