We have carried out an approximate analytical solution to precisely considerthe influence of magnetic field on the transverse oscillation of particles incyclotron. The differential equations of transverse oscillation are solved fromthe Lindstedt-Poincare method. After careful deduction, the accurate firstorder analytic solutions are obtained. The analytical solutions are applied tothe magnetic field, comes from an isochronous cyclotron with four spiralsectors, the accuracy of these analytical solutions is verified and confirmedfrom the comparison of numerical method. Finally, we discussed the transverseoscillation at v0=N/2 , using the same analytical solution.
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机译：我们已经进行了近似分析，可以精确地考虑磁场对回旋加速器粒子横向振荡的影响。横向振动的微分方程由Lindstedt-Poincare方法求解。经过仔细的推论，可以获得准确的一阶解析解。将解析解应用于磁场，该解析解来自具有四个螺旋扇形的同步回旋加速器，这些解析解的准确性通过数值方法的比较得到验证和确认。最后，我们使用相同的解析解讨论了在v0 = N / 2处的横向振荡。
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