An Optimal Design Method for High Field and Highly Homogeneous Superconducting Magnets

Abstract

We have been developing optimal design methods for high-field multi-section superconducting magnets for MRI and NMR study using mathematical programing method. To enhance the central magnetic field homogeneity, notch coils are added outside of the main solenoid. In this design, there is difficulty that the distances between notches are continuous design variables while the number of turns and layers of the main solenoids and notch coils are discrete variables. So we tried to develop a method which can deal with such two kinds of design variables at the same time by applying a modified simulated annealing. However, its convergence is relatively slow. Therefore, we adopt the Genetic algorithm, which can obtaine an optimal solution quickly, and combine it with the modified simulated annealing. Furthermore, we developed those method so as to be applied to non-linear optimization problems with constraints, such as characteristics of superconductor (e. g. B-J characteristic), Lorentz force and so on. The details of the algorithm and several examples of its application to three-section superconducting magnets are shown.