谐波垫补原理及其在加速器常规磁铁设计与磁场垫补中的应用

加速器常规磁铁磁场质量评估通常表示为工作气隙好场区内高阶磁场占主磁场的相对含量，它通常要求在10^-4量级内。这些高阶磁场来源于磁极的有限长度与宽度和极面设计参数选择产生的若干过大的系统高阶磁场偏差及加工与材料的不理想等因素产生的若干过大的随机高阶磁场偏差。这些偏差均会导致磁场质量变坏。谐波垫补法针对每个过大的高阶磁场利用磁极形位改变对磁场的扰动效应产生一与现存过大高阶磁场大小相当但符号相反的高阶磁场，用来抵消现存的过大的高阶磁场，达到根本改善磁场质量的目的。本文分析了谐波垫补原理，并具体分析了它们在二极磁铁和四极磁铁设计与磁场垫补中的应用。

Principle of Harmonic Shim and Application for Conventional Accelerator Magnets

The harmonic field errors are an evaluation criterion for field quality of accelerator magnets. The limited magnetic pole width and length of conventional magnets will lead to systemic multipole errors. Also the tolerances of machining and material will bring on random multipole errors. Those multipole errors cause the field quality to be bad. The harmonic shims can counteract each multipole error through the change of pole profile, and it improves the field quality radically. The principle of the harmonic shims was analysed and its applications for dipole and quadrupole magnet were discussed in detail.