  We propose a new acceleration scheme that combines shock wave acceleration
(SWA) and light pressure acceleration (LPA). When a thin foil driven by light
pressure of an ultra-intense laser pulse propagates in underdense background
plasma, it serves as a shock-like piston, trapping and reflecting background
protons to ultra-high energies. Unlike in SWA, the piston velocity is not
limited by the Mach number and can be highly relativistic. Background protons
can be trapped and reflected forward by the enormous "dragging field" potential
behind the piston which is not employed in LPA. Our one- and two-dimensional
particle-in-cell simulations and analytical model both show that proton
energies of several tens to hundreds of GeV can be obtained, while the
achievable energy in simple LPA is below 10 GeV.

Plasma Physics;High Energy Astrophysical Phenomena