Effect of transverse wiggler magnetic field on the growth rate of Raman backscattering of X-mode laser in rippled density plasma

A problem of Raman backscattering of laser beam propagating in a transversely wiggler magnetized plasma is considered in the presence of density ripples. Required dispersion relation of excited upper hybrid wave is derived by using the fluid model and taking into account the coupling between primary upper hybrid wave and density ripples. Using wave equation and nonlinear ponderomotive force and considering the coupling between the sideband wave and the upper hybrid wave, an expression of growth rate of this instability is obtained. The calculations demonstrate that the growth rate decreases by increasing the external magnetic field since the coupling between the scattered wave and upper-hybrid wave is weak and phase matching condition is not well-satisfied for higher external magnetic field. We have observed that instability is suppressed due to the presence of density ripples. Also, the suppression is significant for the case of small wave number density ripples as large faction of energy of upper hybrid electron wave transfers to the secondary hybrid electron wave.