Abstract
We have analytically investigated the influence of quasi-static background random density fluctuations on three-wave parametric coupling processes in a plasma. As an example, the case of stimulated Raman scattering is discussed in detail. After Fourier analysing the time variable and eliminating the amplitude of one of the stimulated waves, the basic equation describing the parametric process reduces to a fourth order differential equation with coefficients which are randomfunctions of the position co-ordinate. Standard methods from theory of wave propagation in random media can now be used. Assuming |ε(x)|=|n(x)-n0/n0|<<1, analytical results correct to order |ε2| are derived for the limiting cases when the correlation length of turbulence is long or short compared to the wavelength of parametrically interacting waves. It is found that in a statistically homogeneous medium, the effect of fluctuations is to enhance the growth length i.e. to make the growth weaier. We next consider convective parametric amplification in a weakly inhomogeneous medium with random density fluctuations superimposed on it. The fourth order differential equation in position space is now Fourier transformed into a second order differential equation in k space. An expression for the convective amplification factor correct to order |ε2| is obtained for the case of long wavelength turbulence and shows that it is unaltered by the presence of background random density fluctuations.
