Abstract
In this paper, the process of second harmonic generation (SHG) is studied in underdense plasma in the presence of a periodic magnetic field. It is shown that the difference of momentums of photon of second harmonic ( ℏ k → ( 2 ω ) ) and two photons of main wave ( 2 ℏ k → ( ω ) ) can be provided by momentum of everyone of Fourier components of periodic magnetic field so that momentum of nth Fourier component can be chosen by n ℏ k → 0 = ℏ k → 2 − 2 ℏ k → 1 . It is also proven that the highest efficiency of second harmonic generation will be provided by the first Fourier component of periodic magnetic field ( k → 0 = k → 2 − 2 k → 1 ) . It is revealed that periodic magnetic field can produce longitudinal waves at ( ω , n k → 0 + k → 1 ) and ( 2 ω , 2 k → 1 ) as well.
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