Theory of laser ion acceleration from a foil target of nanometers

A theory for laser ion acceleration is presented to evaluate the maximum ion energy in the interaction of ultrahigh contrast (UHC) intense laser with a nanometer-scale foil. In this regime the energy of ions may be directly related to the laser intensity and subsequent electron dynamics. This leads to a simple analytical expression for the ion energy gain under the laser irradiation of thin targets. Significantly, higher energies for thin targets than for thicker targets are predicted. Theory is concretized to the details of recent experiments which may find its way to compare with these results.