Self-focusing of a laser pulse in a transient plasma

Following Akhmanov's approach, self-focusing of a laser pulse in a transient plasma has been studied. The beamwidth parameter and hence the laser intensity and the frequency shift (time derivative of the phase) have been evaluated as a function of time and the distance of propagation. It is seen that the time dependence of the axial intensity changes appreciably as the pulse propagates. The present investigation is restricted to a pulse whose incident intensity has Gaussian radial dependence.