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We present a theoretical and simulation study of laser acceleration of quasi-monoenergetic protons in a thin foil irradiated by high intensity laser light. The underlying physics of radiation pressure acceleration (RPA) is discussed, including the importance of optimal thickness and circularly polarized light for efficient acceleration of ions to quasimonoenergetic beams. Preliminary two-dimensional simulation studies show that certain parameter regimes allow for stabilization of the Rayleigh-Taylor instability and possibility of acceleration of monoenergetic ions to an excess of 200MeV, making them suitable for important applications such as medical cancer therapy and fast ignition. © 2010 American Institute of Physics.