Langmuir Wave-Assisted Two-Photon Decay of an Amplitude-Modulated Gaussian Laser Beam in Rippled Density Plasma

Abstract

In this theoretical investigation, two-photon decay of an amplitude-modulated Gaussian laser \({(\omega }_{0},{k}_{0})\) into a pair of electromagnetic waves with frequencies \({\omega }_{1},{ \omega }_{1}\) and wave numbers \({k}_{1},{k}_{2}\), respectively, is shown to be susceptible in the presence of a Langmuir wave \(\left({\omega }_{r},{k}_{r}\right)\) in a density rippled unmagnetized plasma. The decay waves propagate in sideward direction so that the momentum remains conserved. The density ripple plasma compensates for the wave number mismatch between pump and decay waves; otherwise, such decay of electromagnetic wave is not allowed. The necessary phase matching conditions for the interaction are considered as \({\overrightarrow{k}}_{r}={\overrightarrow{k}}_{0}-{\overrightarrow{k}}_{1}-{\overrightarrow{k}}_{2}, {\omega }_{r}={\omega }_{0}-{\omega }_{1}-{\omega }_{2}\). The discrepancy can be attributed to the static density ripple. The momentum transfers between the pump and decay wave by the density ripple. The decay of pair of electromagnetic waves occurs at plasma densities below one-fourth of the critical density. The decay waves propagate at finite angles to the amplitude-modulated Gaussian laser beam. The obtained growth rate is strongly dependent on the rippled density and laser beam modulation index. At the centre of laser beam propagation transverse distance, the growth rate of decay wave is attained the peak value. The various graphical diagrams show that growth rate decreases with the increase in the normalized frequency of pump laser beam and angle \({\theta }_{r}\).