Energetic proton acceleration in ultra-intense laser interaction with super-low density targets

Aiming to increase the maximum energy of laser-accelerated proton beams, we have studied the relation between maximum proton energies and electron distribution functions, which determine electro-static sheath field to accelerate protons. We have proposed to increase the maximum proton energy using a distribution function of hot electrons produced by an interaction between ultra-short pulse laser ($<$ 100 f sec) and low density plasma ($<$ 10$^{20}$ cm$^{-3})$. We have carried out the experiment using a silica foam (aerogel) with a density of 3mg /cc as a solid target and 30 f-sec short pulse laser light at the laser intensity of 10$^{20}$ W/cm$^{2}$. We will report the result of the experiments and simulations.