Analytical Approach for Optimal HTS Solenoid Design

High temperature superconducting (HTS) coils have been designed for various applications such as magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR), and superconducting magnetic energy storage (SMES). Typically, the coils are in kilojoule range and have solenoid structure. These are mostly optimized with MATLAB and electromagnetic analysis using finite element method (FEM) software. In this article, an HTS solenoid with maximum energy density is designed with MATLAB optimization toolbox. The design objective is mathematically formulated to prove the feasibility of optimal solution of design problem. This article also presents a mathematical formulation to determine the critical current of the solenoid coil. The critical current so obtained was compared with the literature. The HTS solenoid was designed using this formulation. Its critical current and magnetic fields were compared with those obtained with COMSOL model.