A new scheme of proton acceleration from a laser-driven near-critical-density plasma is proposed. Plasma with a tailored density profile allows a two-stage acceleration of protons. The protons are pre-accelerated in the laser-driven wakefields, and are then further accelerated by the collisionless shock, launched from the rear side of the plasma. The shock has a small transverse size, and it generates a strong space-charge field, which defocuses protons in such a way, that only those protons with the highest energies and low energy spread remains collimated. Theoretical and numerical analysis demonstrates production of high-energy proton beams with few tens of percents energy spread, few degrees divergence and charge of few nC. This scheme indicates the efficient generation of quasi-monoenergetic proton beams with energies up to several hundreds of MeV with PW-class ultrashort lasers.
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