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We investigated numerically the broadening mechanisms of the energy spectrum of ions accelerated by electrostatic shocks in over dense plasmas irradiated by intense ultra-short laser pulses. It was found that the width of the shock-accelerated ion spectrum could be ineluctably broadened by two mechanisms, which are the continuously decreasing speed of the shock front due to the energy dissipation into ions, and the further acceleration by the sheath field at target rears when energetic ionsdoi:10.1088/1742-6596/244/4/042024 fatcat:tt34bqxbbzgenb6lfr6msrlsi4