Due to their high cost of acquisition and operation, there are still a limited number of high-yield, high-flux neutron source facilities worldwide. In this context, laser-driven neutron sources offer a promising, cheaper alternative to those based on large-scale accelerators, with, in addition, the potential of generating compact neutron beams of high brightness and ultra-short duration. In particular, the predicted capability of next-generation petawatt (PW)-class lasers to accelerate protons beyond the 100 MeV range should unlock efficient neutron generation through spallation reactions. In this paper, this scenario is investigated numerically through particle-in-cell and Monte Carlo simulations, modeling, respectively, the laser acceleration of protons from thin-foil targets and their subsequent conversion into neutrons in secondary heavy-ion targets. Laser parameters relevant to the 1 PW LMJ-PETAL and 1-10 PW Apollon systems are considered. Under such conditions, neutron fluxes exceeding $10^{23},rm n,cm^{-2},s^{-1}$ are predicted, opening up attractive fundamental and applicative prospects.
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