Relativistic self-focusing of finite Airy-Gaussian laser beams in cold quantum plasma

In the present theoretical investigation, the phenomenon of relativistic self-focusing of finite Airy-Gaussian (AiG) laser beams in cold quantum plasma has been explored under standard Wentzel–Kramers–Brillouin (WKB) and paraxial approximations. It is worth and interesting to note at the beginning that AiG laser beams are invariant under paraxial transformation. Thus, the paraxial approximation adopted herein is naturally justified. The added interest to investigate finite AiG laser beams is due to their unique features of propagation. This leads them to be potential candidate beams to travel several Rayleigh lengths through plasma. Based on these vital characteristic, it would be interesting to study the propagation dynamics of finite AiG laser beams in cold quantum plasma. At the end, the effect of modulation parameter, critical initial beam radius and critical intensity parameter on the phenomenon of self-focusing is studied. The results are presented graphically and discussed.