Target shape effects on monoenergetic GeV proton acceleration

When a circularly polarized laser pulse interacts with a foil target, there are three stages: pre-hole-boring, hole-boring and the light sail acceleration. We study the electron and ion dynamics in the first stage and find the minimum foil thickness requirement for a given laser intensity. Based on this analysis, we propose to use a shaped foil for ion acceleration, whose thickness varies transversely to match the laser intensity. Then, the target evolves into three regions: the acceleration, transparency and deformation regions. In the acceleration region, the target can be uniformly accelerated producing a mono-energetic and spatially collimated ion beam. Detailed numerical simulations are performed to check the feasibility and robustness of this scheme, such as the influence of shape factors and surface roughness. A GeV mono-energetic proton beam is observed in the three dimensional particle-in-cell simulations when a laser pulse with the focus intensity of 1022W=cm2 is used. The energy conversion efficiency of laser pulse to accelerated proton beam is more than 23%. Synchrotron radiation and damping effects are also checked in the interaction.