Multi-Objective Design of C-Shaped Targets for Energy--Divergence Control in Laser-Driven Proton Acceleration

Abstract

We optimize the energy-divergence trade-off of laser-driven protons from a C-shaped target using two-dimensional particle-in-cell simulations and constrained multi-objective Bayesian optimization. Five geometry and focusing parameters are varied to maximize proton cutoff energy and minimize the RMS divergence of forward protons with E_k >= 5 MeV under a proton-only conversion-efficiency constraint of eta_H >= 9%. Of 82 designs, 60 are feasible and 15 Pareto-optimal. The Max-Energy and Min-Divergence endpoints yield 28.64 MeV at 52.51 degrees and 11.47 MeV at 11.13 degrees, respectively; a representative compromise yields 21.44 MeV at 38.44 degrees. Matched-stage diagnostics link these regimes to optical-field buildup, electron energization, charge separation, and outer-sheath organization. Numerical tests support the principal trends. Reflection timing does not support a monotonic trapping-duration law, and the charge-sheath relation remains non-local. These results establish a design-resolved route to controlling proton energy and angular quality.