Scaling of ion energies in the relativistic-induced transparency regime

Experimental data are presented showing maximum carbon C6+ ion energies obtained from nm-scaled targets in the relativistic transparent regime for laser intensities between 9 × 1019 and 2 × 1021 W/cm2. When combined with two-dimensional particle-in-cell simulations, these results show a steep linear scaling for carbon ions with the normalized laser amplitude a0(a0∝(√I)). The results are in good agreement with a semi-analytic model that allows one to calculate the optimum thickness and the maximum ion energies as functions of a0 and the laser pulse duration τλ for ion acceleration in the relativistic-induced transparency regime. Following our results, ion energies exceeding 100 MeV/amu may be accessible with currently available laser systems.