  The propagation of ultra intense laser pulses through matter is connected
with the generation of strong moving magnetic fields in the propagation channel
as well as the formation of a thin ion filament along the axis of the channel.
Upon exiting the plasma the magnetic field displaces the electrons at the back
of the target, generating a quasistatic electric field that accelerates and
collimates ions from the filament. Two-dimensional Particle-in-Cell simulations
show that a 1 PW laser pulse tightly focused on a near-critical density target
is able to accelerate protons up to an energy of 1.3 GeV. Scaling laws and
optimal conditions for proton acceleration are established considering the
energy depletion of the laser pulse.
