Direct algorithm for the rapid calculation of magnetic field spherical harmonics

Author

Snape-Jenkinson, Christopher J. ; Forbes, Larry K. ; Crozier, Stuart

Author_Institution

Dept. of Math., Queensland Univ., St. Lucia, Qld., Australia

Volume

35

Issue

5

fYear

1999

fDate

9/1/1999 12:00:00 AM

Firstpage

4159

Lastpage

4165

Abstract

Expressions for the direct calculation of the spherical harmonics of a magnetic field, generated by a circular current-carrying arc 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

Keywords

Legendre polynomials; harmonics; magnetic fields; superconducting coils; superconducting magnets; Gauss-Legendre quadrature; Legendre polynomials; azimuthal length; circular current-carrying arc; double integral; magnetic field; optimization problems; rectangular cross section; spherical harmonics; three-term recurrence relations; Australia; Conductors; Fusion power generation; Gaussian processes; Magnetic fields; Magnetic resonance; Polynomials; Solenoids; Superconducting coils; Superconducting magnets;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/20.799063

Filename

799063