## 2 HTS Magnet Design with Genetic Algorithm  
SuNAM REBCO tapes (4.1 mm width and 0.14 mm thickness) were used to fabricate the 3 T HTS magnet. The superconducting layer of the tape is located between the 20 \(u\)m copper stabilizer and the stainless steel substrate layer as shown in reference [40]. The minimum critical current of the tape is about 200 A @ 77 K self-field. As mentioned in the introduction, MI winding method was applied to the magnet for the quench protection with charging delay reduction [37; 38; 39]. Figure 2 shows the quench-protection mechanism of the MI technique. There are three types of winding methods for a REBCO magnet: (1) insulation winding, as shown in Figure 2a; (2) no-insulation winding, as shown in Figure 2b [41; 42]; and (3) metallic insulation winding, as shown in Figure 2c [37; 38; 39]. For the insulation type of winding, an insulation layer with a material such as Kapton is co-wound with the HTS tape to electrically insulate each HTS tape. Accordingly, the turn-to-turn contact resistance of the magnet is very high and the magnet current does not bypass when a fault occurs. As the normal zone propagation velocity of HTS tape is very slow, the generated heat is accumulated at that hot spot and the magnet is easily damaged. On the other hand, the no-insulation type of winding has very low contact resistance, and the magnet current is very easily bypassed through the turn-to-turn contact when a fault occurs. This technique protects the HTS magnet, but it leads to a charging delay when charging the magnet [38; 43]. The MI is a compromise technique between protection and charging delay of a HTS magnet. Given that the turn-to-turn contact resistance of the MI is not exceedingly high, the charging delay is reduced without sacrificing the self-protection capability. Many studies demonstrate protecting performance by the MI technique [37; 38; 39]. As the target RT bore is approximately 1 inch (25 mm), the inner radius of the RT bore cylinder is 12.5 mm. Considering the thickness of the RT bore thermal shield and multi-layer insulation (MLI) between the RT bore and HTS magnet bobbin for conduction cooling, the required distance between the RT bore cylinder and bobbin is about 12.5 mm. Therefore, the required minimum winding radius is 30 mm. The objective function of the design is the HTS tape total length, and there are six constraints to consider during the optimization process. The design variables and the design constraints are shown in Figure 3 and Table 1, respectively. The variable 1 is the number of the double pancake coil (DPC) related to the stack number of the module coil and the variable 2 is the radial  
Figure 2: Quench-protection mechanism of the (**a**) insulation winding, (**b**) no-insulation winding, and (**c**) metallic-insulation winding. turn number of the each DPC. The variable 3 and 4 are the thickness of a spacer located inside a DPC, which insulates two adjacent pancake coils electrically and the thickness of a wing between two adjacent DPCs, respectively. The last variable is magnet operating current. As the magnetic field and uniformity are influenced by the radial-direction turn (variable 2) and axial-direction turn (variable 1), a magnet designer optimally selects these turn numbers to satisfy the field performance. The variable 3 and 4 are especially related with the field uniformity at the magnet center. By changing these terms, we can get the desired field uniformity of the magnet. The last variable is related with only field strength and should be carefully selected considering critical current margin and generated joule heat at the current leads [6; 8]. The design algorithm based on the Genetic algorithm (GA) finds the optimized design variables which minimize the tape consumption while satisfying the six constraints [35; 36]. Figure 4 represents the main algorithm of the design. An optimization variables set refers to an 'individual', and a 'population' is composed of several tens of individuals.