Temporal behavior of backscattering instabilities in a three-dimensional cylindrical hot spot: I. Standard decay regime

The space and time behavior of backscattering instabilities in a three-dimensional cylindrical hot spot of finite lifetime is computed analytically in the so-called standard decay (or weak coupling) regime. A uniform expression for the instantaneous backscattered power, valid for any time and any hot spot intensity in the standard decay regime, is proposed. It is shown that the finite transverse size of the hot spot leads to important diffraction effects that can significantly reduce the hot spot backscattered energy. The plasma is assumed to be homogeneous and the hot spot depletion is ignored. The coupled mode equations are solved in terms of fluctuating source terms corresponding to the noise from which the instability grows. Diffraction effects on the growth of the absolute instability inside a long lifetime hot spot is investigated.