Parametric study of laser-driven proton beams through laser spatio-temporal shaping for machine-learning assisted...

We present a parametric and machine-learning-assisted study of laser-driven proton acceleration using spatio-temporal laser-beam shaping employed in the most routinely used acceleration regime, the so-called Target Normal Sheath Acceleration (TNSA) regime. By employing 20 of the 48 actuators of a deformable mirror in combination with an acousto-optic programmable dispersive filter, we independently tailored the laser's spatial wavefront and spectral phase. Irradiating 4.5-μm-thick aluminum targets (that produce the most stable TNSA-accelerated beam in our conditions) with a fixed laser energy of 3.2 J reveals that spatial beam shaping strongly influences experimental observables associated with proton acceleration, while temporal shaping produces only a minor effect. Through correlation analysis and surrogate modeling, we further identify the maximum proton energy as a robust and predictive proxy for overall TNSA performance within the present dataset, making it a practical metric for optimization under our experimental conditions.