Analysis of laser-proton acceleration experiments for development of empirical scaling laws

Numerous experiments on laser-driven proton acceleration in the MeV range have been performed with a large variety of laser parameters since its discovery around the year 2000. Both experiments and simulations have revealed that protons are accelerated up to a maximum cut-off energy during this process. Several attempts have been made to find a universal model for laser proton acceleration in the target normal sheath acceleration regime. While these models can qualitatively explain most experimental findings, they can hardly be used as predictive models, for example, for the energy cut-off of accelerated protons, as many of the underlying parameters are often unknown. Here we analyze experiments on laser proton acceleration in which scans of laser and target parameters were performed. We derive empirical scaling laws from these parameter scans and combine them in a scaling law for the proton energy cut-off that incorporates the laser pulse energy, the laser pulse duration, the focal spot radius, and the target thickness. Using these scaling laws, we give examples for predicting the proton energy cut-off and conversion efficiency for state-of-the-art laser systems.