Effect of femtosecond laser pulse duration on thin-foil accelerated protons

The influence of pulse duration on proton acceleration using sub-ps (300-30 fs), ultra-intense (3.6 × 10¹⁸ W / cm² to 3.6 × 10¹⁹ W / cm²), constant energy (0.14 J) laser pulses is studied using 2D simulations. The entire pulse duration is modelled, so that during the rising edge of the pulse a preplasma can naturally expand from the target front and rear sides into vacuum, altering, respectively, laser absorption and electrostatic field generation. In this paper, we study this effect for two target profiles-sharp-edge profile and smooth density gradient at the front side-and we point out the existence of a weak optimum pulse duration for proton acceleration. For the different pulse durations we considered, we first show that the maximum proton energy variations are similar to those of the rear side electrostatic field amplitude. The energy variations, however, are smaller than expected from the field variations, and we explain this effect by considerations on the characteristic proton acceleration time.