Relativistic self-distortion of a laser pulse and ponderomotive acceleration of electrons in an axially inhomogeneous plasma

Relativistic self distortion of a Gaussian laser pulse in inhomogeneous plasma in one dimension is investigated. The relativistic mass effect causes different portions of the pulse to travel with different group velocities leading to the steepening of the pulse front and broadening of the rear. This asymmetry created in the pulse shape gives rise to stronger ponderomotive force on electrons at the front and weaker at the rear. The fast moving electrons under this force are shown to have very significant net energy gain. The energy gain increases with the density scale-length and then saturates.