圆形加速器平衡轨道的计算

使用有限差分法,对方程中的非线性部分做泰勒展开,将其中的一次项和二次项都移至方程左端,对一次项直接离散,二次项进行半隐式处理,采用多层网格法外推方案,只需要很小的计算量就可以得到准确的解.将计算结果与龙格-库塔法以及传统的近似解析法做了比较,磁场调变度较小时三种方法符合很好.当磁场调变度变大时,传统的近似解析法由于未考虑非线性效应呈现出较大的误差,本方法具有更高的精度.本方法可用于计算磁场调变度很大的圆形加速器(例如固定磁场交变梯度加速器)的粒子平衡轨道.

Calculation of equilibrium orbit of charged particles in a circular accelerator

The nonlinear part of the equation was expanded into Taylor series by finite diffevence scheme(FDM).Then all the first order terms ware discreted directly,while the second order terms are dealt through a semi-implicit way.Finally the multi-grid extrapolation is used to find the solution.Results are compared with those of the conventional analytic solution and of Runge-Kutta one.Good agreement is found among all the methods when the magnetic field flutter is small.However,for large magnetic flutter,the presented method is more accurate than the conventional analytic solution in which the nonlinear effect is not considered.The method can be used to calculate the equilibrium orbit of particles in those circular accelerators with very large magnetic flutter,say,the fixed field alternating gradient(FFAG) accelerator.