Effect of self-focusing of bessel gauss laser beam on excitation of electron plasma wave in collisionless plasma with axial density ramp

A theoretical investigation has been conducted to analyze the dynamics of electron plasma waves (EPWs) induced by Bessel-Gauss laser beams in plasmas featuring an axial density ramp. The study involves evaluating how the self-focusing of the laser beam influences the power of the laser-excited EPWs. As the laser beam traverses the plasma, it triggers the generation of an EPW at the frequency omega ep\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\varvec{\omega}}}_{\mathbf{e}\mathbf{p}}$$\end{document}. This EPW, affected by the optical nonlinearity of the plasma, becomes nonlinearly coupled to the laser beam due to the ponderomotive nonlinearity of plasma electrons. Employing variational theory, semi-analytical solutions for the coupled nonlinear wave equations governing the pump wave and EPW have been obtained using the W.K.B approximation technique. The findings highlight a significant impact of the self-focusing effect of the pump beam on the power of the EPW.