Proton acceleration from short pulse lasers interacting with ultrathin foil

Two-dimensional particle-in-cell simulations using 50 nm Si$_{3}$N$_{4}$ and DLC foils are compared to published experimental data of proton acceleration from ultra-thin foils (\textless 1 $\mu $m) irradiated by short pulse lasers (30-50 fs), and some underlying physics issues pertinent to proton acceleration have been addressed. 2D particle-in-cell simulations show that the maximum proton energy scales as $I^{2/3}$, stronger than Target Normal Sheath Acceleration for thick foils (\textgreater 1 $\mu$m), which is typically between $I^{1/3}$ [1] and $I^{1/2}$ [2]. Published experimental data were found to depend primarily on the laser energy and scale as $E^{2/3}$. The different scaling laws for thick (\textgreater 1 $\mu $m) and ultra-thin (\textless 1 $\mu$m) foils are explained qualitatively as transitioning from Target Normal Sheath Acceleration to more advanced acceleration schemes such as Radiation-Induced Transparency and Radiation Pressure Acceleration regimes. This work was performed with the support of the Air Force Office of Scientific Research under grant FA9550-14-1-0282. \\[4pt] [1] F. N. Beg, et. al., Phys. Plasmas \textbf{4}, 447 (1997)\\[0pt] [2] K. Krushelnick, et. al., Plasma Phys. Control. Fusion \textbf{47}, B451 (2005)