Multivariate scaling of maximum proton energy in intense laser driven ion acceleration

The production of high-energy ions is a momentous goal of ultraintense laser lights. So far a number of experiments and numerical simulations have been conducted to obtain the scaling of the ion energy to find the optimal experimental condition. Due to the complexity of the relativistic laser-plasma interactions, it is not easy to evaluate the ion energy for different experimental configurations. We propose a statistical approach using the Bayesian inference to obtain a multivariate scaling to predict the maximum proton energy via the target normal sheath acceleration. We derive the scaling for the experimental parameters and also for the hot electron temperature and density observed in the corresponding particle-in-cell simulations. We demonstrate the effectiveness of our approach in the prediction of the maximum proton energy and provide the experimental condition to achieve a proton energy over 100 MeV.