## 4 Implementation of Spacecraft Using Interplanetary Medium  
Proceeding from the provided data regarding the distribution of the interplanetary medium in the near-Earth region, it becomes apparent that the direct utilization of the interplanetary medium as fuel for future plasma engines is impossible. So, we ought to apply some technical means of providing the required characteristics of a spacecraft thruster. For example, we should provide the required density of neutral gas \(n_{0}\) in the discharge chamber (say, \(n_{0}=10^{10}\) cm\({}^{-3}\); this value will be used in the subsequent estimations). To enhance the efficiency of capturing the interplanetary medium for the designed plasma engine out, a conical trap can be utilized. This trap is placed on a moving spacecraft in the direction of its motion (see Figure 1), allowing for an increased density of neutral particles in the narrow section of the trap compared to the area of the inlet trap. For example, assuming the inlet diameter of the conical trap is \(=200\) m and the effective inlet diameter of the discharge chamber is \(d=20\) cm, we can then achieve a density increase of \(\Gamma=D^{2}/d^{2}=10^{6}\) times solely through the geometric properties of the trap. In this case, we assume that the entire process of capturing the interplanetary medium occurs in a free molecular mode as long as the medium remains collisionless even in the narrow region of the trap. In other words, the mean free path, calculated from the density in the outlet chamber area, should be at least comparable to the characteristic size of the device (e.g., the diameter \(d\)). An estimation for the mean free path can be obtained using the following formula:  
\[\lambda(n_{0})=1/\left(\sigma_{g}n_{0}\right),\]  
Considering the gas kinetic cross-section, \(\sigma_{g}=10^{-16}\) cm\({}^{2}\), we find that for the chosen value of \(n_{0}\), the mean free path \(\lambda(n_{0})\sim d\) is approximately equal to the chosen characteristic dimension of the discharge chamber, \(d\). Hence, the collisionless regime may be maintained with the chosen geometric parameters of the discharge chamber. Furthermore, the effective operation of this method requires a relatively high spacecraft velocity. This is because the accumulation time of particles in the discharge chamber is proportional to its volume, \(V\), and inversely proportional to the spacecraft's speed. To illustrate these points, let us consider a specific example of a real discharge chamber that could be utilized in the given context. Similar to the concept of a space scavenger [9; 31], we can take a cylindrical discharge chamber with a volume of \(V=10^{5}\) cm\({}^{3}\), operating at low pressure. Typically, radio frequency fields can produce such discharges in different gas media at pressures of around \(p\geq 10^{-1}\) Pa [32; 33; 34]. This corresponds to particle densities inside the discharge chamber of \(n_{0}\geq~{}10^{10}-10^{11}\). Then, based on the continuity condition of the flow, we conclude that the flow of particles incident on the concentrator shall fill the selected volume \(V\) in time \(\tau_{n}\) up to a number of particles \(N=n_{0}V\):  
\[\tau_{n}=\frac{4N}{\pi D^{2}v\pi\tau_{\Sigma}}=\frac{n_{0}}{n\tau_{\Sigma}} \frac{d^{2}}{D^{2}}\frac{L_{c}}{v}, \tag{24}\]  
where \(L_{c}\) is the length of the discharge chamber and \(L_{c}=3\) m. At this stage, we want to emphasize once again that the speed of particles entering the trap relative to the ship coincides with the instantaneous speed of the spacecraft since only immobile interplanetary dust was chosen as fuel. Figure 4 shows the characteristic particle accumulation times for these values as a function of the spacecraft's speed for different values of the geometric parameter \(\Gamma\), which provides an indication of the time scale of the process. As seen from Figure 4, with allowance for the time scale of plasma production and thrust, one may pay no regard to the time of capturing matter from space for \(\Gamma\leq 10^{-6}\) and \(\beta\geq 10^{-3}\).