One-dimensional model of the electrostatic ion acceleration in the ultraintense laser-solid interaction

The electrostatic field at the solid-vacuum interface produced during the interaction of an ultrashort relativistically intense laser pulse with a thin solid target has been analytically calculated from the Poisson equation and investigated in terms of plasma parameters. Assuming the presence of a relativistic electron population on the rear target surface, the Poisson equation has been solved in a finite spatial domain, and the ion motion in the given potential distribution has been calculated; the energy spectrum of an accelerated proton bunch initially distributed in a thin layer has been also derived. The model allows to make comparison between experimental data and theoretical predictions as well as evaluations of the laser intensities and pulse energies required to achieve ion energies in the order of hundreds MeV.