Parametric study on ion acceleration from the interaction of ultra-high intensity laser pulses with near-critical density gas targets

We present a parametric study based on 1-D particle-in-cell (PIC) simulations conducted with the objective of understanding the interaction of intense lasers with near-critical non-uniform density gas targets. Specifically, we aim to find an optimal set of experimental parameters regarding the interaction of a $\lambda_L$ = 0.8 $\mu$m, $I_L =10^{20}$ W/cm$^2$ ($a_0 = 8.8$), $\tau_L = 30$ fs laser pulse with a near-critical non-uniform pure nitrogen gas profile produced by a non commercial gas nozzle. The PIC code Calder developed at CEA was used, and both the maximum electron density and the direct laser contribution to ion acceleration were studied. Shock formation was achieved for a peak electron density $n_e$ ranging between 0.35 $n_c$ and 0.7 $n_c$. In this density interval, the survival of a percentage of the laser pulse until the gas density peak, while being strongly absorbed ($>$90$\%$) and creating a hot electron population in the gas up-ramp, is singled out as a necessary condition for shock formation. Moreover, the laser absorption must give rise to a super ponderomotive heating of the target electrons in order to launch an electrostatic shock inside the plasma. The direct laser effect on ion acceleration consists in a strong initial density perturbation that enhances charge separation while the electron pressure gradients are identified as fundamental for shock formation. The production of a controlled and repetitive gas profile as well as the possibility of performing measurements with statistical meaning are highlighted as fundamental for conducting a thorough experimental study.