Proton acceleration in an overdense hydrogen plasma by intense CO2 laser pulses with nonlinear focusing effects in the underdense preplasma

We report on proton acceleration from intense CO₂ laser-irradiated hydrogen plasmas at near-critical densities, with the density gradient steepened by Nd:YAG ablation-driven hydrodynamic shocks. While the experimental results, including quasi-monoenergetic proton spectra and their scaling law with respect to the laser energy, generally agree with simulations, with some laser shots we observed much higher proton energies than expected. The increased proton energy may be linked to nonlinear propagation effects in the steepened plasma density ramp before the critical surface, including relativistic self-focusing and, for the case of temporally-structured laser pulses observed in the experiment, focusing of the trailing pulse through the plasma channel formed by the leading pulse 25 ps ahead. Formation of plasma ion channels by CO₂ laser pulses was observed in a supplemental experiment.