Accurate calculation of field expansion coefficients in FEM magnetostatic simulations

TL;DR

This paper introduces a new method for calculating field expansion coefficients in FEM magnetostatic simulations that improves accuracy, especially with coarse meshes, by utilizing magnetization data instead of local solutions.

Contribution

It presents a novel approach and closed-form formulas for more accurate calculation of field expansion coefficients using magnetization data in FEM simulations.

Findings

Accurate coefficients achievable with coarse meshes

Method reduces dependence on mesh refinement

Implemented as an ANSYS add-on

Abstract

FEM simulations are a standard step in the design of accelerator magnets. It is custom for accelerator applications to characterize the field quality in terms of field expansion coefficients. With a commonly accepted approach, expansion coefficients are calculated by means of a Fourier transform of the local FEM solution at points on an arc. The accuracy of the coefficients calculated this way depends strongly on the FEM mesh configuration and simple refinement of the mesh does not always improve accuracy. The accuracy of the expansion coefficients calculation can be improved by using the data on the magnetization of elements in the magnet yoke, obtained in the solution, instead of using directly the local solution. Since currents and the yoke magnetization are the only sources of the field, with these data the field expansion coefficients can be calculated at any remote point. We derive closed forms for calculating expansion coefficients and implemented these results in the ANSYS add-on. Results for a case study are presented, which demonstrate that expansion coefficients can be calculated with good accuracy even for a rather coarse mesh.