Self-focusing of the high intensity ultra short laser pulse propagating through relativistic magnetized plasma

In this paper, evolution of the spot size of the ultra short intense laser beam propagating in underdense magnetized cold plasma, taking into account the nonlinearity up to third order and the relativistic effect, has been studied. The plasma embedded in a constant external magnetic field that is set in the plane perpendicular to the electric field vector of the laser beam with different directions. The paraxial wave equation in plasma has been used and the source dependent expansion (SDE) method is employed to solve the equation. Using continuity equation and equation of motion for plasma electrons in the electric field of laser beam a set of equations for the evolution of laser beam structure in plasma is found. Results show that imposing the external magnetic field enhances self-focusing property of the laser beam. Taking into account the relativistic effect increases the effect of the external magnetic field on self-focusing of the laser beam. Increasing the angle between the laser beam magnetic field and external magnetic field will decrease the self-focusing property.