Effect of a periodic magnetic field on phase matching condition in second harmonic generation at interactions of laser-plasma

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 ((h) over right arrow(k) over right arrow (2 omega)) and two photons of main wave (2 (h) over right arrow(k) over right arrow(omega)) 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 (h) over right arrow(k) over right arrow (0) = (h) over right arrow(k) over right arrow (2) - 2 (h) over right arrow(k) over right arrow (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) over right arrow (0) = (k) over right arrow (2)-2 (k) over right arrow (1)). It is revealed that periodic magnetic field can produce longitudinal waves at (omega, n (k) over right arrow (0) + (k) over right arrow (1)) and (2 omega, 2 (k) over right arrow (1)) as well. (C) 2010 Elsevier GmbH. All rights reserved.