In this manuscript, we present a theoretical investigation of the self-focusing propagation of higher-order circular cosine-hyperbolic-Gaussian beams (CiChGB) in non-relativistic collisionless plasma under the higher-order paraxial approach. The analysis employs the framework of the Wentzel–Kramers–Brillouin approximation (WKB) and supplemented by the higher-order paraxial contribution of the spatial intensity distribution. The study examines the influence of the beam order components of the cosine-hyperbolic function and decentered parameter on the intensity distribution of the CiChGB. The attention is given to the impact of the beam order on the self-focusing propagation of the CiChGB and the higher-order contributions to the local dielectric constant of collisionless plasma. It is observed that, at higher decentered parameter of the beam profile, the higher-order coefficients of dielectric constant of the collisionless plasma are significantly suppressed. This theoretical framework provides insights into the self-focusing propagation of higher-order CiChGB in the plasma environments.
Pawar et al. (Fri,) studied this question.