###### Abstract
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**Serial Number** & **Abbreviations and Acronyms** & **Original Text before Abbreviation** \\ \hline
1 & JASTEC & Japan Superconductor Technology, Inc. (Kobe, Japan) \\
2 & JMTA-16T50 MF & Large-gradient high-field superconducting magnet with a central magnetic field of 16 T and a room-temperature bore of 50 mm \\
3 & LH15T40 & Large-gradient high-field superconducting magnet with a central magnetic field of 15 T and a room-temperature bore of 40 mm \\
4 & WM4 & Large-gradient high-field superconducting magnet in the Chinese High Magnetic Field Laboratory (Hefei, China) \\
5 & LG-HMF & Large-gradient high magnetic field \\
6 & S-HGMS & Superconducting high-gradient magnetic separation \\
7 & HG-TFM & High-gradient trapped-field magnet \\ \hline \hline \end{tabular}
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Table 1: The abbreviations and acronyms mentioned in this article. \begin{table}
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**Magnets** & **Room-Temperature** & **Center Field** & **Advantages and Disadvantages** \\  & **Bore Size** & **Strength** & **JMTA-16T50 MF** \\ \hline JMTA-16T50 MF & 50 mm & 16.12 T & The magnetic field gradient value is high and the operation is stable, but it requires a continuous supply of liquid helium and the aperture is small at room temperature. \\ \hline LH15T40 & 40 mm & 15 T & The magnet can generate magnetic field gradients up to 150 T/m and operates normally without current. \\ \hline WM4 & 32 mm & 23.5 T & This magnet can reach extremely high field strengths, and both the gradient value and the field strength value can be adjusted. However, the use space is limited, and it is not highly adaptable to large-sized experimental materials.  
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Table 2: The advantages and disadvantages of various high-field-strength gradient magnets. electromagnetic system of their designed magnetic separator, accompanied by preliminary testing activities. From the above cases, two pieces of information can be found:  
1. The main method of researchers is to directly utilize gradient magnets as experimental tools, while paying limited attention to the design process and stress analysis of the high-gradient magnet itself. 2. Although existing high-gradient magnets can achieve higher gradient values, their room-temperature pore sizes are usually small, which makes them insufficient to meet the changing needs of technological advancement. During the operation of the magnet coil, the electromagnetic stress generated by the Lorentz force will become an inducing factor for the displacement of the superconducting wire in the coil winding. When the electromagnetic stress is too large, it will also cause the magnet to lose its superconductivity. Most importantly, as the center-field strength of the magnet increases, the effect of electromagnetic stress in the magnet windings becomes more severe. Given that these types of gradient magnets typically exhibit a substantial central magnetic field strength and a high magnetic field gradient, the operation of the magnets can result in the generation of significant electromagnetic stress in the superconducting coils and supporting structures [16]. The commonly used methods for calculating electromagnetic stress include the analytical method and the finite element method. For gradient superconducting magnets, due to their complex magnetic field distribution and uneven stress distribution, it is generally difficult to handle these problems using the analytical method. In particular, as the design diameter of the magnet becomes larger, the design difficulty of the magnet gradually increases. For large-diameter high-field-intensity gradient magnets, the stress condition of the mechanical system is severe. Through finite element analysis, one can attain the results that have been shown in the aforementioned literature, as well as understanding the stress distribution state inside the magnet coil; you can also calculate the stress and strain conditions of mechanical systems beyond those of the magnet coil, through multi-field coupling analysis.