Laser ion-acceleration scaling laws seen in multiparametric particle-in-cell simulations

The ion acceleration driven by a laser pulse at intensity I= 10(20)-10(22) W/cm(2) x (microm/lambda)(2) from a double layer target is investigated with multiparametric particle-in-cell simulations. For targets with a wide range of thickness l and density n(e), at a given intensity, the highest ion energy gain occurs at certain electron areal density of the target sigma = n(e)l, which is proportional to the square root of intensity. In the case of thin targets and optimal laser pulse duration, the ion maximum energy scales as the square root of the laser pulse power. When the radiation pressure of the laser field becomes dominant, the ion maximum energy becomes proportional to the laser pulse energy.