Self-Focusing of Rippled Elliptical q-Gaussian Laser Beam in Plasma with Axial Density Ramp

Theoretical investigation on self-focusing of an elliptical q-Gaussian laser beam, carrying an intensity ripple over its cross section, in plasma with an axial density ramp has been presented. The optical nonlinearity of plasma has been modeled by the relativistic mass nonlinearity of plasma electrons in the field of a laser beam. Using the variational theory approach, semi-analytical solutions of the wave equations for the fields of the main beam and that of the ripple have been obtained. Emphasis has been put on the evolutions of the beam widths of the main beam and that of the ripple.