非平面对称磁场的空间展开及样条函数表述

为了研究带电粒子光学系统的光学特性,需要知道系统中磁场的空间分布。实际磁场往往不具有严格的平面对称性质,一些作者曾就这类磁场的空间展开做过不少工作。但他们的工作是在柱坐标系统中进行的,适用于诸如回旋加速器、双向聚焦磁分析器、环形磁β谱仪等一类装置的磁场分析。对于大型同位素电磁分离器(calutron)那样一类装置,其磁场分布需要

SPACE EXPANSION AND SPLINE REPRESENTATION OF MAGNETIC FIELD WITHOUT SYMMETRIC PLANE

The space expansion for each component of the magnetic field without symmetric plane is derived in Cartesian coordianate system, which is in Taylor series of z. The coefficients of the expansions are expressed with the three components of the field and their partial derivatives with respect to x and y in a given plane z = z_0. The bicubic spline function fit of the discrete field distributions in the given plane is discussed, and the space expansions of the field represented with spline functions are further developed.