This study investigates the impact of self-focusing on higher harmonic generation (HHG) within a pre-formed, collisionless parabolic plasma channel. A \(q\) -Gaussian laser beam’s non-uniform intensity profile induces a ponderomotive force, leading to carrier redistribution and a transverse density gradient. This gradient excites a plasma wave that interacts with the laser, generating HHG. Using moment theory, we derived a differential equation describing the laser beam’s spot size evolution and numerically solved it to analyze the effects of laser intensity, wavefront distortion, plasma density, channel depth, and harmonic order on beam width and HHG yield. Our findings contribute to understanding the interplay between self-focusing and HHG in parabolic plasma channels, providing valuable insights for optimizing HHG efficiency.
