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

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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

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. 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

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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

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

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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.