## 3 Results
### Identification of the Worst-Case Scenarios  
The relevant worst-case scenarios (WCSs) to be used as input to the TH model must now be identified. In the WCS selection, both EL and EM aspects must be considered. Indeed, a fast current discharge is fundamental to protect, promptly, the magnet from the quench, but at the same time, it deposits a lot of energy in the coil casing, contributing to the coil temperature increase. For this reason, it is relevant to evaluate the \((K,\beta)\) couples which cause the slowest discharge (WCS1) and which lead to the highest energy deposition in the coil casing (WCS2), and to perform their TH analysis. These two extreme scenarios in the ballpark of possible values of K and \(\beta\) provide a preliminary indication of the evolution of possible transients to be refined with the future introduction of statistics in the TH model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(P_{max,3D-FOX}\) & \(P_{max,PCE}\) & \
\begin{tabular}{c} **Relative** \\ **Difference—** \\ \(\varepsilon_{PVE}\) \\ \end{tabular} & \(E_{3D-FOX}\) & \(E_{PCE}\) **[M]** &
\begin{tabular}{c} **Relative** \\ **Difference—** \\ \(\varepsilon_{E}\) \\ \end{tabular} \\ \hline \(\sigma_{1}\) & 0.975 & 0.977 & \(+0.28\%\) & 4.40 & 4.40 & \(-0.03\%\) \\ \(\sigma_{2}\) & 0.628 & 0.625 & \(-0.45\%\) & 3.51 & 3.51 & \(-0.11\%\) \\ \(\sigma_{3}\) & 0.726 & 0.728 & \(+0.31\%\) & 3.82 & 3.82 & \(+0.01\%\) \\ \(\sigma_{4}\) & 1.39 & 1.39 & \(+0.28\%\) & 5.28 & 5.28 & \(+0.02\%\) \\ \(\sigma_{5}\) & 1.30 & 1.30 & \(+0.05\%\) & 5.08 & 5.07 & \(-0.06\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison between the peak power obtained using the 3D-FOX and the PCE metamodel using the UT sigma points (\(\sigma\)) as input parameters.  
Figure 7: Average evolution of the power deposited within the TF coil casing with its 1-99% confidence range evaluated with PCE.  
The two scenarios are clearly distinct, as the slower the discharge, the smaller the energy deposited in the casing (driven by the time derivative of the current). Thus, they will be generated by points standing at the opposite boundaries of the \((K,\beta)\) plane. This statement is confirmed by Figure 8, in which the \(\tau\) and deposited energy values have been mapped, using the PCE model, on the \((K,\beta)\) plane. The specific values of K and \(\beta\) generating the two WCSs are (\(K=8.134\), \(\beta=0.562\)) for WCS1 and (\(K=13.05\), \(\beta=0.595\)) for WCS2.  
Using these values of \(K\) and \(\beta\), the inputs to the TH model have been computed.  
The first required input is the evolution of the coil current, evaluated with the EL model, and it is reported in Figure 9. As expected, the two evolutions are very different, and this will strongly influence the quench evolution.  
The second required input is the power deposited in the casing, including both its evolution and distribution (to account for its non-uniformity). The PCE metamodel has been trained on a set of 3D-FOX simulations, considering the evolution of the overall power deposition, to reduce the computational cost. Therefore, a dedicated run of the 3D-FOX has been performed for each of the two selected WCSs to prepare the detailed input to the 4C code, namely, the spatial discretization of the power deposition in the casing [8]. The total power deposited in one TF coil casing in the two WCSs is reported in Figure 9, confirming that the fastest discharge is actually responsible for the larger energy deposition.