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We study the one-dimensional expansion of a thin foil plasma irradiated by a high intensity laser with multi-picosecond (ps) pulse durations by using particle-in-cell simulation. Electrons are found to recirculate around the expanding plasma for many times, which results in stochastic heating leading to increase of the electron temperature in the multi-ps time scale beyond the ponderomotive scaling. The conventional isothermal model cannot describe such an expansion of plasmas in the long time scale. We here developed a non-isothermal plasma expansion theory that takes the time dependence of electron temperature into account for describing the multi-ps interactions in one-dimensional geometry. By assuming that the time scale of electron temperature evolution is slow compared with the plasma expansion time scale, we derived a non-self-similar solution. The time evolution of ion maximum energy obtained by the non-isothermal theory explains the details of that observed in the simulation.

Fast ion acceleration in a foil plasma heated by a multi-picosecond high intensity laser