# Digitalization of the Ex-Core Neutron Flux Monitoring System for APR1400 Nuclear Power Plant
## 3 Simulation  
### Modelling of the Neutron Flux Detector Current  
A simplified model of a fission chamber is designed to describe the relationship between the reactor power and the current output from the fission chamber. The characteristics of the fission chamber and preamplifier is given in Table 1 while the relationship between reactor power and neutron flux is listed in Table 2. The electric charge collected by the electrodes, \(q(t)\), and the resulting current pulse, \(i_{Q}(t)\), are expressed as [19]:  
\[q(t)=\sum_{i}Q_{Ti}\bigg{(}1-e^{-\frac{t-t_{i}}{t_{n}/2.197}}\bigg{)},\quad i =0,1,2,3,\ldots \tag{38}\]  
\[i(t)=\frac{d}{dt}q(t)=\sum_{i}I_{Qi}e^{-\frac{t-t_{i}}{t_{n}/2.197}} \tag{39}\]  
where \(Q_{Ti}\) is the maximum amplitude of the electric charge generated by the \(i\)-th interaction, \(t_{i}\) is the time when the \(i\)-th interaction occurs, and \(t_{ri}\) is the rise time of the electric charge generated by the \(i\)-th interaction. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Description** \\ \hline DC Neutron Current Sensitivity & \(1.7\times 10^{-13}\) Amp./nv nominal \\ Neutron Counting Sensitivity & 0.65 cps/nv nominal \\ AC Current Sensitivity & \(>\)1.7 \(\times 10^{-13}\) V\({}^{2}\)/nv \\ Operating Thermal Neutron Flux & \(4\times 10^{9}\) nv. Maximum \\ Operating Gamma Flux & \(1\times 10^{3}\) Gy/hr. maximum \\ Alpha Background & \(5.5\times 10^{-9}\) Amp. \\ Gamma Sensitivity & \(<\)1 \(\times 10^{-8}\) Amp./Gy/hr. \\ Output Charge Pulse & \(>\)0.03 pC \\ Electron Collection Time & \(300\pm 100\) nsec. \\ Detector \& Cable Capacitance & 1786–2295 pF. nominal \\ Detector Cable Resistance & 72 Ohm \\ Neutron Sensitivity Material and quantity & Enriched \(U_{3}O_{8}\) (\(>\)90\(\%\)) in \(U^{235}\), 0.5 mg/cm\({}^{2}\) \\ Saturated Output Voltage of Preamplifier & 10 Vp-p \\ Rise Time of Preamplifier & \(<\)100 nsec. \\ Clipping Time Constant of Preamplifier & \(225\pm 25\) nsec. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data of the selected fission chamber and the preamplifier [20]. MATLAB Simulink was used to design a model for realizing Equations (38) and (39). \(I_{Qi}\) is assumed as a pulse with random maximum amplitude, mean of \(0.9524\times 10^{-6}\) [A] and variance of \(0.0286\times 10^{-12}\) [A\({}^{2}\)]. \(t_{i}\) is also random with a mean of \(i\) multiplied by \(T\), which is the nominal period of pulse at a certain interaction rate, and with variance. Simulated current signals at interaction rates of \(5\times 10^{5}\), \(5\times 10^{6}\), and \(5\times 10^{7}\) [events/sec.] between incident neutrons and the gas in the detector is shown in Figure 4. The detector signal does not show pulse overlaps at \(5\times 10^{5}\) while the pulse signal processing can produce reliable information on the neutron interaction rate. So much pulse pile-ups occur between successive neutron interactions at \(5\times 10^{6}\) that the pulse signal processing loses count and leads to misreading of the interaction rate. In the case of \(5\times 10^{7}\), the fluctuation signal is produced by the overlapping of individual pulses, hence, MSV signal processing is required. The pulse height distribution with pulse pile-ups is shifted to the right of those without the pile-ups in Figure 5a. Figure 5b shows that the pile-up of multiple gamma ray events may be erroneously counted as a neutron interaction event, and that the pile-up between neutron and gamma ray interaction events increases the amplitude of the pulse signal relative to those of single events. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reactor Power [\%]** & **Neutron Flux [nv]** & **Mode of Operation** \\ \hline \(2.00\times 10^{-1}\) to 200 & \(2.60\times 10^{6}\) to \(2.60\times 10^{9}\) & Current Mode \& MSV Mode \\ \(2.00\times 10^{-2}\) & \(2.60\times 10^{5}\) & MSV Mode \& Pulse Mode \\ \(2.00\times 10^{-8}\) to \(2.00\times 10^{-3}\) & \(2.60\times 10^{-1}\) to \(2.60\times 10^{4}\) & Pulse Mode \\ \hline \hline \end{tabular}
\end{table}