This paper presents an investigation of self-focusing of a q-Gaussian laser beam and its effect on harmonic generation in a preformed collisionless parabolic plasma channel. In the presence of a q-Gaussian laser beam, the carriers get redistributed from high field region to low field region on account of ponderomotive force as a result of which a transverse density gradient is produced in the channel which in turn generates plasma wave at pump frequency. Generated plasma wave interacts with the incident laser beam and generate higher harmonics of the incident laser beam. Moment theory has been used to derive differential equation for the spot size of laser beam propagating through the channel. The differential equation so obtained has been solved numerically. The effect of the intensity of laser beam, deviation of intensity distribution of laser beam along its wave front from Gaussian distribution, plasma density and depth of channel on beam width of laser beam and harmonic yield has been investigated. The effect of order of higher harmonic on harmonic yield has been also investigated.
