Direct algorithm for the rapid calculation of magnetic field spherical harmonics

被引：8

作者：

Snape-Jenkinson, CJ ^{[1
]}

Forbes, LK

Crozier, S

机构：

[1] Univ Queensland, Dept Math, St Lucia, Qld 4072, Australia

[2] Univ Queensland, Ctr Magnet Resonance, St Lucia, Qld 4072, Australia

来源：

IEEE TRANSACTIONS ON MAGNETICS | 1999年 / 35卷 / 05期

关键词：

fast computation algorithm; generalized Biot-Savart law; section of rectangular coil; spherical harmonics;

D O I：

10.1109/20.799063

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

Expressions for the direct calculation of the spherical harmonics of a magnetic field, generated by a circular current-carrying are of rectangular cross section and arbitrary azimuthal length, are described. The final form contains a double integral with fixed range and no special functions. Solutions can be obtained rapidly and accurately by using Gauss-Legendre quadrature for numerical integration, and three-term recurrence relations for the calculation of associated Legendre polynomials. A comparison shows the distinct speed advantage this algorithm holds over an alternative, currently used technique, making the expressions ideal for inclusion in optimization problems, particularly with the explicit calculation of the magnetic field not required.

引用

页码：4159 / 4165

页数：7

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