# In-Target Proton-Boron Nuclear Fusion Using a PW-Class Laser
## 3 Results  
The energy spectrum of the \(\alpha\)-particles that were emitted backward from the target's front surface is shown in Figure 3a. This energy distribution was recalculated from the signal recorded by the CR39 detectors that were covered by 10-\(\upmu\)m and 30-\(\upmu\)m Al filters (Figure 3b,c, respectively). The measured \(\alpha\)-particle flux in the energy range of 5-10 MeV and at the detection angle of 80\({}^{\circ}\) (with respect to the target normal) was \(1.2\times 10^{10}\)/sr \(\pm\) 17%. This estimation was carried out by integrating the curve shown in Figure 3a and using a reasonable extrapolation (the red dashed line in Figure 3a) of the spectrum between 7 and 8 MeV (this was not measured due to the limitations of our calibration [6]). Particles with energy \(<\)5 MeV could not be detected since they were stopped in the 10-\(\upmu\)m Al filter, and particles with energy potentially \(>\)10 MeV (diameter \(<\) 4 \(\upmu\)m) were not counted since they were outside the CR39 calibration.  
Figure 2: (**a**) The experimental setup; (**b**) the Thomson parabola (TP) snapshot showing the presence of protons and heavier ions being accelerated forwards from the target’s rear surface (TNSA acceleration mechanism), i.e., not contributing to the generation of \(\alpha\)-particles via p–B fusion.  
The presence of a relatively large pre-plasma region that longitudinally extended for a length of \(\sim\)100 \(\upmu\)m in front of the target was estimated by the 2D hydrodynamic simulations. This information was implemented in the geometry that was used for the 2D PIC run, as shown in the proton density map of Figure 4a (the red dashed rectangle). The interface between the pre-plasma and the solid density region (around 175 \(\upmu\)m in Figure 4a) along with the relatively long laser pulse feature (\(\sim\)2 ps) allowed the onset of an effective HB-RPA process at the target's front surface [21,22], which ultimately led to the efficient acceleration of the protons that were propagating forward into the target bulk. This can be clearly seen in Figure 4b, which reports the proton phase space plot (p\({}_{\rm x}\) > 0). The energy distribution of the protons that were propagating forward, which was obtained from the 2D PIC simulation, is shown in Figure 4c (the black line). Protons with an energy of 0.5-19 MeV were accelerated toward the BN target interior, thus generating p-B fusion events inside the target. We noted that, according to the simulation outputs, the highest proton flux lay in the range of 0.5-1 MeV, which was an optimal condition for an efficient p-B fusion process (the high cross-section of the nuclear reaction). Furthermore, the flux of protons with energies > 8 MeV was relatively low, hence their contribution in terms of p-B fusion yield was negligible (also due to the low cross-section of the nuclear reaction at such energies). Therefore, the low-energy part of the proton spectrum was responsible for the high-flux \(\alpha\)-particle streams that were propagating backward, as predicted by the 3D Monte Carlo simulation output shown in Figure 4d. The corresponding \(\alpha\)-particle energy distribution that was calculated by the Monte Carlo simulation for an angle corresponding to the position of the CR39 detector (80\({}^{\circ}\)) is reported in Figure 4c (the red line). The energy cutoff of the \(\alpha\)-particle stream that was calculated numerically was \(\sim\)14 MeV, but this could not be verified experimentally due to the limitations in the available \(\alpha\)-particle calibration.  
Figure 4: _Cont._  
Figure 3: (a) The experimental spectrum of the \(\alpha\)-particles that were emitted in the backward direction from the target’s front surface; (b) the corresponding CR39 raw image in the case of the 30-\(\upmu\)m Al filter and (c) the 10-\(\upmu\)m Al filter.