Characteristics of Self-Focusing of a Gaussian Laser Pulse Under Lateral and Axial Plasma Density Variations

In this paper, we present a paraxial description of relativistic self-focusing of a Gaussian laser beam in a plasma channel with the density distribution as a function of radial and axial variations. We have derived the nonlinear dielectric permittivity of plasma due to ponderomotive force and relativistic effects. The effect of different conditions of the inhomogeneous plasma and the laser pulse on self-focusing and defocusing of Gaussian laser beam propagation in the plasma is studied. We find that with an increase in the value of intensity of the beam, self-focusing enhances and shifts toward lower values of normalized propagation distance. The self-focusing length also increases with an increase in channel width. When the density rapidly increases along the propagation distance, the nonlinearity increases and gives self-focusing at shorter values of z.