Ion energy spectrum of expanding laser-plasma with limited mass

A simple analytical model is presented for hydrodynamic expansion of laser-produced plasma with a limited mass, which expands quasi-isothermally during laser irradiation and quasiadiabatically after turning off the laser. During the isothermal expansion, the masses undergo entire disintegration under a relatively long laser pulse, while the ions are being kept accelerated. This physical picture significantly contrasts with that described by the orthodox self-similar solution for a semi-infinite planar rarefaction wave. The two successive expansions, i.e., isothermal expansion followed by adiabatic expansion, are described, respectively, by different self-similar solutions, which are found to be connected smoothly with each other in time and space. The ion energy spectrum obtained by the model reproduces well experimental results obtained under different geometrical conditions. The maximum ion kinetic energy is also estimated in terms of the laser and target parameters.