## 4 Modelling & Simulation Results
### Sensitivity of the Control System  
The first test for the sensitivity of the control system is based on the compensation of the thermal feedback when the core temperature will be changed by \(\pm 50\)\({}^{\circ}\)C. The three reflector positions for the investigated reference case as well as for the reduced and increased temperature cases are shown in Figure 16, with the detailed numbers presented in Table 2. When the temperature of the core is increased from the reference temperature by 50 \({}^{\circ}\)C, the reflector has to be moved upwards to compensate for the reduced density of the fuel as well as for the increased absorption through the Doppler effect. The reflector has to be moved 24 cm upwards for the compensation of the increased temperature, which means that, based on an initial guess, a temperature change of 2 \({}^{\circ}\)C will be compensated by a movement of 1 cm within the calculation accuracy of the criticality iteration (\(\pm 30\) ppm) and the accuracy of the Monte Carlo method (\(\pm 33\) ppm at a confidence of 95%). This seems to be a reasonable position change, which can be easily controlled through a modern movement system (comparable to a control rod drive in an LWR), as detected by modern measurement technologies for the determination of the reflector position. However, it has to be kept in mind that the weight of the reflector will be significantly higher than for a control rod group moved by one drive.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Reflector Position (cm)** & **Multiplication Factor** & **Std Dev** \\ \hline ref & \(-29\) & \(1.0003\) & \(0.0001\) \\ \hline +50 K & \(-5\) & \(1.00001\) & \(0.00011\) \\ \hline \(-50\) K & \(-43.6\) & \(1.00017\) & \(0.0001\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Exact criticality data and reflector position for the reference system and a postulated temperature change of \(\pm 50\) K.  
Figure 16: Study of the reflector position required to compensate for the system temperature change.  
The compensation of the cooldown of the core works in a similar manner. When the fuel temperature is reduced, the density of the salt will increase, and the absorption in the fuel will decrease, both leading to a higher criticality of the reactor. To compensate this criticality change, the reflector must be moved downwards by ~14 cm. The required movement is less strong than for the heat-up since the efficiency of the control system is higher at a position closer to the center of the core (see discussion of the control reactivity curve in Figure 11). Thus, in this case, a temperature change of 2 \({}^{\circ}\)C will be compensated by a movement of the reflector by of ~0.6 cm or 6 mm, which is still a value that is reliably detectable. In addition, it should not be forgotten that the temperature in this system is strongly negative, and that the reactor will self-stabilize due to the feedback effect. However, the results shown are for a system with molten salt at a temperature level of ~700 \({}^{\circ}\)C. A real reactor physics experiment would most probably be operated at room temperature with a solid core in the first instance to reduce the regulatory challenge by applying a stepwise approach. In this temperature range, the feedback effects in the solid salt eutectic block will be substantially different. Thus, a study based on the effectiveness of the proposed control system at room temperature should be performed as soon as reliable data on the thermal expansion coefficient of the proposed fuel salt in the room temperature range are available.