  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.
