  We briefly report on some results regarding the impact of very short and
intense laser pulses on a cold, low-density plasma initially at rest, and the
consequent acceleration of plasma electrons to relativistic energies. Locally
and for short times the pulse can be described by a transverse plane
electromagnetic travelling-wave and the motion of the electrons by a purely
Magneto-Fluido-Dynamical (MFD) model with a very simple dependence on the
transverse electromagnetic potential, while the ions can be regarded as at
rest; the Lorentz-Maxwell and continuity equations are reduced to the Hamilton
equations of a Hamiltonian system with 1 degree of freedom, in the case of a
plasma with constant initial density, or a collection of such systems
otherwise. We can thus describe both the well-known "wakefield" behind the
pulse and the recently predicted "slingshot effect", i.e. the backward
expulsion of high energy electrons just after the laser pulse has hit the
surface of the plasma.
