Multi-Cascade Proton Acceleration by Superintense Laser Pulse in the   Regime of Relativistically Induced Slab Transparency
  A regime of multi-cascade proton acceleration in the interaction of $10^{21}-10^{22}$ W/cm$^2$ laser pulse with a structured target is proposed. The regime is based on the electron charge displacement under the action of laser ponderomotive force and on the effect of relativistically induced slab transparency which allows to realize idea of multi-cascade acceleration. It is shown that a target comprising several properly spaced apart thin foils can optimize the acceleration process and give at the output quasi-monoenergetic beams of protons with energies up to hundreds of MeV with energy spread of just few percent. 
A. A. Gonoskov, A. V. Korzhimanov, V. I. Eremin, A. V. Kim and A. M.   Sergeev