Ponderomotive scaling of laser-accelerated electrons using a machine learning approach*

The ponderomotive scaling of hot electrons plays an essential role in the understanding of laser- plasma interactions, e.g., the absorption of a high intensity laser by a solid target. Many applications, including laser-driven particle acceleration, radiography and fast ignition rely on the characteristics of these fast electrons generated from such interactions. While the general ponderomotive scaling of the electron temperature with the laser intensity is well recognized, it is also known that in some configurations of the wave-particle interaction, where a background field or a second wave exists, super-ponderomotive electrons can be generated. The Hamiltonian systems underlying these configurations are of stochastic nature, thus making the analysis difficult. Here we aim to use a machine learning approach to provide a surrogate of the particle dynamics. Our neural network surrogate employs symplectic constraint to ensure the robustness of the model prediction and has the capability to embed the major parameters of the interactions. We train such surrogate models for various interaction configurations and compare their predictions of the characteristics of hot electrons. The result will also be compared to previous ponderomotive scalings from an empirical or analytical footing.