A foil–ramparts target interaction with an ultra-short, ultra-intense laser pulse (pulse duration between 10−12 and 10−15 s, intensity above 1018 W cm−2) to produce proton beams with controlled divergence and concentrated energy density in target normal sheath acceleration regime is studied. Two-dimension-in-space and three-dimension-in-velocity particle-in-cell simulations show that the foil–ramparts target helps to reshape the sheath electric field and generate a transverse quasi-static electric field of ~6.7 TV m−1 along the inner wall of the ramparts. The transverse electric field suppresses the transverse expansion of the proton beam effectively, as it tends to force the produced protons to focus inwards to the central axis, resulting in controlled divergence and concentrated energy density compared with that of a single plain target. The dependence of proton beam divergence on length of the rampart h is investigated in detail. A rough estimation of h ranges depending on dimensionless parameter a0 of the incident laser is also given.
