Fig. 5: Protons.

a Proton number in arbitrary units as a function of proton energy. Yellow dots are proton number evaluated in case of laser interaction with aerogel-foams combined with thin metal foils at 10¹⁹ W/cm² intensity (setup 1a), while the magenta dots describe proton number obtained in laser interactions with thin metal foils at 10²¹ W/cm² laser intensity (setup 2a). Error bars represent the accuracy of reaction yield and the width of nuclear resonance used for spectral reconstruction. The dashed curves demonstrate the different slopes of proton spectra. PIC-simulated proton spectrum is shown as blue solid line. b IP signal produced by electrons above 7.5 MeV directed along the laser axis (FWHM range, black dashed circle) with positions of activation samples for detection of (p,xn)-reactions and expected direction of TNSA-accelerated proton beam (foil-target normal was +10^∘ to laser direction). The half protons divergence angle of 6^∘–7^∘ was estimated assuming a Gaussian angular distribution at the target normal and taking into account proton-induced reaction yields measured at 5^∘ and 15^∘ (black dotted circle). c Momentum diagram of protons from 3D PIC simulation (VLPL code). Transversal and longitudinal momenta are shown as normalized values, where the colors display the proton energies. Dashed lines indicate the half divergence angle ranges at 5^∘ and 10^∘.