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A superintense laser pulse illuminating a thin solid-density foil can, inprinciple, accelerate the entire foil, therefore yielding dense, collimated,and quasi-monoenergetic ion beams. These unique features render radiationpressure acceleration in the light sail regime a promising accelerationmechanism suited for applications where dense and high-flux ion beams arerequired. However, the onset of several instabilities typically results intofoil deformation and heating, which cause premature termination of theradiation pressure acceleration stage and strong broadening of the ionspectrum. Here we show that (i) a relation between the attainable ion energyper nucleon and the development of instabilities exists, such that increasingthe ion energy results into an increase of transverse modulation effects and,(ii) that the above relation can be weakened with proper matching of laserpulse-foil parameters, such that high-energy dense ion beams with high-qualityspectral features can be produced.

High-Energy and High-Quality Ion beams in Light Sail Acceleration