# Optimal Interplanetary Transfer of Solar Wind Ion Focusing Thruster-Based Spacecraft
## 4 Numerical Simulations and Mission Applications  
The previous SWIFT thrust model is now used to evaluate the spacecraft propulsive performance for a given set of design parameters. To that end, we use the main assumptions made in the original work by [PERSON] et al. [34], with a few changes. More precisely, the main differences between the data reported in Table 2 and those indicated in Ref. [34] are the values of \(\{d,\,N_{\rm s}\}\) that were originally chosen as \(\{1\,\mathrm{m},\,1\}\). In addition, recall that in this work the thrust model accounts for the presence of a sort of \"payload\" mass term (which coincides with the term \(m_{b}\) in the current notation), a contingency angle \(\Delta\alpha\), and a maximum thrust angle constraint, which are not considered in the simplified model discussed in Ref. [34].  
The design parameters of the SWIFT-based spacecraft are summarized in Table 2, where the main spacecraft mass \(m_{b}\) is assumed to be \(250\)  kg, while \(\beta\) is a trade-off value between flight-qualified solar panels (i.e., \(10^{-3}\,\mathrm{kg}/\mathrm{W}\)) and cutting-edge photovoltaic (i.e., \(5\times 10^{-2}\)  kg/W) [34; 50]. Using these design parameters, the spacecraft characteristics and its propulsive performance are those detailed in Table 3. In particular, according to Equation (8), the assumed values of \(\delta\) and \(\Delta\alpha\) provide \(\alpha_{\rm max}=90\)  deg, so that the steerable propulsive force \(T\) has a non-negative radial component, as happens in a typical solar sail [16] or E-sail [22] mission scenario. This aspect is highlighted in Figure 9, which shows the SWIFT force bubble used in the numerical simulations at a distance \(r=r_{\oplus}\) from the Sun. Note that, according to Equation (11), the value \(k=1\) gives a steerable thrust magnitude equal to \(D\) and an exhaust velocity of \(400\) km/s. The assumed value of \(v_{\rm ex}\) is well above the current typical range, but it is consistent with the recent development in the area of electric  
Figure 8: Comparison between the optimal control law SWIFT (black line) and an ideal flat solar sail (red line) when \(\delta=60\)  deg and \(\Delta\alpha=0\), that is, \(\alpha_{\rm max}=150\)  deg.  
proulsion systems [51]. Figure 9 shows that in this case the maximum radial acceleration \(a_{r}\) is equal to twice the maximum transverse component \(a_{\theta}\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Units** \\ \hline \(d\) & 10 & m \\ \hline \(m_{b}\) & 250 & kg \\ \hline \(N_{e}\) & 100 & – \\ \hline \(N_{s}\) & 4 & – \\ \hline \(R\) & 3 & km \\ \hline \(r_{w}\) & \(2\times 10^{-5}\) & m \\ \hline \(v_{\rm ex}\) & 400 & km/s \\ \hline \(\beta\) & \(2\times 10^{-3}\) & kg/W \\ \hline \(\delta\) & 120 & deg \\ \hline \(\Delta\alpha\) & 30 & deg \\ \hline \(\phi_{0}\) & 10 & kV \\ \hline \(\rho_{lb}\) & \(4\times 10^{-2}\) & kg/m \\ \hline \end{tabular}
\end{table}
Table 2: SWIFT propulsion system design parameters used in the thrust vector mathematical model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Units** \\ \hline \(a_{D_{\odot}}\) & 0.035 & mm/s\({}^{2}\) \\ \hline \(D_{\odot}\) & 0.0552 & N \\ \hline \(m\) & 1 582 & kg \\ \hline \(p\) & 11.1 & kW \\ \hline \(k\) & 1 & – \\ \hline \(a_{\rm max}\) & 90 & deg \\ \hline \end{tabular}
\end{table}
Table 3: Characteristics and propulsive performance of the SWIFT-based spacecraft used in the numerical simulations.