This research investigates how intense, \(\:q\) -Gaussian-shaped laser beams are affected as they propagate through pre-shaped, parabolic channels in hot, ionized gas (plasma). The study employs an approximate numerical technique based on the moment theory approach within the W.K.B. approximation to solve the non-linear Schrodinger wave equation for the laser beam’s behavior. The analysis focuses particularly on how the beam’s width and its phase delay change as it travels along the channel, additionally exploring the possibility of self-trapping, where the laser beam becomes confined by the plasma channel.
