Magnetic Field Effect on the Nonlinear Propagation of Hollow Gaussian Laser Beam Inside Relativistic Plasma

In this manuscript the electrons in the collision less plasma will earn a high relativistic motion caused by the high intensity Hollow Gaussian laser beam (HGLB) thus the dielectric constant of plasma will be modified and the plasma will manifest a nonlinear a self-focusing phenomenon.

The final differential equation of (HGLB) self-focusing has been derived then it is solved numerically by designing an appropriate Matlab program.

This technique has prove that, in presence of an external longitudinal magnetic field, the self-focusing of (HGLB) will enhance thus the initial laser intensity will raise to ten times or more.