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Generation of the Second Harmonic to the Extraordinary Wave in Inhomogeneous Plasmas

Second harmonic generation in cold inhomogeneous magnetoactive plasma is investigated by means of the mode coupling theory. It is demonstrated that the generation from the upper-hybrid layer, where the pump field has a second-order singularity is negligible compared to the contribution of the wave-number matching region k(2ω0) = 2k(ω0), which can exist in the case of the extraordinary polarized pump wave. Numerical results are presented, predicting the energy transfer efficiency ∼ 10%.