Self-compression of elliptical q-Gaussian laser pulse in plasmas with axial density ramp

Theoretical investigation on self-compression of a laser pulse with q-Gaussian spatial irradiance profile propagating through collisionless plasmas with axial density ramp has been presented. Particularly the dynamics of pulse width, beam widths and axial phase of the laser pulse have been investigated in detail. Effect of the ellipticity of the cross section of the laser pulse also has been incorporated. Using variational theory based on Lagrangian formulation nonlinear partial differential equation (P.D.E) governing the evolution of the pulse envelope has been reduced to a set of coupled ordinary differential equations for the pulse width and beam widths of the laser pulse. The evolution equation for the axial phase of the laser beam has been obtained by the Fourier transform of the amplitude structure of the laser pulse from coordinate space to (k(x), k(y)) space. The differential equations so obtained have been solved numerically to envision the effect of laser-plasma parameters on the propagation dynamics of the laser pulse.