Matrix method for the solution of RF field perturbations due to local frequency shifts

SUN Zhi-Rui; PENG Jun; FU Shi-Nian

doi:10.1088/1674-1137/33/9/018

Chinese Physics C> 2009, Vol. 33> Issue(9) : 798-803 DOI: 10.1088/1674-1137/33/9/018

Matrix method for the solution of RF field perturbations due to local frequency shifts

Abstract
HTML
Reference
Related

PDF

Abstract：
To tune the accelerating field to the design value in a periodical radio frequency accelerating structure, Slater's perturbation theorem is commonly used. This theorem solves a second-order differential equation to obtain the electrical field variation due to a local frequency shift. The solution becomes very difficult for a complex distribution of the local frequency shifts. Noticing the similarity between the field perturbation equation and the equation describing the transverse motion of a particle in a quadrupole channel, we propose in this paper a new method in which the transfer matrix method is applied to the field calculation instead of directly solving the differential equation. The advantage of the matrix method is illustrated in examples.

References

[1]

. WANG Shu-Hong, LUO Zi-Hua, LUO Ying-Xiong. Princi-ples of Proton Linear Accelerators. Beijing: Atomic EnergyPress, 1986. 81|87, 164|169 (in Chinese)2. FU Shi-Nian. HEP NP, 2002, 26(8): 870 (in Chinese)3. Thomas P W. Principles of RF Linear Accelerators.Canada: John Wiley Sons, Inc., 1998. 203|2104. PENG Jun et al. Chinese Physics C (HEP NP), 2008,32(2): 146|1505. Naito F. Tuning of the RF eld on the DTL for the J-PARC. Proceedings of the 2003 Particle Accelerator Con-ference. Tsukuba, Japan6. Deibele C. DTL Cavity Tuning at SNS, SNS-NOTE-ENGR-74. June 2002, Figure.1

