The future applications of the short-duration, multi-MeV ion beams produced in the interaction of high-intensity laser pulses with solid targets will require improvements in the conversion efficiency, peak ion energy, beam monochromaticity, and collimation. Regimes based on Radiation Pressure Acceleration (RPA) might be the dominant ones at ultrahigh intensities and be most suitable for specific applications. This regime may be reached already with present-day intensities using circularly polarized (CP) pulses thanks to the suppression of fast electron generation, so that RPA dominates over sheath acceleration at any intensity. We present a brief review of previous work on RPA with CP pulses and a few recent results. Parametric studies in one dimension were performed to identify the optimal thickness of foil targets for RPA and to study the effect of a short-scalelength preplasma. Three-dimensional simulations showed the importance of ``flat-top radial intensity profiles to minimise the rarefaction of thin targets and to address the issue of angular momentum conservation and absorption.
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