## 3 Results
### Results of the Thermal-Hydraulic Model  
The inputs have been adopted to simulate an FD triggered by the magnet quench. In the simulation, the quench has been obtained via a local heat deposition at the location where the minimum temperature margin is computed in nominal operation, i.e., in the  
Figure 8: Map of (**a**) \(\tau\) and (**b**) energy deposited in the coil casing in the \(K,\beta\) plane. Figure 9: Evolution of (**a**) current and (**b**) total power deposited in the coil casing during the two WCSs. first turn of the two central pancakes at the inboard equator. In this work, \(50\,\mathrm{kW/m}\) of external power (e.g., a very concentrated beam of particles coming from the plasma) have been deposited in 10 cm of SC cable around the minimum margin location of pancake 6 for 0.1 s. The power deposition erodes the temperature margin, leading the magnet to quench initiation and propagation. The FD is triggered by the quench detection system when the voltage computed across the coil overcomes the 100 mV threshold, waiting, then, for a validation time of 1.5 s [28] to reduce the spurious detections. The evolution of the voltage computed with the 4C code in the two WCSs is reported in Figure 10. The WCS2, characterized by a faster discharge, leads to a faster response to quench protection, reducing the quench propagation (and therefore the voltage buildup) in the Winding Pack (WP). Due to the inter-pancake thermal coupling, the neighboring pancakes (namely, 5 and 7) are also heated up, possibly quenching. However, the voltage raise in pancakes 5 and 7 is almost negligible in WCS2 due to the faster reduction of the current; on the contrary, in WCS1, the delayed current decrease also causes a quench initiation and propagation in those pancakes. Quench initiation in pancake 7 is slightly delayed with respect to pancake 5 due to the smaller magnetic field there, with it being further away from the coil center. The two scenarios also differ in terms of the hot-spot (HS) temperature, that may lead to permanent damages to the coil. Indeed, as shown in Figure 11, where the HS temperature reached during the transient is plotted for each pancake, the hot spot temperature is larger, in the central pancakes, in the WCS1, featuring a larger Joule power deposition. The opposite trend is observed in side pancakes (e.g., pancake 1) in which the quench is not initiated and the heating is due to thermal contact with the casing, where the eddy current power is deposited. Given that the power deposition in the casing is larger in WCS2 (see Figure 9b), the power transferred from the casing to the WP is also larger; thus, the conductor temperature increases more. From the bar plot in Figure 11, it is also possible to appreciate the effect of the inter-pancake heat diffusion, visible in the progressive temperature decrease moving far away from the quenched (central) pancakes. The importance of reducing the current in the fastest possible way is clear when comparing the hot spot temperature in the two scenarios. Indeed, the HS temperature is much larger in WCS1 due to the faster current decrease in WCS2. On the contrary, the temperature increase in the side pancakes, given by the eddy current power deposition in the casing, is similar in the two cases, despite the consistent difference in the casing power deposition between them, as can be seen from Figure 9b. Actually, the timescale of the heat transfer from the casing to the WP is quite slow if compared to the current discharge duration, also in the slower WCS1. Figure 10: Voltage evolution computed in pancakes 5, 6, and 7 in both WCS1 and WCS2. The current evolution for WCS1 (solid) and WCS2 (dashed) is also plotted, to be read on the right axis. These results show that the uncertainty in the characteristic parameters of the varistors leads, eventually, to a wide range of quench evolutions. Increasing as much as possible the precision on the varistor parameters during their manufacturing is fundamental to attaining reliable predictions and therefore a safe reactor operation.