The scaling of the flux and maximum energy of laser-driven sheath-accelerated protons has been investigated as a function of laser pulse energy in the range of 15–380 mJ at intensities of 1016–1018 W/cm2. The pulse duration and target thickness were fixed at 40 fs and 25 nm, respectively, while the laser focal spot size and drive energy were varied. Our results indicate that while the maximum proton energy is dependent on the laser energy and laser spot diameter, the proton flux is primarily related to the laser pulse energy under the conditions studied here. Our measurements show that increasing the laser energy by an order of magnitude results in a more than 500-fold increase in the observed proton flux. Whereas, an order of magnitude increase in the laser intensity generated by decreasing the laser focal spot size, at constant laser energy, gives rise to less than a tenfold increase in observed proton flux.
