The maximum energy to which ions are accelerated in the interaction of a high power laser pulse with a thin foil target scales with the laser intensity, with a power-law that varies with the acceleration mechanism and laser pulse parameters. For fixed laser energy and pulse duration, maximizing the intensity by focusing to a smaller focal spot does not, however, necessarily result in higher-energy ions. For the case of relatively thick foil targets, it has been shown that self-generated magnetic fields and unfavourable changes to the temperature and divergence of the fast electron population injected into the target can result in lower-energy sheath-accelerated ions compared to that expected from intensity scaling laws.
We report results from an investigation of the influence of laser focusing on ion acceleration in the ultrathin target regime, for which high energy protons have been achieved by our group . We compare the interaction physics resulting from the use of f/3 and f/1 focusing geometries. Although f/1 focusing (achieved using a focusing plasma optic) produces a smaller nominal laser focal spot size and thus higher nominal peak intensity, more efficient ion acceleration to higher energies is achieved with the f/3 geometry for the case of expanding ultrathin foils undergoing relativistic self-induced transparency. Particle-in-cell simulations reveal that self-focusing in the expanding plasma produces a near-diffraction-limited focal spot, resulting in up to an order of magnitude higher focused intensity in the f/3 case. We also report on the extent to which this intensity enhancement is expected in the case of the short-pulse, ultrahigh-intensity regime that will soon be accessible using multi-petawatt lasers. The study is published in reference .
 A. Higginson et al., Nature Communications 9, 724 (2018)
 T. P. Frazer et al., Phys. Rev. Research 2, 042015(R) (2020)