Effect of a wiggler magnetic field on the sum frequency generation in laser-plasma interactions

In this paper, we consider the process of sum frequency generation (SFG) in an underdense plasma in the presence of a wiggler magnetic field. It is shown that the presence of magnetic field leads to generate not only the even-order nonlinear phenomena such as transversal sum frequency waves but also longitudinal waves at fundamental and sum frequencies. It is also revealed that the wave vector k→0 of wiggler magnetic field acts as a virtual photon of quantum energy zero and momentum ℏk→0 so that phase-matching condition is provided by the conservation of the momentum. Efficiency of the sum frequency generation is considered at different intensities, frequencies and number densities.