Analytical Solution of Transverse Oscillation in Cyclotron Using LP Method
Accelerator Physics
2018-01-30 v1
Abstract
We have carried out an approximate analytical solution to precisely consider the influence of magnetic field on the transverse oscillation of particles in cyclotron. The differential equations of transverse oscillation are solved from the Lindstedt-Poincare method. After careful deduction, the accurate first order analytic solutions are obtained. The analytical solutions are applied to the magnetic field, comes from an isochronous cyclotron with four spiral sectors, the accuracy of these analytical solutions is verified and confirmed from the comparison of numerical method. Finally, we discussed the transverse oscillation at v0=N/2 , using the same analytical solution.
Cite
@article{arxiv.1801.02284,
title = {Analytical Solution of Transverse Oscillation in Cyclotron Using LP Method},
author = {Kai Zhou and Yuntao Song and Kaizhong Ding and Jian Ge and Kai Yao},
journal= {arXiv preprint arXiv:1801.02284},
year = {2018}
}
Comments
This peper will be published in Chinese Physics C