On Modulational Instability of Turbulent Spectra

Abstract The character of the modulational instability of a Langmuir wave packet is usually assumed to be similar to that of the instability of a monochromatic pump Langmuir wave if the width of the packet is small when compared to the rate of the instability. This assumption has been confirmed only for the case corresponding to the “hydrodynamical” development of the modulational instability, i.e., for the case when the phase velocity of the modulational perturbations exceeds the ion thermal velocity. Here we consider the opposite case (when the phase velocity of the modulational perturbations is less than the ion thermal velocity) which corresponds to the “static” development of the instability. We demonstrate that the above assumption is valid for the situation considered.