# In-Target Proton-Boron Nuclear Fusion Using a PW-Class Laser
## 4 Discussion and Conclusions  
The results presented in this work provide the first proof of principle experimental demonstration of efficient \(\alpha\)-particle generation from p-B fusion using a PW-class laser and the \"in-target\" geometry. The measured \(\alpha\)-particle flux was \(\sim\)10\({}^{10}\)/sr, thus one order of magnitude higher than previous results that were obtained with the same laser parameters but in the \"pitcher-catcher\" geometry [5,6]. This achievement is in line with the experimental progress in p-B fusion that has been reported in the last 15 years (see Figure 1) and confirms the advantage of triggering p-B fusion reactions using a direct irradiation scheme, at least in terms of \(\alpha\)-particle flux [2, 3, 4]. A crude estimate of the total \(\alpha\)-particle generation could be provided under the assumption of quasi-isotropic emission, which was based on the fact that the kinetic energy of the accelerated protons was relatively low (unlike the pitcher-catcher geometry that was reported in our previous p-B fusion experiment at LFEX [6]), hence there was no substantial momentum transfer from the protons to the \(\alpha\)-particles. Therefore, under such a rough assumption, the total number of \(\alpha\)-particles (including those particles absorbed inside the thick BN target) was \(\sim\)1.4 \(\times\) 10\({}^{11}\). However, despite the high \(\alpha\)-particle flux that was experimentally measured, we noted that the overall conversion efficiency of the process (laser to \(\alpha\)-particle energy) was still low (\(\sim\)0.005%). It is worth noting that the \(\alpha\)-particle flux that was measured experimentally was a clear underestimation of the number of \(\alpha\)-particles that were emitted backward due to the limited energy range (5-10 MeV) that was detectable by the diagnostics that were used. In fact, the numerically predicted \(\alpha\)-particle energy range was much broader (1-14 MeV). Thus, considering the diagnostic limitations, we could expect a produced \(\alpha\)-particle flux and conversion efficiency in line with the previous results that were reported in [4] with a kJ (TW-class) laser and in-target geometry (see Figure 1). Nevertheless, the start-to-end numerical simulation study that was performed (hydrodynamic, PIC, and Monte Carlo) allowed the qualitative support of the basic mechanism of multi-MeV proton acceleration at the target's front side and the subsequent generation of \(\alpha\)-particles via p-B fusion that occurred inside the BN target. These results are propaedeutic for the preparation of future experiments with PW-class lasers with the aim of generating high-flux \(\alpha\)-particle streams in the laser-plasma environment that are tunable in energy, which is of potential interest for the study of ion stopping power in plasma, including the related implications in inertial confinement fusion schemes [26, 27, 28, 29]. In fact, in contrast with TW-class kJ-laser pulses, the use of PW-class kJ-laser beams allows us to achieve high laser intensities on target (10\({}^{19}\)-10\({}^{20}\) W/cm\({}^{2}\)) and thus, to explore acceleration regimes occurring at the target's front surface (e.g., HB-RPA)  
Figure 4: **(a)** The proton density map that was calculated by 2D PIC simulations at t = 2.8 ps (i.e., 1.2 ps after the highest intensity peak entered the highest density part of the target); **(b)** the proton phase space plot at t = 2.1 ps (the proton density is shown in units of plasma critical density); **(c)** the proton energy distribution (p\({}_{\rm x}\) > 0) and \(\alpha\)-particle energy distribution at the target’s front side from PIC and Monte Carlo simulations, respectively; and **(d)** the \(\alpha\)-particle angular distribution from the same simulation run. that could potentially be used to tune the energy of the protons that are responsible for p-B fusion reactions in the target bulk and, ultimately, to tune the average kinetic energy of the \(\alpha\)-particles.