Bayesian optimization of double-pulse temporal shaping for enhanced target-normal-sheath proton acceleration under fixed laser energy

Splitting an ultrashort drive pulse into a weak leading pulse and a strong main pulse is known to raise the energy of protons accelerated by the target-normal-sheath-acceleration (TNSA) mechanism, because the leading pulseforms a preplasma that increases the absorption of the main pulse. The allocation of energy between the two pulses and their temporal separation are coupled control parameters, and under a fixed total energy they have not been optimized jointly in a systematic way. We address this problem with twodimensional particle-in-cell simulations driven by Bayesian optimization. Treating the prepulse energy fraction r and the interpulse delay Δt as free parameters under a fixed total energy, a campaign of 32 simulations, of which 16 are Sobol-initialized and 16 adaptively selected, locates an optimum at r ≈ 0.07 and Δt ≈ 234 fs. The proton cutoff energy increases from 7.7 MeV for the single pulse to 17.7 MeV at the optimum, a gain of about 130%. The optimum is asymmetric with only about 7% of the energy in the leading pulse. At the optimum the laser absorption rises from 4.84% to 20.09%, the bulk hot-electron temperature from 1.20 to 1.94 MeV, and the time-integrated rear sheath field by a factor of about 1.7. The optimum lies on a broad plateau in Δt, which relaxes the timing tolerance required in an experiment.