Two-XUV-photon double ionization of Ne, induced by an intense few-pulse attosecond train with a \ensuremath{\sim}4 fs envelope duration is investigated experimentally and theoretically. The experiment is performed at ELI-ALPS (Extreme Light Infrastructure Attosecond Light Pulse Source) utilizing the recently constructed 10 Hz gas phase high-order harmonic generation SYLOS GHHG-COMPACT beamline. A total pulse energy up to \ensuremath{\sim}1 \ensuremath{\mu}J generated in argon in conjunction with high-reflectivity optics in the XUV region allowed the observation of the doubly charged state of Ne induced by 40 eV central XUV-photon energies. The interaction of the intense attosecond pulse train with Ne is also theoretically studied via second-order time-dependent perturbation theory equations of motion. The results of this work, combined with the feasibility of conducting XUV-pump--XUV-probe experiments, constitute a powerful tool for many potential applications. Those include attosecond pulse metrology as well as time-resolved investigations of the dynamics underlying direct and sequential double ionization and their electron correlation effects.
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