Deep learning approaches for modeling laser-driven proton beams via phase-stable acceleration

Deep learning (DL) has recently become a powerful tool for optimizing parameters and predicting phenomena to boost laser-driven ion acceleration. We developed a neural network surrogate model using an ensemble of 355 one-dimensional particle-in-cell simulations to validate the theory of phase-stable acceleration (PSA) driven by a circularly polarized laser driver. Our DL predictions confirm the PSA theory and reveal a discrepancy in the required target density for stable ion acceleration at larger target thicknesses. We discuss the physical reasons behind this density underestimation based on our DL insights.