The present article investigates the nonlinear self-focusing of an intense laser beam circularly polarized inside a non-Maxwellian magnetized plasma. It has been assumed that the plasma is embedded in a non-uniform axial magnetic field with a positive slope. Through applying relativistic fluid momentum and Maxwell’s equations, the nonlinear equation of electromagnetic wave propagation for a circular polarized laser beam with right-and left-hand polarizations has been derived. Subsequently, a differential equation was obtained for the evolution of the laser spot-size through applying the source-dependent expansion method. The equation was then solved using the fourth-order Runge-Kutta method. Effects of the simultaneous presence of the superthermal particles and non-uniform magnetic field on the evolution of laser spot-size were studied, and variations of the normalized spot-size of the laser with respect to the variables κe and κi were discussed. It was also indicated that the solution of the present study confirms the results of the Maxwellian plasma in extreme conditions. Numerical results indicate that the self-focusing of the laser beam in the presence of an external nonuniform magnetic field inside non-Maxwellian plasma was improved in comparison with Maxwellian plasma. In addition, results show that an increase in the nonuniform external magnetic field leads to the reduction of the critical power required for the self-focusing of the laser beam inside the plasma.
