Analytical solution of transverse oscillation in cyclotron using LP method

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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
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 shu
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Received: 2017-10-31
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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

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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