Breakdown of hot-spot model in determining convective amplification in large homogeneous systems

The study of convective amplification in large homogeneous system, both analytically and numerically, in the case of a linear diffraction-free stochastic amplifier, was presented. It was shown that overall amplification does not result from successive amplifications in small scale high intensity hot spots (HS), but from a single amplification in a delocalized mode of the driver field spreading over the whole interaction length. The hot-spot approach was found to systematically underestimate the gain factor by more than 50%,. It was shown that the behavior of α_HS consists of four phases and the first three correspond to well-defined populations of realizations.