## 2 High-Field-Gradient Magnet Structures
### Magnet Electromagnetic Field Simulation and Analysis  
In this article, the finite element analysis software COMSOL Multiphysics 6.1 is employed for the simulation and analysis of the magnet's electromagnetic scheme. During the simulation process, the following settings need to be made to the model. Model selection: This study selected a two-dimensional axisymmetric electromagnetic model, which was created from the solidworks 2021 version and imported into COMSOL; COMSOL was used to simplify the model. For the boundaries of the simulation domain, this study uses the infinite element function to add additional boundaries to the air domain. This processing can increase the speed of calculation and obtain more accurate results. Grid processing: In order to simplify the calculation amount and improve the convergence speed, quadrilateral meshes are used for rectangular-shaped superconducting coils, and triangular meshes are used for irregularly shaped domains to ensure the continuity and continuity of the grids between each domain's coupling. In particular, the grid in the air domain of this study is densified along the central axis, and the number of densification intervals is set to 500 to obtain an accurate simulation curve. At an operating current of approximately 176.5 A, the magnet's total energy storage is theoretically estimated to be around 1623.457 kJ, with an inductance value close to 104.23 H. The central (O\({}_{1}\)) and peak magnetic fields of the magnet are 10.78 T and 13.04 T. Figure 4a illustrates the standard magnetic field concerning the radial coordinates of the magnet (z = 0), while Figure 4b illustrates the standard magnetic field concerning the axial coordinates of the magnet (r = 0). From Figure 4a, the radial standard magnetic field distribution can be obtained. When the magnetic induction line passes through the coil, the magnetic field will undergo a sudden change, and the corresponding point of change has been marked in the figure. At the same time, the cloud map in the lower left corner shows the distribution status of the magnetic field on the cross-section of the coil. From Figure 4b, the standard axial magnetic field distribution can be obtained. It can be seen that the magnetic field strength of the central axis of the magnet reaches a peak of 10.8 T in the middle of the three coils below. At the same time, the cloud map in the lower left corner shows the distribution of the magnetic field on the cross-section of the coils. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameters** & **HF Nb\({}_{3}\)Sn** & **ITER Nb\({}_{3}\)Sn** & **ITER PF NbTi** \\ \hline Dwire-insulated/mm & 0.98 & 0.97 & 0.777 \\ Dwire-bare/mm & 0.85 & 0.818 & 0.727 \\ Cu/non-Cu & 0.46 & 1.0 & 2.3 \\ RRR & \textgreater{}100 & \textgreater{}100 & \textgreater{}100 \\ [EMAIL_ADDRESS] K/A & \textgreater{}622 @12T & \textgreater{}240 @12T & \textgreater{}190 @7T \\ \hline \end{tabular}
\end{table} 
Table 5: Parameters of wires. Based on the simulation results, load lines for the sub-coils can be plotted under the variation of the critical current with the magnetic field for the given superconducting short wire samples. The current utilization efficiency for coil 1 (defined as the ratio of the operating current to the critical current from the load line) is estimated to be 78.59%, for coil 2 it is estimated to be 76.79%, for coil 3 it is estimated to be 85.58%, and for coil 4 it is estimated to be 80.88%. These results are presented in Figure 5a. It can be seen from the figure that the current margin of the magnet coil is within an appropriate range and the risk of magnet quench is low. The gradient value constitutes a critical design parameter for gradient magnets. To generate any horizontal simulated gravity field within the range of 0-2 g during the operation of superconducting magnets, the design requirements specify that the absolute value of the maximum gradient on the central axis of the magnet must exceed 400 T\({}^{2}\)/m. Figure 5b illustrates the gradient distribution along the center axis.