[1]	Ke Li , Yuxin Liu , Qi-Shu Yan , Xiaoran Zhao . Shifts in the BCFW method for QED. Chinese Physics C, 2022, 46(9): 093111. doi: 10.1088/1674-1137/ac745a
[2]	Tian-Lu Chen , Wei Liu , Qi Gao , Mao-Yuan Liu , Hai-Jin Li , Danzengluobu , Ying Shi . Cosmic ray electron spectrum due to the dispersion ofinjection spectrum. Chinese Physics C, 2018, 42(7): 075001. doi: 10.1088/1674-1137/42/7/075001
[3]	Yunlong Zheng , Yicen Mou , Haomin Rao , Mingzhe Li . Conformal invariant cosmological perturbations via the covariant approach: multicomponent universe. Chinese Physics C, 2018, 42(3): 035102. doi: 10.1088/1674-1137/42/3/035102
[4]	Kai Zhou , Yun-Tao Song , Kai-Zhong Ding , Jian Ge , Kai Yao . Analytical solution of transverse oscillation in cyclotron using LP method. Chinese Physics C, 2018, 42(3): 037001. doi: 10.1088/1674-1137/42/3/037001
[5]	Ibrahim Sener . Self duality solution with a Higgs field. Chinese Physics C, 2018, 42(10): 103104. doi: 10.1088/1674-1137/42/10/103104
[6]	Jing Wang , Jian-Long Huang , Xiao-Qi Zhang , Bin Zhang , Yuan He , Zhou-Li Zhang , Ai-Min Shi . Frequency tuning with RFQ temperature in China ADS Injector Ⅱ. Chinese Physics C, 2016, 40(3): 037003. doi: 10.1088/1674-1137/40/3/037003
[7]	Jin-Tao Zhu , Guo-Fu Liu , Jun Yang , Xiao-Liang Luo , Lei Zhang , Li-Feng Ji . A new method of charged particle identification based on frequency spectrum analysis. Chinese Physics C, 2016, 40(3): 036202. doi: 10.1088/1674-1137/40/3/036202
[8]	Jia-Jun Zheng , Yong-Liang Yang , Bao-Gen Sun , Fang-Fang Wu , Chao-Cai Cheng , Kai Tang , Jun-Hao Wei . Central RF frequency measurement of the HLS-Ⅱ storage ring. Chinese Physics C, 2016, 40(4): 047005. doi: 10.1088/1674-1137/40/4/047005
[9]	Wen-Jun Chen , Hong Ma , De Yu , Xiao-Hu Zeng . Numerical solution to the Bloch equations: paramagnetic solutions under wideband continuous radio frequency irradiation in a pulsed magnetic field. Chinese Physics C, 2016, 40(8): 088201. doi: 10.1088/1674-1137/40/8/088201
[10]	CHENG Xue-Rui , DAI Hai-Yang , QI Ze-Ming , WANG Yu-Yin , ZHANG Guo-Bin . Local structure of oxygen-deficient Yttrium oxide. Chinese Physics C, 2013, 37(9): 098002. doi: 10.1088/1674-1137/37/9/098002
[11]	YE Qing , CHEN Xing , ZHOU Jing , ZHAO Hai-Feng , CHU Wang-Sheng , ZHENG Xu-Sheng , WU Zi-Yu . Local hydrated structure of an Fe²⁺/Fe³⁺ aqueous solution: an investigation using a combination of molecular dynamics and X-ray absorption fine structure methods. Chinese Physics C, 2013, 37(3): 038003. doi: 10.1088/1674-1137/37/3/038003
[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]	R. G. Nazmitdinov , E. I. Shahaliev , M. K. Suleymanov . Central nucleus-nucleus collisions at relativistic energies with a new method based on Random Matrix Theory. Chinese Physics C, 2010, 34(8): 1076-1081. doi: 10.1088/1674-1137/34/8/007
[14]	MEI Hua , CHEN Hong , YAO Jiang-Ming . Single-particle resonance states of ¹²²Zr in relativistic mean-field theory combined with real stabilization method. Chinese Physics C, 2009, 33(S1): 101-104. doi: 10.1088/1674-1137/33/S1/033
[15]	LIU Chu-Yu , WANG Fang , WANG Er-Dong , QUAN Sheng-Wen , HAO Jian-Kui , LU Xiang-Yang , ZHANG Bao-Cheng , ZHAO Kui . Impact on the magnetic compressor due to CSR. Chinese Physics C, 2008, 32(8): 665-667. doi: 10.1088/1674-1137/32/8/016
[16]	WEI Gao-Feng , LONG Chao-Yun , LONG Zheng-Wen , QIN Shui-Jie . Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space. Chinese Physics C, 2008, 32(4): 247-250. doi: 10.1088/1674-1137/32/4/001
[17]	PENG Jun , SUN Zhi-Rui , FU Shi-Nian . A new tuning procedure for the DTL RF field pattern. Chinese Physics C, 2008, 32(2): 146-150. doi: 10.1088/1674-1137/32/2/014
[18]	Chen Min , Hou Boyu , Shi Kangjie . Reflection Matrix of Z_n Belavin Model. Chinese Physics C, 1996, 20(S4): 325-331.
[19]	Qiu Zhihong , Chen Zhiqing , Wang Yansen , Chen Jianxin . Coulomb Correction of the p-⁴He Low-Energy Scattering Phase Shifts. Chinese Physics C, 1988, 12(S3): 321-327.
[20]	Xue Shesheng . A Mean Field Solution of the Fokker-Planck Equation in Lattice Gauge Theories. Chinese Physics C, 1988, 12(S2): 117-122.

Access

Get Citation

SUN Zhi-Rui, PENG Jun and FU Shi-Nian. Matrix method for the solution of RF field perturbations due to local frequency shifts[J]. Chinese Physics C, 2009, 33(9): 798-803. doi: 10.1088/1674-1137/33/9/018

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2008-11-28
Revised: 2009-04-09

Article Metric

Article Views(2753)
PDF Downloads(590)
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

Matrix method for the solution of RF field perturbations due to local frequency shifts

Corresponding author: SUN Zhi-Rui,

Received Date: 2008-11-28

Accepted Date: 2009-04-09

Available Online: 2009-09-05

Abstract:

To tune the accelerating field to the design value in a periodical radio frequency accelerating structure, Slater's perturbation theorem is commonly used. This theorem solves a second-order differential equation to obtain the electrical field variation due to a local frequency shift. The solution becomes very difficult for a complex distribution of the local frequency shifts. Noticing the similarity between the field perturbation equation and the equation describing the transverse motion of a particle in a quadrupole channel, we propose in this paper a new method in which the transfer matrix method is applied to the field calculation instead of directly solving the differential equation. The advantage of the matrix method is illustrated in examples.

HTML

Reference (1)

Matrix method for the solution of RF field perturbations due to local frequency shifts

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article