A hybrid optimal analysis for the design of passive shimming elements in high homogeneous permanent magnets

Passive shimming is cheaper, simpler and more effective than active shimming. However it is very tedious to realize passive shimming because the position determination of shimming elements is concerned with the experience of the designer. This paper presents a useful and simple method to design the passive shimming system for homogeneous permanent magnets. An optimal model is set up to determine the location and size of the ferromagnetic shimming elements. To obtain a global solution of the optimization problem with less computational effort, a hybrid optimal algorithm is presented. First, the improved genetic algorithm is used as the initial optimal tool. Then the optimal shim's size is computed by steepest descent algorithm combined with design sensitivity analysis starting from the proper initial solution. Finally, the shim's position is chosen as the design variables to obtain the global optimal solution. A numerical implementation shows the proposed method can design the shimming system intelligently and effectively.