High-Accuracy, Two-Dimensional Magnetic Field Multipole Calculations for Accelerator Magnets

Abstract

High precision magnetic field computer programs are required to accurately calculate the multipole content and magnetic field strength associated with a given accelerator magnet design. In this work, a specialized version of the finite element computer program WEMAP (Westinghouse Electric and Magnetic Analysis Program) is applied to field harmonic calculations. The computer program relies on a higher-order finite element formulation and high-precision computer representation to minimize calculation error. Several calculations are made for a SSC CDM cross section design. The effects of mesh fineness and finite element order are investigated by examining finite element grids with increasing mesh density and element order. A key feature of this computer program is the capability to minimize the truncation error associated with a finite element mesh by increasing the order of the finite element interpolating polynomial. Finite elements of order one through six are incorporated. Inaccuracies which may occur using the lower-order finite elements with a coarse mesh are identified in this paper. Care must be taken in meshing the yoke iron region to accurately account for field harmonics due to nonuniform iron permeability. Methods of extracting the spatial harmonics from the finite element solution are discussed. The field strength and harmonics are calculated for a full-section model of a CDM magnet cross section.