Radiation pressure acceleration: The factors limiting maximum attainable ion energy

Radiation pressure acceleration (RPA) is a highly efficient mechanism of laser-driven ion acceleration,with near complete transfer of the laser energy to the ions in the relativistic regime. However,there is a fundamental limit on the maximum attainable ion energy, which is determined by thegroup velocity of the laser. The tightly focused laser pulses have group velocities smaller than thevacuum light speed, and, since they offer the high intensity needed for the RPA regime, it is plausiblethat group velocity effects would manifest themselves in the experiments involving tightlyfocused pulses and thin foils. However, in this case, finite spot size effects are important, andanother limiting factor, the transverse expansion of the target, may dominate over the group velocityeffect. As the laser pulse diffracts after passing the focus, the target expands accordingly due tothe transverse intensity profile of the laser. Due to this expansion, the areal density of the targetdecreases, making it transparent for radiation and effectively terminating the acceleration. The off normalincidence of the laser on the target, due either to the experimental setup, or to the deformationof the target, will also lead to establishing a limit on maximum ion energ