Conformal Mapping Approach to Dipole Shim Design

TL;DR

This paper presents an analytic method for designing magnetic dipole shims that accounts for magnetic saturation, optimizing shim dimensions to reduce size and cost, validated by finite-element simulations.

Contribution

It extends existing analytic shim design methods by incorporating magnetic saturation effects and derives an abacus curve for optimal shim dimensions.

Findings

Shims can reduce pole width by at least half a gap height for fields below 1.2 T.

The analytic predictions align with finite-element simulation results.

The approach's validity range is discussed and verified.

Abstract

Passive shims are often used to reduce the size and cost of room-temperature magnetic dipoles. In this paper we revisit an analytic approach to the problem of optimum shim design, and we extend it by taking into consideration the effect of magnetic saturation. We derive an abacus curve to determine optimum shim dimensions as a function of the desired dipole nominal field. We show that, for nominal fields below 1.2 T, a pole with such shims can be made at least one half gap height narrower than a pole without. We discuss the range of validity of this approach and verify its predictions using 2 and 3-dimensional finite-element calculations.