Self-focusing of a circularly polarized hollow Gaussian laser beam in the parallel propagation through a relativistic two-temperature hot magnetoplasma

In this paper, the self-focusing (SF) process of an intense hollow Gaussian laser beam (HGLB) in a hot magnetoplasma is studied. Based on a relativistic two-fluid model, the propagation of an intense circularly polarized (CP) HGLB along the external magnetic field is considered. In a hot magnetoplasma with ions and electrons at different temperatures, the nonlinear wave equation describing the parallel propagation of the HGLB is derived for right- and left-handed circularly polarized modes. The laser beam’s transverse evolution under SF for both polarizations and all HGLB modes is considered, and the effects of electron and ion temperatures, plasma density, initial spot size, and external magnetic field on the SF dynamics are studied. It is observed that for both polarizations and across all modes, SF occurs within a specific range of initial laser beam amplitudes. For the third-order Kerr nonlinearity, the existence of a minimum value (threshold) of the initial amplitude has been proven. However, in this study, the appearance of a maximum in the initial amplitude is due to the exponential terms in the ponderomotive nonlinearity. For all modes, below the threshold, the beam width parameter increases continuously with propagation distance. However, for a range larger than the maximum amplitude, even when the beam width parameter is greater than unity and the laser beam is defocused, it oscillates periodically while remaining confined.