标题： 横向振荡在回旋加速器中的解析解使用LP方法 显示英文标题

标题： Analytical Solution of Transverse Oscillation in Cyclotron Using LP Method

摘要： 我们已经进行了近似解析解，以精确考虑磁场对回旋加速器中粒子横向振荡的影响。 横向振荡的微分方程是通过林德斯泰特-庞加莱方法求解的。 经过仔细推导，得到了准确的一阶解析解。 这些解析解被应用于来自具有四个螺旋区的等时回旋加速器的磁场，通过与数值方法的比较验证和确认了这些解析解的准确性。 最后，我们讨论了v0=N/2时的横向振荡，使用相同的解析解。 显示英文摘要

摘要： 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.