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The generation of compact, high-energy ion beams is one of the most promisingapplications of intense laser-matter interactions, but the control of the beamspectral quality remains an outstanding challenge. We show that in radiationpressure acceleration of a thin solid target the onset of electron heating isdetermined by the growth of the Rayleigh-Taylor-like instability at the frontsurface and must be controlled to produce ion beams with high spectral qualityin the light sail regime. The growth rate of the instability imposes an upperlimit on the laser pulse duration and intensity to achieve high spectral beamquality and we demonstrate that under this optimal regime, the maximum peak ionbeam energy per nucleon is independent of target density, composition, andlaser energy (transverse spot size). Our predictions are validated by two- andthree-dimensional particle-in-cell simulations, which indicate that for recentand upcoming experimental facilities using ultrashort ($\lesssim 25$ fs) laserpulses it is possible to produce $100 - 300$ MeV proton beams with $\sim 30\%$energy spread and high laser-to-proton energy conversion efficiency.

Radiation pressure acceleration of high-quality ion beams using ultrashort laser pulses