## 3 Results and Discussion
### Analysis of the Laser Driven Proton Tracks in CR-39 Detectors by Atomic Force Microscopy (AFM)  
The investigation of proton tracks by AFM is more precise with respect to an optical microscopy as it can perform a direct physical measurement of the revealed pits on the post-etched surface of the detector [23]. However, optical microscopy is currently considered as a standard method to perform the analysis of proton tracks [3; 8]. The mismatch in the results supplied by these two methods appears mainly because of microscope focusing issues, knowing that the optical image of the CCD camera attached to the microscope consists of a matrix of pixels (with x; y coordinates) and associated grey scale values [24]. Thus, AFM analysis of the post etched CR-39 detectors can be very useful to identify all questions related to the evidence of proton tracks by optical microscopy, issues that mainly appear due to detector transparency, depth of the proton tracks, and microscope focusing. Proton beams generated as a result of high-power, laser-thin solid target interaction were identified by AFM, after the tracks left in the post-etched surface of both CR-39 detectors that comprise the irradiated stack (10 \(\upmu\)m thick Al foil, 2 CR-39 detectors, each one 1 mm thick). The CR- 39 detectors irradiated with laser driven proton beams were etched for 6 h in 6.25 N NaOH solution at 70 \({}^{\circ}\)C.  
A SPM-NTegra Prima AFM (NT-MDT) atomic force microscope was used, operating in semi-contact mode with a NSG 01 cantilever (resonance frequency: 87-230 kHz, force constant: 1.45-15.1 N/m). The proton track diameters were also measured using the Image J software. Figure 7 shows the AFM images of the proton tracks observed on front side of both post etched CR-39 detectors irradiated with laser driven proton beams. The proton tracks mainly exhibit circular shapes of different diameters as an indication of various proton energies of normal incidence on the detector plate. There are no so much elliptic shapes of proton tracks, (which could indicate that the incident angle of the protons on the detector surface is not normal [3]). The images also point out the influence of the target thickness and material type on the proton number for the \(50\times 50\)\(\upmu\)m\({}^{2}\) investigated area. Similar spatial distributions of the proton tracks on few mm\({}^{2}\) areas were also observed. The number of proton tracks in the \(50\times 50\)\(\upmu\)m\({}^{2}\) area identified on the first detector, in case of high-power laser pulses interaction with Al targets (with 10 and 5 \(\upmu\)m thickness), is higher than in case of Ag (with 10 and 5 \(\upmu\)m thickness) targets. The AFM images in Figure 7 emphasize the presence of proton tracks, with diameters ranging from 1 to 7 \(\upmu\)m, on both CR-39 detectors. The circular proton tracks with diameters of \(\sim\)1 \(\upmu\)m are very well illustrated in the AFM images of the post-etched CR-39 detectors, shown in Figure 7. The differences between the proton track diameters of \(\sim\)1 \(\upmu\)m and the rugged surface of the chemical process detectors (pits of about 0.6 \(\upmu\)m) were also revealed. Thus, the uniform distributed tracks with diameters of about 0.6 \(\upmu\)m observed on the post-etch surface of the CR-39 detectors, cannot be attributed to protons. On the other hand, as the linear energy transfer (LET) of protons with energy higher than 10.7 MeV is very low in the first CR-39 slab their corresponding track diameters cannot be differentiated from the rugged surface pits. We suppose that the non-uniform distribution of the proton tracks on the surface of post-etched CR-39 detectors could be attributed to the surface morphology of Al and Ag targets (see Figure 1d). The tracks with diameters greater than \(\sim\)1 \(\upmu\)m identified on the surface of the first and second CR-39 detectors (see Figure 7), irradiated during the performed laser-proton accelerated experiments, present an exponential distribution.