  The ion beam bunching in a cascaded target normal sheath acceleration is
investigated by theoretical analysis and particle-in-cell simulations. It is
found that a proton beam can be accelerated and bunched simultaneously by
injecting it into the rising sheath field at the rear side of a
laser-irradiated foil target. In the rising sheath field, the ion phase
rotation may take place since the back-end protons of the beam feels a stronger
field than the front-end protons. Consequently, the injected proton beam can be
compressed in the longitudinal direction. At last, the vital role of the ion
beam bunching is illustrated by the integrated simulations of two successive
stages in a cascaded acceleration.
