  A comprehensive theory is proposed to describe the propagation and absorption
of ultra-intense, short laser pulse through the under-dense plasma. The kinetic
aspects of plasma are fully incorporated using extensive particle-in-cell (PIC)
simulations. It is turned out that the plasma behavior is characterized by both
its density and the ratio of the pulse length to the plasma wavelength.
According to exact analyses and direct simulation evidences, at ultra-low
densities the laser pulse is adiabatically depleted (absorbed) by the wake
excitation. And the depletion is accompanied by the overall radiation
red-shift. At these densities, for pulse lengths larger than the plasma
wavelength the Raman type scatterings also occur without causing instability.
When the plasma density grows toward the critical density, a completely new
regime appears with the main character of highly unsteady light propagation.
Here, based on analyses and simulations, the radiation pressure induced wave
breaking (RPIWB) heavily destroys the oscillatory structure of the electron
wave behind the first plasma period. On the other hand, the electron density
profile induced by the ponderomotive force ahead of the pulse begins to steepen
and eventually acts as a flying mirror. As a result, the pulse becomes bake
scattered and its penetration becomes limited. The radiation pressure of
reflecting pulse sustains a longitudinal electric field which accelerates
electrons produced via RPIWB causing the plasma to undergo volumetric heating.
Mostly important, based on a newly proposed model it is shown that the
interaction becomes saturated at a definite time and that the overall
absorption and plasma heating are directly related to this time. Also it is
found that the saturation time decreases by a factor of ( , and are initial
electron density, critical density and initial laser gamma factor)...
