Plane elliptic or toroidal multipole expansions for static fields: Applications within the gap of straight and curved accelerator magnets

Purpose - The purpose of this paper is to present new basis functions suitable to parameterize two-dimensional static potentials or (magnetic) fields and to show their application in practical cases. Design/methodology/approach - Regular multipole solutions of the potential equation in plane ellipti...

Full description

Saved in:
Bibliographic Details
Published in:Compel 2009-01, Vol.28 (4), p.1044-1058
Main Authors: Schnizer, P., Schnizer, B., Akishin, P., Fischer, E.
Format: Article
Language:English
Subjects:
Electric fields
Electrical equipment
Electrostatics
Magnetic fields
Mathematical analysis
Studies
Validity
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Purpose - The purpose of this paper is to present new basis functions suitable to parameterize two-dimensional static potentials or (magnetic) fields and to show their application in practical cases. Design/methodology/approach - Regular multipole solutions of the potential equation in plane elliptic coordinates are found by separation. The resulting set of functions is reduced to complete subsets suitable for expanding regular potentials or irrotational source-free fields. Approximate regular plane solutions of the potential equation in local toroidal coordinates are computed by R-separation and power series expansions in the inverse aspect ratio. The harmonic signals induced in a coil rotating in such a toroidal multipole field are computed from the induction law by similar expansions. Findings - The elliptic expansions are useful in a larger area than circular multipole expansions and give better fits. The toroidal expansions permit one to estimate the effect of the curvature of magnets on the field and give better adapted expansions. However, while the scalar multipoles for the potential are orthogonal the vector fields derived for the two-dimensional field are not. Research limitations/implications - Derivations presuppose analytical fields. Practical implications - Field data obtained from numeric field calculations or measurements do not represent exactly analytic fields. Application of the expansion requires care and checks. Originality/value - The paper presents novel approaches for parameterizing longitudinally uniform cylindrical or toroidally uniform potentials and fields. [PUBLICATION ABSTRACT]
ISSN:0332-1649
2054-5606
DOI:10.1108/03321640910959099