The self-focusing of hollow gaussian laser beam in magnetized plasma with transverse magnetic field by operating relativistic nonlinearity

This article presents a theoretical study of the self-focusing process of a hollow Gaussian laser beam (HGLB) inside a plasma medium placed in a magnetic field perpendicular to the direction of the hollow Gaussian laser beam propagation. The self-focusing was studied using relativistic nonlinearity. Particular mathematical equations were derived that describe the nonlinear behavior of hollow Gaussian laser beam when they propagate inside the plasma, and they were solved. This behavior was simulated using the MATLAB program. This study dealt with the effect of order and initial intensity of hollow Gaussian laser beam on the self-focusing process and the impact of the applied magnetic field and plasma density on the self-focusing process.