  We review recent PIC simulation results which show that double-sided
irradiation of a thin over-dense plasma slab with ultra-intense laser pulses
from both sides can lead to sustained comoving Poynting flux acceleration of
electrons to energies much higher than the conventional ponderomotive limit.
The result is a robust power-law electron momentum spectrum similar to
astrophysical sources. We discuss future ultra-intense laser experiments that
may be used to simulate astrophysical particle acceleration.
