Parametric Study of Laser Driven Proton Beams from a Critical Density Gas Jet

Laser driven ion acceleration (LDIA) is studied via particle-in-cell simulations in a novel parameter space for laser-plasma interactions of a relativistic laser pulse with a gas jet target at the critical plasma density (n$_{c})$. Previous LDIA studies have been based on the interaction of a 1$\mu $m laser pulse with either a solid foil (n$\sim $100n$_{c})$ or a gas jet (n$\le $0.1n$_{c})$. Here we propose focusing a high power CO$_{2}$ laser pulse at a H$_{2}$ gas jet which is tunable around the critical plasma density for 10$\mu $m radiation (10$^{19}$cm$^{-3})$. A rectangular H$_{2}$ gas jet operated near n$_{c}$ lends itself to efficient coupling of the laser light to forward directed electrons instigating the target normal sheath acceleration mechanism to produce a beam of protons. Results are presented here on a parametric study of the peak plasma density and plasma profile to find optimal conditions for total charge, divergence, and energy of the accelerated proton beam. These simulations support an ongoing LDIA experiment at the Neptune Laboratory at UCLA using a 3ps 1TW CO$_{2}$ laser pulse for the production of collimated proton beams.