Numerical Simulations of the Acceleration of Fast Protons and of the Excitation of Nuclear Reactions ${}^{\textrm{11}}\textrm{B}\boldsymbol{(p,3\alpha)}$ and ${}^{{11}}\textrm{B}\boldsymbol{(p,n)}^{{11}}\textrm{C}$ at the Intensities of Picosecond Laser Radiation in the Range of $\boldsymbol{10^{18}{-}10^{19}}$ W/cm${}^{{2}}$

Abstract

Results of numerical simulations for acceleration of proton beams at the irradiation of Al target by a superintense laser pulse are presented. There is a good agreement with the experimental data in a broad range of laser intensities from $I=10^{18}$ W/cm${}^{2}$ to $I=10^{19}$ W/cm${}^{2}$ at the fixed laser pulse duration. The obtained parameters of proton beams were used for calculation of the total yield of $\alpha$ particles and neutrons for the nuclear reactions ${}^{11}$B($p,3\alpha$) and ${}^{11}$B($p,n$)${}^{11}$C at the collisions of proton beams with boron targets. It is shown that the number of $\alpha$ particles escaping boron target and arriving at track detectors is less than 5$\%$ of the total amount of $\alpha$ particles, because the majority of these particles remain inside the target owing to ionization losses. The derived values of the yield of $\alpha$ particles’ which arrive at detectors are in good agreement with the experimental data. We also calculate the total yield of neutrons in the reaction ${}^{11}$B($p,n$)${}^{11}$C. It is found that, at the intensity $I=10^{19}$ W/cm${}^{2}$ of the picosecond laser pulse, the yield is equal to $N_{n}=1.4\times 10^{8}$, this value is approximately of 3$\%$ of the total yield of $\alpha$ particles.