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-dime nsional cylindrical hot spot of finite lifetime is computed analytically in the so-called standard decay (or weak coupling) regime. A uniform expressi on for the instantaneous backscattered power, valid for any time and any ho t spot intensity in the standard decay regime, is proposed. It is shown tha t the finite transverse size of the hot spot leads to important diffraction effects that can significantly reduce the hot spot backscattered energy. T he plasma is assumed to be homogeneous and the hot spot depletion is ignore d. The coupled mode equations are solved in terms of fluctuating source ter ms corresponding to the noise from which the instability grows. Diffraction effects on the growth of the absolute instability inside a long lifetime h ot spot is investigated. (C) 1999 American Institute of Physics. [S1070-664 X(99)02709-3].