INTERACTION OF A WEAKLY NONLINEAR LASER-PULSE WITH A PLASMA

Based on a one-dimensional model, a perturbation expansion is carried out to solve the equations describing a weakly nonlinear laser pulse i n a plasma in which the electrons are treated relativistically and the plasma frequency is much less than the laser frequency. To lowest ord er, the expansion yields two coupled equations for the vector and scal ar potentials. For a pulse which is long compared with a plasma wavele ngth, the coupled equations reduce to the nonlinear Schrodinger equati on with well-known soliton solutions. An initial pulse of hyperbolic-s ecant shape which is short compared with a plasma wavelength broadens and acquires a characteristic asymmetric shape with a steep trailing e dge and a much broader, gently sloping front portion, and has a freque ncy and wave-number shift which vary from a positive value at the fron t to a negative value at.the rear of the pulse. The peak and rear part of a short pulse are strongly influenced by nonlinear effects, wherea s the front is governed primarily by linear dispersion. The average pu lse frequency continually decreases as energy is lost to the plasma wa ke. The wake-field phase velocity is shown to be approximately equal t o the velocity of the pulse peak.