# Laser-Accelerated Plasma-Propulsion System
## 8 Conclusions  
The original LAPPS scheme has been revised and expanded starting from the basic principles of closed-cycle engines. A relativistic treatment of the propellant has been used to determine the LAPPS performance limit and the role of the radiation in space propulsion. From a theoretical point of view, we find that optimal results in terms of specific impulse can be obtained well before the achievement of the relativistic limit of the propellant. In fact, it is not convenient to accelerate the particles by consuming a mass (\(E_{R}/c^{2}\)) comparable to the mass of the expelled propellant as the specific impulse is linear in \(v_{r}^{*}\) even in the relativistic limit; this is a general property of all thrusters based on particle acceleration. For the same reason, we find that the radiation contribution to the propulsion is negligible when the equivalent mass-energy used to accelerate the propellant is negligible with respect to the mass of the vaporized target. In these conditions, the massive fraction of the propellant defines the specific impulse.  
The LAPPS has been analyzed in detail by considering a realistic model including the acceleration of ions close to relativistic speed by means of a pure TNSA mechanism, besides an additional amount of particles accelerated to non-relativistic speed during the laser ablation process. The relative weight of these components determines the figures of merit of the LAPSS engine. An analytical description of LAPPS specific impulse and thrust has been obtained as a function of typical laser-plasma interaction parameters. We find that better performances in terms of \(I_{sp}\) are reached for high laser intensities using a thin low atomic number target. For intensities close to \(I_{0}\simeq 10^{21}\) W/cm\({}^{2}\), a specific impulse \(I_{sp}^{LP}\simeq 10^{5}\) s can be achieved, with a negligible dependence on secondary acceleration mechanisms. These results suggest that LAPPS is potentially capable of an impressive specific impulse compared to other advanced electric-propulsion schemes. On the other side, the realization of an ideal thrust-mass ratio of 1 N for each tonne is much more challenging as it roughly requires a laser pulse with an energy of \(\varepsilon_{L}\simeq 10^{3}\) J and a repetition rate of \(\
u_{L}\simeq 1\) kHz for a spacecraft of a total mass of few tonnes, which must include a reactor with a thermal power of \(P_{R}\simeq 20\) MW. Moreover, the increase of the thrust implies a drastic reduction of the specific impulse down to values comparable to other advanced schemes. In short, optimized thrusts are obtained when a large amount of mass is accelerated at low velocities rather than when a few particles are brought close to relativistic speed, i.e., when the ion acceleration due to laser ablation becomes dominant with respect to the TNSA scheme. Nevertheless, unlike other closed-cycle electric propulsion, the thrust can be continuously adjusted by varying the laser intensity (e.g., by tuning the relative position of the target with respect to the focal spot) to produce a local increasing of the thrust only when required and thus preserving the possibility of deep space traveling using an ultra-high specific impulse.  
Realistically, although the TNSA mechanism is widely explored and well-known, the comprehension of secondary accelerating mechanisms is crucial in LAPPS to correctly characterize its performance, especially in the low intensity limit. For these reasons, dedicated experimental measurements are required in order to fix the free parameters of the theory.  
Conceptualization, D.P.; methodology, D.P.; validation, D.P. and G.C.; formal analysis, D.P. and G.C.; writing--original draft preparation, D.P. and G.C.; writing--review and editing, D.P. and G.C.; All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.