Analytical calculation of the amplification and angular divergence of the stimulated backscattered light from a Gaussian hot spot

The problem of backscattering instabilities from a single laser hot spot is considered analytically in the frame of the paraxial approximation. An analytical calculation of the convective gain and of the far-field angular divergence of the backscattered light is presented for both homogeneous and inhomogeneous plasmas. It is shown that the far-field angular divergence is determined by the propagation of the backscattered light not only within the amplification region but also outside it, where the coupling is very weak. For homogeneous plasmas, the far-field angular divergence computed at the end of the interaction region is always less than what it would be if it were computed at the end of the amplification region. For inhomogeneous plasmas, both the power and the far-field angular divergence of the backscattered beam depend on the sign of the inhomogeneity gradient.