# Laser-Accelerated Plasma-Propulsion System
###### Abstract  
In this paper, the laser-accelerated plasma-propulsion system (LAPPS) for a spacecraft is revisited. Starting from the general properties of relativistic propellants, the relations between specific impulse, engine thrust and rocket dynamics have been obtained. The specific impulse is defined in terms of the relativistic velocity of the propellant using the Walter's parameterization, which is a suitable and general formalism for closed-cycle engines. Finally, the laser-driven acceleration of light ions via Target Normal Sheath Acceleration (TNSA) is discussed as a thruster. We find that LAPPS is capable of an impressive specific impulse \(I_{sp}\) in the \(10^{5}\) s range for a laser intensity \(I_{0}\simeq 10^{21}\) W/cm\({}^{2}\). The limit of \(I_{sp}\lesssim 10^{4}\) s, which characterizes most of the other plasma-based space electric propulsion systems, can be obtained with a relatively low laser intensity of \(I_{0}\gtrsim 10^{19}\) W/cm\({}^{2}\). Finally, at fixed laser energy, the engine thrust can be larger by a factor \(10^{2}\) with respect to previous estimates, making the LAPPS potentially capable of thrust-power ratios in the N/MW range.  
laser-plasma accelerator; TNSA; space propulsion; LAPPS; laser-plasma thruster; high specific impulse +
Footnote †: journal: Applied Sciences  
0000-0002-2000-20000-  
development of the LAPPS has been considered until today [17; 18]. Because of the inadequate expected thrust, LAPPS is generally unmentioned in the list of the advanced space propulsion systems, which are potentially developable in the near future [19]. In contrast, in the last 10 years, laser-plasma ion acceleration has been widely explored from both theoretical and experimental points of view [20; 21].  
The aim of this work is therefore to revisit the LAPPS scheme, to explore its potentialities and to obtain more accurate figures of merit of its performance. Relying on laser-plasma acceleration parameters, as given by the Target Normal Sheath Acceleration (TNSA) scheme, as the main mechanism of light ions acceleration scheme [22; 23; 24; 25; 26; 27], we present a general theory able to estimate the LAPPS performance over a large variety of configurations. Remarkably, the results differ by orders of magnitude from previous estimates, potentially making this propulsion system competitive with other mechanisms. Finally, we discuss the possibility of a realistic implementation in a spacecraft by using the current technology.  
The article is organized as follows: in Section 2, we introduce the basic kinematic relations of a rocket-propellant system; a fully covariant formalism of momentum conservation is introduced here for a correct treatment of the relativistic propellant. In Section 3, the covariant formalism is extended to the dynamics of the rocket, deriving the expression of the engine thrust. In Section 4, we discuss the complete energy balance of a closed-cycle rocket engine, including the efficiency of the different processes and the channels of energy dissipation. In Section 5, we discuss the figures of merit and the performance limits of a generic LAPPS engine, relying on the parametrization introduced in Section 4. In Section 6, we present a detailed analytical model of a LAPPS engine, where the propellant includes both TNSA-accelerated high-energy particles and low-velocity massive particles accelerated by other mechanisms. The conditions for obtaining the optimization of thrust and impulse of the engine are discussed, for different laser intensities and experimental setups. In Section 7, we discuss the relevance of radiation contribution in a LAPPS system. Finally, in Section 8, we summarize the main results obtained in previous sections and discuss possible directions of future research for refining the above described LAPPS model. A nomenclature section is also reported at the end of the paper.