With the advent of high power laser facilities new opportunities for scaled laboratory experiments of astrophysical processes have become available. Here we show that experiments at National Ignition Facility (NIF) laser have reached the condition where second order Fermi acceleration can be directly investigated with the available diagnostics. This requires measuring the diffusion of 3 MeV protons produced within a turbulent plasma. Since Fermi acceleration is essentially a biased diffusion process and using existing solutions, we show that a significant broadening of the initial proton distribution is expected for those particles existing the plasma.