Effect of self-focusing of a \(q\) -Gaussian laser beam on higher harmonic generation in a preformed collisionless parabolic plasma channel has been investigated. The ponderomotive force due to non uniform intensity distribution of the laser beam redistributes carriers from high field region to low field region, resulting in a transverse density gradient in the channel. This gradient generates a plasma wave at the pump frequency, which interacts with the incident laser beam and generates higher harmonics of the incident laser beam. The moment theory has been used to derive a differential equation for the spot size of the laser beam propagating through the channel. The differential equation has been solved numerically. The study investigates the effect of the intensity of the laser beam, deviation of intensity distribution of the laser beam along its wave front from Gaussian distribution, plasma density, and depth of channel on the beam width of the laser beam and harmonic yield. The effect of the order of higher harmonic on harmonic yield has also been investigated.
