## 7 Characterisation Simulations
### Simulations and Comparison with Physical Measurements
Figure 21: Simulated energy resolution in terms of FWHM (%) fit with Equation (6) and coefficients \(a=0\), \(b=0.6274\) and \(c=1.3940\times 10^{-2}\). The model is in good agreement with the relationship fit to the measured spectra (grey solid line). Relative statistical errors in the resolution values are under 4%. Figure 20: GMOD simulated \(\sigma\) as a function of energy, fitted with Equation (5) and coefficients \(a=0\), \(b=0.6810\) and \(c=9.6791\times 10^{-3}\). The model is in good agreement with the relationship fit to the measured spectra (grey solid line). Relative statistical errors in the sigma values are under 4%. The effective area as a function of energy of the simulated detector was determined, as seen in Figure 22. As expected, the effective area of the model is slightly higher across all energies, with the average difference between the measured and simulated energies being 0.5 cm\({}^{2}\). This is due to the previously explained difference in photopeak counts of the simulated spectra in comparison to the measured spectra. The second set of simulations performed was to investigate the accuracy of the MEGAlib GMOD model's angular effective area. Source files for the measurements at the 34 angles were run with Cosima. The spectra were processed using Revan and analysed to calculate the effective areas. Table 4 compares the calculated effective areas at polar angle 0\({}^{\circ}\) and polar angle 180\({}^{\circ}\), which correspond to the source being 22.5 cm from the \(+\)Z and \(-\)Z of the spacecraft, respectively. Figures 23 and 24 compare the measured (grey) and simulated (teal) angular response of GMOD FM at 662 keV and 59.4 keV, respectively. The updated FM model produces the expected angular response from GMOD in agreement with the measured results. Across all angles, the simulated effective area is higher due to there being more counts in the simulated photopeaks. There is also a larger difference in values for the 59.4 keV peak due to the physical FM not fully detecting this peak in \({}^{241}\)Am. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Polar Angle** & **Peak Energy (keV)** & **Measured \(A_{eff}\) (cm\({}^{2}\))** & **Simulated \(A_{eff}\) (cm\({}^{2}\))** \\ \hline \multirow{2}{*}{0} & 662 & 1.72 & 1.86 \\  & 59.4 & 5.23 & 5.33 \\ \hline \multirow{2}{*}{180} & 662 & 0.73 & 1.15 \\  & 59.4 & 0.05 & 0.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of effective area for measured and simulated GMOD FM at 662 keV and 59.4 keV at \(+\)Z (polar angle 0\({}^{\circ}\)) and \(-\)Z (polar angle 180\({}^{\circ}\)). Figure 22: GMOD FM simulated effective area as a function of energy, where all the simulated source positions were above the \(+\)Z face of the spacecraft at the CoC. Figure 23: GMOD FM simulated angular response compared with the measured FM response at 662 keV. Errors in measured values are mainly due to systematic uncertainties. Errors for simulated values are purely statistical and under 1%. Figure 24: GMOD FM simulated angular response compared with the measured FM response at 59.4 keV. Errors in measured values are mainly due to systematic uncertainties. Errors for simulated values are purely statistical and under 1%.