In current work, the beam-width parameter (BWP) equation is reduced to two variables such as q and critical beam power (p 0) which govern the propagation dynamics and intervals of critical beam power p 0 of a q-Gaussian laser beam have been investigated. The non-linear dependence of dielectric function in collisional plasma used herein is primarily because of heterogeneous heating of carriers along the wavefront of the laser beam. The influence of intervals of p 0 is further used to explore propagation dynamics of q-Gaussian laser beam in isotropic, homogeneous and collisional plasma has been studied. The Akhmanov’s parabolic equation approach under WKB (Wentzel-Kramers-Brillouin) and paraxial approximations are used in current work. The results have been found reasonably interesting which are revealed graphically and discussed.

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