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The self-focusing of an intense electromagnetic beam in a collisional magnetoactive plasma has been investigated by the perturbation method. Considering the relativistic and ponderomotive nonlinearities and the first three terms of perturbation expansion for the electron density and velocity, the nonlinear wave equation is obtained. This wave equation is solved by applying the source dependent expansion method and the evolution of electromagnetic beam spot-size is discussed. It is shown that the laser spot-size decreases with increasing the collision frequency and external magnetic field strength.

The linear response theory has been employed to investigate the effect of electrons' intrinsic spin on the propagation of surface waves in a magneto-active quantum plasma half-space. Using fluid Maxwell equations, we obtained two coupled differential equations for perturbed magnetic field and density. The method of characteristic equation is used to find the exact solution to the system of coupled differential equations and exact dispersion relation for the quantum surface waves. The dispersion relation is numerically analysed to study spin and magnetization effects, and it is shown that both of these effects increase group velocity of surface waves, while spin effect reduces phase velocity as a result of the opposite direction of magnetic moment of electrons with respect to external magnetic field. KEYWORDShalf-spin quantum plasma, magnetization current, magnetized plasma, surface waves 1

The nonlinear dynamics of filamentation instability and magnetic field in a current-carrying plasma is investigated in the presence of quantum effects using the quantum hydrodynamic model. A new nonlinear partial differential equation is obtained for the spatiotemporal evolution of the magnetic field in the diffusion regime. This equation is solved by applying the Adomian decomposition method, and then the profiles of magnetic field and electron density are plotted. It is shown that the saturation time of filamentation instability increases and, consequently, the instability growth rate and the magnetic field amplitude decrease in the presence of quantum effects.

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