Note: Parametric tuning of the Helmholtz coil and its optimal designs with thick winding pairs

Thick winding pairs are generally utilized in high-power Helmholtz coil systems, where the coil-heating and insulation are usually of concern for their field uniformity. Beyond the ideal thin model, we discuss the field uniformity of thick Helmholtz coils and their optimal designs based on the numerical and experimental analysis. Furthermore, the design tuning parameters, i.e., ampere-turn configurations, are introduced to the numerical models to investigate their influence on the magnets’ field uniformity. The results show that different ampere-turn realizations of one ideal Helmholtz coil could induce up to ∼30% uniformity variation within the central region. Regardless of whether it is the conventional Helmholtz coil or its optimal designs, the increase in layer number and axial insulation gaps tends to improve the field uniformity. However, the increase in turns per layer results in a great reduction in their field uniformity. By optimizing the ampere-turn arrangement, it is possible to further improve the performance of a Helmholtz-coil-based magnet.