Self-focusing of higher-order asymmetric elegant Hermite-cosh-Gaussian laser beams in collisionless magnetized plasma

In the present paper, we have explored the complexity in self-focusing of asymmetric elegant Hermite-cosh-Gaussian (EHChG) laser beams in magnetized plasmas. We have studied transverse electromagnetic (TEM) mode indices (m, n) of laser with distinct values (0, 0), (0, 2) and (0, 4). The nonlinearity in dielectric constant considered herein is mainly due to the ponderomotive force. General form of differential equations for beam-width parameters in both transverse dimensions of the beam are established by using WKB and paraxial approximations through parabolic wave equation approach. The behaviour of beam-width parameters with dimensionless distance of propagation is studied at different parameters of plasma and those of the considered beams family