Effect of small focus on electron heating and proton acceleration in ultra-relativistic laser-solid interactions

Acceleration of particles from the interaction of ultra-intense laser pulses up to $5\times10^{21}$ Wcm$^{-2}$ with thin foils is investigated experimentally. The electron beam parameters varied with decreasing spot size, not just laser intensity, resulting in reduced temperatures and divergence. In particular, the temperature saturated due to insufficient acceleration length in the tightly focused spot. These dependencies affected the sheath-accelerated protons, which showed poorer spot-size scaling than widely used scaling laws. It is therefore shown that maximizing laser intensity by using very small focii has reducing returns for some applications.