The Self-focusing of High Power Hollow Gaussian Laser Beam in Magnetized Plasma by Operating the Relativistic Nonlinearity

Abstract

This article examines the influence of the order and intensity of a paraxial hollow Gaussian laser beam (HGLB) on the self-focusing phenomenon through magnetized plasma due to the relativistic nonlinearity. The appropriate differential equations of the nonlinear propagation of (HGLB) are derived then they have been solved numerically by designing a Matlab program. It is found that the self-focusing of (HGLB) will be decreased when its order are raised. It is observed that the HGLB is manifesting a soliton wave guide form at the order (n=2) of (HGLB) this happened because the equilibrium between the diffraction term and self-focusing term. as The relationship of laser beam intensity with self-focusing is important where The amount of self-focusing increases with increasing intensity of (HGLB) where  . The self-focusing is weak to the point that it may not appear, but the phenomenon of natural diffraction may occur as a result of the absence of a relativistic nonlinear interaction if the intensity of the incident laser beam is insufficient for the occurrence of such an interaction inside the magnetised plasma.