The effects of intervals of the critical beam power \({p}_{0}\) of q-Gaussian laser beams in collisional plasma have been investigated theoretically in the present study. The beam-width parameter (BWP) equation is minimized into two variables, the critical beam power \({(p}_{0})\) and the q parameter, which governs the self-trapping, self-focusing, and defocusing of q-Gaussian laser beams in collisional plasmas. By utilizing Akhmanov’s parabolic wave equation approach under paraxial and Wentzel–Kramers–Brillouin (WKB) approximations in the present study, the nonlinear second-order differential equation is set up for the BWP f and solved numerically using fourth-order Runga–Kutta method. Primarily, the nonlinearity of the dielectric function used herein is due to collisional plasma. Non-linearity arises due to the heating of carriers. To explore the propagation behaviour of q-Gaussian laser beam in collisional plasma the effect of intervals of critical beam power \({p}_{0}\) is further utilized in the present study. The results are revealed graphically and discussed. These results may have potential applications in laser-based plasma technologies, like inertial confinement fusion and particle acceleration.
