有限尺寸矩形截面螺线管轴向分量磁场的理论及模拟计算研究

Studies of the axial magnetic field distribution for a rectangular solenoid with finite dimension

在多层多匝矩形截面螺线管轴向分量磁场解析表达式难以求得的情况下,利用单匝矩形线圈及单层多匝矩形截面螺线管轴向分量磁场的解析表达式,采用切片求和的方法,求得了可用于软件编程的矩形截面螺线管轴向分量磁场分布的表达式,并编写了相应的Matlab计算程序.最终,利用所编写的计算程序,对各类小型加速器中应用较多的束流轨道校正磁铁轴向分量磁场的分布进行了计算,并与三维静态电磁场计算软件CST EM Studio的模拟结果进行了对比,两者符合较好.

For the mutiturn and muhilayer solenoid with finite rectangular dimension, it is very difficult to obtain the analytical formula for the axial magnetic field distribution. Based on the analytical formulae for the single turn rectangular wire and that for the multitun and single layer rectangular solenoid, the sum expression of the axial magnetic field distribution for the the mutiturn and multilayer solenoid is obtained. A Matlab script is written based on the slice and sum method proposed in this paper. Finally, an analysis on the axial magnetic field distribution for a beam orbit corrector most applied at the low energy stage of the accelerators is done. The result calculated by the Matlab script and the numerical simulation result by CST EM studio agree well.