  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.
