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.

中文翻译：

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优化 HTS 电磁阀设计的分析方法

高温超导 (HTS) 线圈设计用于各种应用，例如磁共振成像 (MRI)、核磁共振 (NMR) 和超导磁能存储 (SMES)。通常，线圈在千焦耳范围内并具有螺线管结构。这些大多使用 MATLAB 和使用有限元法 (FEM) 软件的电磁分析进行优化。在本文中，使用 MATLAB 优化工具箱设计了具有最大能量密度的 HTS 螺线管。设计目标通过数学公式来证明设计问题最优解的可行性。本文还提出了确定电磁线圈临界电流的数学公式。将如此获得的临界电流与文献进行比较。HTS 螺线管就是使用这种配方设计的。