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By using three-dimensional particle-in-cell simulations with synchrotron radiation damping incorporated, dynamics of ultra-intense laser driven mass-limited foils is presented. When a circularly polarized laser pulse with a peak intensity of ∼1022 W/cm2 irradiates a mass-limited nanofoil, electrons are pushed forward collectively and a strong charge separation field forms which acts as a “light sail” and accelerates the protons. When the laser wing parts overtake the foil from the foil boundaries, electrons do a betatron-like oscillation around the center proton bunch. Under some conditions, betatron-like resonance takes place, resulting in energetic circulating electrons. Finally, bright femto-second x rays are emitted in a small cone. It is also shown that the radiation damping does not alter the foil dynamics radically at considered laser intensities. The effects of the transverse foil size and laser polarization on x-ray emission and foil dynamics are also discussed.


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