Parametric decay of wide band Langmuir wave spectra

Previous results obtained for modulational instability of a Langmuir wave spectrum are extended to account also for the Langmuir wave decay. The general model is tested by considering first the parametric decay of single-mode Langmuir waves, and also two-wave models, where several combinations are considered: one wave is modulationally unstable, another decay unstable and one where both waves are unstable with respect to decay. For the general case with continuous wave spectra it is found that distribution of the Langmuir wave energy over a wide wavenumber band reduces the decay rate when the correlation length for the spectrum becomes comparable to the wavelength of the most unstable sound wave among the possible decay products.