This paper describes an optimal design method for highly homogeneous superconducting magnet systems with ferromagnetic shield. The presented design technique is a combination of the equivalent magnetization current method for the computation of the magnetic field problem, which includes nonlinear and saturated iron, and the simulated annealing for solving the corresponding optimization problem. The equivalent magnetization current method is superior in estimating the field homogeneity of the center of the magnet systems. By using the simulated annealing, the positions of each solenoid coil are optimized as continuous design variables, while the number of turns and layers of the coil windings are treated as discrete design variables. The details of the algorithm and some examples of its application to 1.5-tesla magnet systems with three types of magnetic shielding are shown.
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