Scaling Laws of Ion Acceleration in Ultrathin Foils Driven by Laser Radiation Pressure*

Scaling laws of laser-driven ion acceleration can be used to evaluate the laser and target parameters needed to produce ion beams of interest, which are very important for the construction of laser facilities. The scaling laws of target normal sheath acceleration have been investigated widely, however, that of radiation pressure acceleration (RPA) is still not very clear, especially for that of the maximum energy. Considering the instabilities are inevitable during laser plasma interaction, the maximum energy of ion beams in RPA should have two contributions: the bulk acceleration driven by radiation pressure and the sheath acceleration in the moving foil reference induced by hot electrons. A theoretical model is proposed to quantitatively explain the results that the cutoff energy and energy spread are larger than the predictions of the “light sail” model, which have been observed in simulations and experiments for a large range of laser and target parameters. Scaling laws derived from this model and supported by the simulation results are verified by the previous experiments.