This paper describes an optimal design method for high-field and highly homogeneous superconducting magnet systems with hybrid iron and active shielding. 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 at the center of the magnet systems. By using the simulated annealing, the positions of each coil are optimized as continuous design variables, while the number of turns and layers of the coil windings are treated as discrete design variables. In this paper, the detail of the algorithm and the example of its application to 9-tesla magnet system with hybrid iron and active shield are shown.
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