# In-Target Proton-Boron Nuclear Fusion Using a PW-Class Laser
## 2 Materials and Methods  
The relatively short-pulse (2.2 ps) and high-energy (\(\sim\)1.4 kJ) PW-class laser system LFEX [16], which was operated at relativistic intensities (\(\sim\)3 \(\times\) 10\({}^{19}\) W/cm\({}^{2}\)) at the Institute of Laser Engineering of the Osaka University (Japan), was focused onto the front surface (normal incidence) of a boron nitride (BN) target with a thickness of 0.2 mm. The concentration of hydrogen in the sample was a few %, which came from the chemical synthesis of the material during the manufacturing process. As schematically shown in Figure 2, a Thomson parabola (TP) spectrometer was placed in the forward direction along the target normal to monitor the proton/ion plasma emission from the target's rear surface, which was based on an acceleration mechanism commonly known as \"target normal sheath acceleration\" (TNSA) [17]. Protons that were accelerated via TNSA at the target's rear side did not contribute to the generation of \(\alpha\)-particles from p-B fusion; however, the determination of their cutoff energy was important to confirm that that particular laser shot was representative of an optimal laser-plasma coupling (a high laser intensity on the target's front surface allows the generation of electrons with high temperature, also known as \"hot electrons\", hence efficient TNSA at the target's rear side and protons with high cutoff energies). Plasma ions were deflected by parallel electric and magnetic fields based on their charge-to-mass ratio and were ultimately recorded on an imaging plate [18]. The presence of protons with cutoff energies of \(\sim\)25 MeV confirmed that relativistic electrons were efficiently produced at the target's front side, thanks to the relatively high intensity and long pulse width of the incoming laser beam. The main \(\alpha\)-particle diagnostic was a CR39 nuclear track detector that was shielded with Al filters of different thicknesses (10 \(\upmu\)m and 30 \(\upmu\)m), which was aimed at the target's front side and  
Figure 1: The experimental progress in p–B fusion, measured in terms of \(\alpha\)-particle production in the “in-target” [2, 3, 4,7,14] and “pitcher–catcher” [5,6,8,15] geometries. The left-hand scale indicates the absolute \(\alpha\)-particle flux (particles/sr), while the right-hand scale is normalized to the laser energy delivered on target (particles/sr/J). placed at a distance of 144 cm from the target and at an angle of \(\sim\)80\({}^{\circ}\) from the target normal. Such a large detection angle was deliberately chosen so that the CR39 sample would be out of the main blow-off plasma emission cone, thus excluding the presence of energetic heavy ions (B and N) emitted backwards and impinging on the detector. The calibration of the CR39 detectors with various Al filters is reported elsewhere, along with the etching procedure that was used in this work [6]. We note that tracks that were ascribable to the low-energy blow-off plasma protons (very small pits in the CR39 sample) were unambiguously distinguishable from those ascribable to \(\alpha\)-particles from p-B fusion events (larger pits) when the etching time was kept short enough (\(\leq\)1 h), and that high-energy protons were not visible on the CR39 since they would have generated tracks with diameters below the resolution of the optical microscope that was used to map the sample after particle irradiation (\(<\)1 \(\upmu\)m). A set of start-to-end numerical simulations was carried out with the aim of providing a qualitative interpretation of the experimental results. Additionally, 2D hydrodynamic simulations were performed using the CHIC code [19] with the aim of modeling the interaction of the relatively long (\(\sim\)2 ns) laser pedestal with the solid target.