## 3 Results
### Design of a 2 mN GIT  
To highlight the potential of the developed tool, it has been exploited in the preliminary design of a miniaturized GIT that could meet the requirements of space missions such as LUMIO [15] and M-ARGO [16], which involve the use of a 12U CubeSat. For these two missions, the thruster should be light (<5 kg), characterized by a power of about 100 W or less, able to produce 2 mN of thrust, operative for 200 and 500 days and with a \(\Delta V\) of 0.2 and 3 km/s, respectively. The performances and the main working parameters obtained from the model are shown in Tables 10 and 11. Samarium cobalt has been selected as the magnets' material, i.e., in the literature there are many examples of ion thrusters that work with samarium cobalt [50], and it was chosen for its magnetic strength. SmCo 27 MGOe was chosen among various types of samarium cobalt magnets for this magnetic property, which allows one to obtain the high value of the magnetic field at the cusp of the surface of the anode, and at low cost. Actually, there are stronger SmCo magnets, but a very strong magnet results in a small dimension of the width of the magnetic rings, and it can be a problem in terms of fragility. Rigorously, a thermal analysis [51] would be advisable to assess whether magnets would reach the maximum operating temperature (300 \({}^{\circ}\)C); nevertheless, the temperatures reached in a ion thruster are, in general, lower [13]. The material chosen for the anode has been Stainless Steel 304, a diamagnetic material particularly resistant to the impact erosion of charged particles. The anode and the magnets' dimensions, obtained from the model, are shown in Table 12. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \begin{tabular}{c} **Patterson’s** \\ **GIT** \\ **Performance** \\ **Targets**[42] \\ \end{tabular} & \begin{tabular}{c} **Error** \\ **Error** \\ **(42)** \\ \end{tabular} & \begin{tabular}{c} **Patterson’s** \\ **GIT Performance** \\ \end{tabular} & \
\begin{tabular}{c} **Error** \\ **(49)** \\ \end{tabular} &
\begin{tabular}{c} **Model** \\ **Error** \\ \end{tabular} \\ \hline \(T\) (mN) & 4 & 5.0\% & 3.6 & 5.5\% & 3.8 \\ \(P_{m}\) (kW) & 0.100 & 0.0\% & 0.100 & 0.0\% & 0.100 \\ \(l_{sp}\) (s) & 2000 & 7.2\% & 1760 & 5.5\% & 1857 \\ \(\eta_{T}\) & 0.38 & 7.8\% & 0.31 & 12.9\% & 0.35 \\ \(\eta_{e}\) & 0.70 & 1.4\% & 0.65 & 6.1\% & 0.69 \\ \(\eta_{m}\) & 0.60 & 6.6\% & 0.53 & 5.6\% & 0.56 \\ \(V_{d}\) (V) & 28 & 0.0\% & 26 & 7.6\% & 28 \\ \(l_{d}\) (A) & 1.05 & 4.7\% & 1.13 & 2.6\% & 1.10 \\ \(\eta_{d}\) (W/A) & 333 & 7.2\% & 360 & 0.8\% & 357 \\ \(V_{b}\) (V) & 800 & 0.1\% & 800 & 0.1\% & 801 \\ \(l_{b}\) (mA) & 88.2 & 2.3\% & 80.9 & 6.4\% & 86.1 \\ \(V_{T}\) (V) & 1000 & 0.1\% & 1000 & 0.1\% & 1001 \\ \(|V_{accl}|\) (V) & 200 & 0.0\% & 200 & 0.0\% & 200 \\ \(\eta_{p}\) (mg/s) & 0.21 & 0.0\% & 0.21 & 0.0\% & 0.21 \\ \(|B_{casp}|\) (G) & Not available & / & Not available & / & 1776 \\ \(|B_{l}|\) (G) & Not available & / & Not available & / & 29 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison between the characteristics and the targeted and real performances of Patterson Ion thruster [42; 49], and the results of the developed model, which has as input parameters 4 mN of thrust and 8 cm as discharge chamber diameter. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \begin{tabular}{c} **NSTAR** \\ **(Throttle** \\ **Level 15**[23] \\ \end{tabular} & \begin{tabular}{c} **Developed** \\ **Tool** \\ \end{tabular} & \begin{tabular}{c} **Error** \\ **Error** \\ \end{tabular} & \
\begin{tabular}{c} **Design Tool** \\ **in Ref.**[26] \\ \end{tabular} &
\begin{tabular}{c} **Error** \\ **Error** \\ \end{tabular} \\ \hline \(P_{t}n\) (kW) & 2.3 & 2.3 & 0.0\% & 2.3 & 0.0\% \\ \(T\) (mN) & 92.4 & 91.5 & 1.0\% & 96.0 & 3.9\% \\ \(\eta_{md}\) & 0.90 & 0.90 & 0.0\% & 0.92 & 2.2\% \\ \(l_{b}\) (mA) & 1.76 & 1.78 & 1.1\% & 1.76 & 0.0\% \\ \(\dot{m}_{pd}\) (mg/s) & 2.66 & 2.69 & 1.1\% & 2.62 & 1.5\% \\ \hline \hline \end{tabular}
\end{table}