Scaling laws of ion acceleration in ultrathin foils driven by radiation pressure of intense laser pulses are investigated by theoretical analysis and two-dimensional particle-in-cell simulations. Considering the instabilities are inevitable during laser plasma interaction, the maximum energy of ions 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 light sail model, 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.
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