## 3 Results and Discussion
### Estimation of Proton Energies Incident on the Second CR-39 Detector  
The proton range and consequently the Bragg peak position for different proton energies within the stack of CR-39 detectors stack was calculated using the SRIM code [23] (Figure 4a). Figure 5 and Table 1 present the Bragg curves and the Bragg peak position for protons with 1-15 MeV energy range as a function of the incident proton energy. It can be observed that protons with energies higher than 10.5 MeV are fully stopped into the second CR-39 detector, while the first CR-39 detector (1 mm thick) only acts as a filter. A proton with energy higher than 10.5 MeV could penetrate through 1 mm thick CR-39 detector without losing enough energy to damage it. In [3] it was showed that protons with energies higher than 10.5 MeV do not leave observable traces on the front side of a 1 mm thick CR-39 detector. Reference [3] also reports on the presence of tracks for protons with energies higher than 10 MeV  
Figure 4: (**a**) Proton range calculated with SRIM 2013 and TRACK-P software; (**b**) The dependence of the proton track diameter on energy. (10.5 \(<\) E \(<\) 10.7 MeV) on the rear side of a first CR-39 detector and on the front side of a second CR-39 detector. A direct correlation between the proton track diameter on the front side of the second detector and the proton energy incident on the detector stack was not established. Previously, [3; 7; 9; 10] it was reported that the dependence of the proton track diameter on proton incident energy can be established only for protons that stops in a single detector slice (around Bragg peak). Due to the fact that only protons with energies higher than 10.5 MeV can fully deposit their energies in the second CR-39 detector (the first detector acting as an attenuation energy filter), the correspondence between the proton track diameter identified on the second detector and the incident energy of protons on the second detector can be achieved. Thus, we consider the energy of proton after crossing the first CR-39 detector, as the proton incident energy on the second CR-39 detector. Table 2 presents the correspondence between the energies of the protons incident on the first detector (with energies higher than 10.5 MeV) and the energies of the protons incident on the second detector, calculated using the Stopping and Range of Ions in Matter (SRIM) code [23]. The dependence between the energies of the protons transmitted through the first CR-39 detector, and the energies  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Layer No. **} & \multirow{2}{*}{**Energy (MeV)**} & \multirow{2}{*}{**Proton Range**} & \multirow{2}{*}{**Stopping Power**} & \multicolumn{2}{c}{**Simulation Structures of the**} \\  & & & **(mm)** & **Intensity (eV/A)** & **Experimental Stack (10 \(\upmu\)m Al** \\  & & & & **+ 2 mm of the CR-39 Detectors)** \\ \hline
1 & 1 & \(15.5\times 10^{-3}\) & 4.96 & 5.9 \(\upmu\)m \\
2 & 2 & \(55.3\times 10^{-3}\) & 4.23 & layer  
of the protons incident on the detector stack (in 1-15 MeV range) is shown in Figure 6a. Previously, in [3; 13] only the transmittance of protons with energies ranging between 10 to 10.7 MeV through 1 mm thick CR-39 detector was analyzed. The number of protons with energies higher than 10 MeV that travel through a first CR-39 detector and stopped in a second detector can be determined with the SRIM code following a similar calculation procedure with the one used for finding the proton transmitted energy. The assessment of number of protons with known energy stopped in a slice of CR-39 detector material has also been calculated (see Figure 6b). Firstly, we estimate the range of protons with energies from 1 to 15 MeV in the 2 mm thick CR-39 detector stack. Then, a CR-39 material slab (2 mm in thick) was sliced in sheaths of different thicknesses. The thickness of each slice was determined by iterative calculations taking into account the proton incident energy and the Bragg peak position into the CR-39 detector slice (see Table 1).