Relativistic self-focusing of finite Airy-Gaussian beams in collisionless plasma using the Wentzel‐Kramers‐Brillouin approximation

In this paper, we present a preliminary study of relativistic self-focusing of finite Airy-Gaussian beams in collisionless plasma taking into consideration the relativistic nonlinearity in the dielectric constant. The differential equation for the beam width parameter of the finite Airy-Gaussian beam is derived by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations through parabolic wave equation approach. The behavior of beam width parameter with distance of propagation is investigated at different parameters of plasma and those of the considered beams family. Our results detect that the beam is more focused at higher values aperture coefficient and higher intensity parameter. Furthermore, a strong oscillatory behavior of the beam width parameter and better focusing during laser propagation in plasma is apparent.