Analytical solution of transverse oscillation in cyclotron using LP method

Kai Zhou; Yun-Tao Song; Kai-Zhong Ding; Jian Ge; Kai Yao

doi:10.1088/1674-1137/42/3/037001

Chinese Physics C> 2018, Vol. 42> Issue(3) : 037001 DOI: 10.1088/1674-1137/42/3/037001

Analytical solution of transverse oscillation in cyclotron using LP method

Kai Zhou ^1,3 ,
Yun-Tao Song ² ,
Kai-Zhong Ding ² ,
Jian Ge ^2,, ,
Kai Yao ³

1.
School of Physics, University of Science and Technology of China, Hefei 230026, China
2.
Hefei CAS Ion Medical and Technical Devices Co., Ltd, Hefei 230031, China
3.
Institute of Plasma Physics Chinese Academy of Sciences, Hefei 230031, China
4.
Hefei CAS Ion Medical and Technical Devices Co., Ltd, Hefei 230031, China

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Abstract：
We have carried out an approximate analytical solution to precisely consider the influence of magnetic field on the transverse oscillation of particles in a cyclotron. The differential equations of transverse oscillation are solved from the Lindstedt-Poincare method. After careful deduction, accurate first-order analytic solutions are obtained. The analytical solutions are applied to the magnetic field from an isochronous cyclotron with four spiral sectors. The accuracy of these analytical solutions is verified and confirmed from comparison with a numerical method. Finally, we discussed the transverse oscillation at v₀=N/2, using the same analytical solution.
- cyclotron ,
- perturbation method ,
- transverse oscillation ,
- LP method

References

[1]	J. E. Chen, J. X. Fang, The Foundation of Accelerator Physics, First edition (Beijing:Peking University Press, 2012), p.140-204(in Chinese)
[2]	M. M. Gordon and D. O. Jeon, Nuclear Instruments Methods in Physics Research, 301(2):182-190(1991)
[3]	H. L. Hagedoorn and N. F. Verster, Nuclear Instruments Methods, 18:201-228(1962)
[4]	M. M. Gordon and W. S. Hudec, Nuclear Instruments Methods, 18:243-267(1962)
[5]	M. M. Gordon, Nuclear Instruments Methods, 18:281-293(1962)
[6]	M. M. Gordon, Part Accel., 16:39-62(1984)
[7]	S. H. Chen, The Definite Quantitative Methods for Strongly Non-linear Vibration, First edition (Guangzhou:Guangdong Science and Technology Press, 2004) (in Chinese)
[8]	J. C. Li and X. C. Zhou, Asymptotic Methods in Mathematical Physics, First edition (Beijing:Science Press, 1998) (in Chinese)
[9]	J. Y. Tang and B. W. Wei, Theory and Design of Cyclotrons, (Hefei:University of Science and Technology of China Press, 2008) (in Chinese)

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Kai Zhou, Yun-Tao Song, Kai-Zhong Ding, Jian Ge and Kai Yao. Analytical solution of transverse oscillation in cyclotron using LP method[J]. Chinese Physics C, 2018, 42(3): 037001. doi: 10.1088/1674-1137/42/3/037001

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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

Analytical solution of transverse oscillation in cyclotron using LP method

Corresponding author: Jian Ge,

1. School of Physics, University of Science and Technology of China, Hefei 230026, China

2. Hefei CAS Ion Medical and Technical Devices Co., Ltd, Hefei 230031, China

3. Institute of Plasma Physics Chinese Academy of Sciences, Hefei 230031, China

4. Hefei CAS Ion Medical and Technical Devices Co., Ltd, Hefei 230031, China

Received Date: 2017-10-31

Available Online: 2018-03-05

Abstract: We have carried out an approximate analytical solution to precisely consider the influence of magnetic field on the transverse oscillation of particles in a cyclotron. The differential equations of transverse oscillation are solved from the Lindstedt-Poincare method. After careful deduction, accurate first-order analytic solutions are obtained. The analytical solutions are applied to the magnetic field from an isochronous cyclotron with four spiral sectors. The accuracy of these analytical solutions is verified and confirmed from comparison with a numerical method. Finally, we discussed the transverse oscillation at v₀=N/2, using the same analytical solution.

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Analytical solution of transverse oscillation in cyclotron using LP method

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