Conformal Mapping Approach to Dipole Shim Design

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.