Hole and dot sensitivity analysis and level set-based topology optimization of superconducting systems operating under critical current density

A topology optimization method based on sensitivity analysis is proposed for designing superconducting systems operating under critical current densities. The topology changes in the structure of the superconducting materials are achieved by creating air holes in the superconducting material and superconducting dots in the vacant space. The positions of the air holes and superconducting dots are determined via hole and dot sensitivity analyses. The hole and dot sensitivity expressions are derived based on the continuum sensitivity of the superconducting system. The proposed design optimization method can not only achieve fast convergence based on the sensitivity-based approach, but also alter the topology through the introduction of holes and dots and obtain a high-quality optimal solution. The level set method is used to express the topology and shape changes of the superconductors. The topology changes due to the air holes and superconducting dots are represented by adding a zero-level set to the newly formed material interface. The proposed method is validated through numerical examples involving the design of superconducting magnets. The results demonstrate that the hole and dot sensitivity analysis accurately predicts the optimal locations for air holes and superconducting dots to improve the system performance. Additionally, the design examples show that the holes and dots created near material boundaries accelerate shape optimization while minimizing the risk of the divergence.