Fig. 1. Energy-differential cross sections of proton-induced nuclear reactions releasing different numbers of neutrons (solid curves) and of total neutron production by photonuclear reactions (black dashed curve) in Pb, as given by the ENDF/B-VIII database.³⁴

Fig. 2. Number of neutrons emitted per incident proton as a function of the target material and incident proton energy, as simulated by FLUKA.

Fig. 3. Conceptual setup of the numerical study.

Fig. 4. Longitudinal (x − p_x) phase space of the protons from the CALDER-CIRC simulation using the LMJ-PETAL parameters.

Fig. 5. Proton energy spectrum from the CALDER-CIRC simulation using the LMJ-PETAL laser parameters (blue curve). An experimental proton spectrum obtained at LMJ-PETAL (see the text for details) is plotted as orange dots.

Fig. 6. Proton acceleration using the 0.6 PW Apollon laser parameters: x − p_x proton phase spaces at (a) t = −20 fs and (b) t = +4 fs (here t = 0 corresponds to the on-target laser pulse maximum). The blue line is the laser-cycle-averaged longitudinal electric field 〈E_x〉, extracted on axis (y = 0) and normalized to (a) 100E₀ or (b) 50E₀ for readability (E₀ = 3.2 × 10¹² V m⁻¹).

Fig. 7. Proton acceleration using the 6 PW Apollon laser parameters: x − p_x proton phase spaces at (a) t = −20 fs and (b) t = +4 fs (here t = 0 corresponds to the on-target laser pulse maximum). The blue line is the laser-cycle-averaged longitudinal electric field 〈E_x〉, extracted on axis (y = 0) and normalized to (a) 100E₀ or (b) 50E₀ for readability (E₀ = 3.2 × 10¹² V m⁻¹).

Fig. 8. PIC-simulated proton spectra using (a) the 0.6 PW and (b) the 6 PW Apollon laser parameters. In (a), the integrated number of protons above 10 MeV is ∼10¹¹, corresponding to a laser-to-proton energy conversion efficiency of ∼5%. In (b), there are 5 × 10¹¹ protons above 20 MeV, corresponding to a ∼12% conversion efficiency.

Fig. 9. Energy-angle spectrum of the neutrons escaping from a 0.3-mm-thick Pb converter target for (a) LMJ-PETAL, (b) 0.6 PW Apollon, and (c) 6 PW Apollon laser parameters.

Fig. 10. Energy fraction of the incident protons dissipated by nuclear reactions (blue) and transmitted through the target (green) as a function of the thickness l of the Pb converter target for (a) LMJ-PETAL, (b) 0.6 PW Apollon, and (c) 6 PW Apollon laser parameters.

Fig. 11. (a) Number (normalized to unit solid angle) and (b) maximum flux of the neutrons crossing the rear side of the Pb converter target, as a function of its thickness l. The incident proton beam is that predicted by PIC simulations in the LMJ-PETAL and 0.6–6 PW Apollon cases, as labeled.

Fig. 12. (a) Time-dependent neutron flux across the Pb converter backside for the LMJ-PETAL parameters. (b) Neutron energy spectra from a l = 0.3 mm Pb target in the LMJ-PETAL and 0.6–6 PW Apollon cases.

Fig. 13. Transverse size vs duration of the simulated neutron beam in the LMJ-PETAL, 0.6 PW Apollon, and 6 PW Apollon cases, and for various thicknesses, as indicated.