Multi-objective Bayesian optimisation of a double-layer target for quasi-monoenergetic TNSA protons

Abstract

We carry out a six-parameter multi-objective Bayesian optimisation of a carbon--hydrogen double-layer target for target-normal-sheath proton acceleration. The campaign consists of 80 two-dimensional EPOCH simulations with the laser amplitude $a_0$, pulse duration $τ$, carbon-layer thickness $L_1$, hydrogen-layer density $N_2$, hydrogen-layer thickness $L_2$ and hydrogen-layer radius $r_p$ as input variables. Each final proton spectrum is scored by the peak energy, the charge fraction inside a $\pm10\%$ peak-energy window and the charge in that window. Among the Pareto-set evaluations, the cases with peak energies between 64 and 71 MeV occur near $a_0=30$, $τ=45$ fs, $L_1=0.3\,μ{\rm m}$, $L_2=30$ nm and $r_p=0.15\,μ{\rm m}$. Along this branch, increasing $N_2$ raises the in-window charge and increases the bandwidth. The small rear-layer radius keeps the proton source within the flat central region of the transverse sheath field, where the accelerating field is nearly uniform. A 3D calculation is performed for the intermediate-density case $N_2=11.85\,n_c$, which balances bandwidth and in-window charge along this branch. The corresponding 2D spectrum has $E_{\rm peak}=67.4$ MeV and $ΔE/E=18.8\%$, whereas the 3D spectrum has $E_{\rm peak}=34.1$ MeV and $ΔE/E=7.0\%$. The lower 3D peak energy and narrower bandwidth are associated with an earlier decay of the rear-sheath field and an earlier saturation of the proton peak energy, and the quasi-monoenergetic peak is retained in 3D.