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Dense high-energy monoenergetic proton beams are vital for wide applications,thus modern laser-plasma-based ion acceleration methods are aiming to obtainhigh-energy proton beams with energy spread as low as possible. In this work,we put forward a quantum radiative compression method to post-compress a highlyaccelerated proton beam and convert it to a dense quasi-monoenergetic one. Wefind that when the relativistic plasma produced by radiation pressureacceleration collides head-on with an ultraintense laser beam, large-amplitudeplasma oscillations are excited due to quantum radiation-reaction and theponderomotive force, which induce compression of the phase space of protonslocated in its acceleration phase with negative gradient. Our three-dimensionalspin-resolved QED particle-in-cell simulations show that hollow-structureproton beams with a peak energy $\sim$ GeV, relative energy spread of fewpercents and number $N_p\sim10^{10}$ (or $N_p\sim 10^9$ with a $1\%$ energyspread) can be produced in near future laser facilities, which may fulfill therequirements of important applications, such as, for radiography of ultra-thickdense materials, or as injectors of hadron colliders.

Generation of quasi-monoenergetic proton beams via quantum radiative compression