Ion acceleration in the transparent regime and the critical influence of the plasma density scale length

The influence of a plasma density gradient on ions accelerated along the specular (back reflection) direction in the transparent Target Normal Sheath Acceleration regime is investigated. Enhanced acceleration of ions is experimentally observed in this regime using high-intensity and ultra-high contrast laser pulses and extremely thin foils of few nanometer thicknesses. The experimental trend for the maximum proton energy appeared quite different from the already published numerical results in this regime where an infinitely steep plasma gradient was assumed. We showed that for a realistic modelling, a finite density gradient has to be taken into account. By means of particle-in-cell (PIC) simulations, we studied for the first time the influence of the plasma density scale length on ion acceleration from these nanofoil targets. Through a qualitative agreement between our numerical particle-in-cell simulations and our experiments, the main conclusion with regard to the experimental requirements is that, in the transparent regime evidenced with nanofoils as compared to the opaque regime, the plasma expansion has to be taken into account and both the pulse contrast and the damage threshold of the material are essential parameters.