Analytical results on the breakdown of the convective amplifier model caused by space-time random fluctuations

The space and time behavior of backscattering instabilities is computed analytically in the strongly damped regime and in the presence of space-time random fluctuations. The fluctuations are described by a Gaussian process with exponentially decaying correlation function. The breakdown of the strongly damped model of the instability is obtained as a divergence of the average amplitude and intensity of the backscattered light [H. A. Rose and D. F. DuBois, Phys. Rev. Lett. 72, 2883 (1994)]. The length and time it takes for this divergence to occur is analytically computed.