Advances in Spectral Distribution Assessment of Laser Accelerated Protons using Multilayer CR-39 Detectors

We show that a spectral distribution of laser-accelerated protons can be extracted by analyzing the proton track diameters observed on the front side of a second CR-39 detector arranged in a stack. The correspondence between the proton track diameter and the incident energy on the second detector is established by knowing that protons with energies only higher than 10.5 MeV can fully deposit their energy in the second CR-39 detector. The correlation between the laser-accelerated proton track diameters observed on the front side of the second CR-39 detector and the proton incident energy on the detector stack is also presented. By calculating the proton number stopped in the CR-39 stack, we find out that its dependence on the proton energy in the 1-15 MeV range presents some discontinuities at energies higher than 9 MeV. Thus, we build a calibration curve of the track diameter as a function of the proton incident energy within the 1-9 MeV range, and we infer the associated analytical function as the calculations performed indicate best results for proton spectra within the 1-9 MeV range. The calibration curve is used as a tool to ascertain the pits identified on the surfaces of both CR-39 detectors to proton tracks. The proton tracks spatial distribution analyzed by optical and atomic force microscopy is correlated with the peculiarity of the used targets.