Abstract This study investigates the propagation of a hollow Gaussian beam (HGB) through a collisionless plasma medium containing superimposed ripples, incorporating relativistic nonlinear effects. The Wentzel-Kramers-Brillouin (WKB) paraxial ray approximation and the eikonal method are employed to derive governing equations for the self-focusing of the main beam, the ripples, and the excitation of plasma waves under these conditions. Our analysis demonstrates that the presence of ripples significantly alters the propagation dynamics of HGBs and influences the excitation of electron plasma waves (EPWs). The order and phase angle of ripples influence the main beam dynamics and EPW propagation. Both the HGB order and ripple order affect the ripple dynamics and EPW power. The various orders of the HGB and the angle between the ripple and the main beam affect the ripple’s focusing behavior. These factors collectively influence the intensity of the excited plasma wave. Our findings contribute to a deeper understanding of laser-plasma interactions involving pre-existing ripples on HGB.
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