Nonlinear third-harmonic generation in a plasma by a Gaussian electromagnetic beam: Effect of self-focusing

With the use of expressions for the nonlinear current density derived previously, the generation of the third harmonic in a collisional plasma by a Gaussian electromagnetic beam has been studied when the power of the beam exceeds the critical power for self-focusing. The self-focusing is caused by the nonuniform heating and redistribution of electrons. It is seen that the self-focusing of the main beam enhances the power of harmonic output by about three orders of magnitude in a typical case in the paraxial-ray approximation. The treatment is applicable after a time on the order of the energy relaxation time [$\sim {\left(\frac{2m\nu }{M}\right)}^{-1\mathrm{}}$].