## 3 Codes and General Modeling  
The salt system is based on density versus temperature curve data from a Russian study [24] (see Table 1). The data are used for the analysis based on a reference temperature of 980 K, with changes of \(\pm 50\) K, for the analysis of feedback effects. The data should be seen as a starting point for initial studies with the limits already discussed in [7]. Based on the coefficients presented in Table 1, the temperature-dependent density is calculated using the following formula:  
\[\rho\Big{[}\frac{\text{g}}{\text{cm}^{3}}\Big{]}=a-bT[\text{K}] \tag{1}\]  
Based on the given salt system investigation [15] and the first investigations on the required dimensions for a zero-power experiment [4], the heavy metal-rich case with 20%NaCl-56.35%UCl4-23.65%UCl3 was used for the following investigations of control and shutdown options. The main part of the simulations for this initial study of zero-power reactor control and shutdown approaches was performed using the KENO-VI, a Monte Carlo solver module of the SCALE code system [25], to analyze the 3D system. \"KENO-VI uses the SCALE Generalized Geometry Package, which provides a quadratic-based geometry system with much greater flexibility in problem modelling but with slower runtimes. Both versions of the KENO perform eigenvalue calculations for neutron transport primarily to calculate multiplication factors (k\({}_{\text{eff}}\)) and flux distributions of fissile systems in both continuous energy (CE) and multi-group (MG) modes. They are typically accessed through the integrated SCALE sequences. KENO's grid geometry capability extends region-based features for accumulating data for source or biasing parameter specifications, as well as for tallying results from a calculation for the visualization or communication of data into or out of a calculation\" [26]. The serial studies on enrichment variation and the analysis of the effect of the removal of the reflector are based on another code of the SCALE package, POLARIS [27], which normally provides a 2D lattice physics analysis capability that uses a multi-group self-shielding method called the embedded self-shielding method (ESSM) and a transport solver based on the method of characteristics (MoC). This code has been compared to different Monte Carlo solvers [28], besides the validation performed by the developer, Oak Ridge National Laboratory. The analysis was extended for creating a deeper understanding of the neutron spectrum by using the multi-group deterministic S\({}_{\text{n}}\) transport calculation sequence TRITION/NEWT. The multi-group KENO-VI analysis is based on the v7-252 cross-section set (based on ENDF/B 7.1) of the SCALE package [25], which is also the basis for the TRITON/NEWT as well as the POLARIS calculations, while the continuous energy version of KENO-IV uses the ce_v7.1_endf library of the SCALE package. For this study, a general 3D KENO-VI model was built (see Figure 2), representing a cylindrical core surrounded by a thin vessel and a reflector on all surfaces, which will be successively modified in dimension and organization for the simulation of the proposed control and shutdown approaches. For completeness, the used POLARIS model is presented in Figure 3, and the used NEWT model for the neutron spectrum analysis in Figure 4 has already been used in the previous study [4]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Concentration** & **\(\boldsymbol{\Delta}\)T (K)** & **a** & **b 103** & **Std Dev 103** \\
**\% NaCl** & & & & \\ \hline
20.0 & 934–1018 & 5.3995 & 1.8646 & 4 \\ \hline
30.0 & 934–1020 & 4.9360 & 1.5276 & 2 \\ \hline
45.0 & 939–1029 & 4.2368 & 1.0256 & 3 \\ \hline
60.0 & 872–1037 & 3.8237 & 0.8774 & 2 \\ \hline
80.0 & 985–1119 & 3.2382 & 0.8012 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Concentration-dependent densities for the system NaCl-UCl3-UCl4 with the uranium salt composition 30% UCl3 + 70% UCl4 and varying NaCl concentrations, part reprinted from [24].