Effect of finite spectral width on the modulational instability of Langmuir waves

The effect of finite spectral width on the modulational instability of Langmuir waves has been investigated applying a method developed by Alber to derive a transport equation for the spectral density. The numerical results presented show that the spectrum is stable against modulational perturbation when the spectral width exceeds some critical value. For a Gaussian spectrum, the maximum growth rate is less than that for a monochromatic wave but the domain of modulational instability is extended. For a uniform distribution the shift in the growth rate curve towards the region of shorter wavelength is more pronounced and, for a certain range of spectral width, the maximum growth rate exceeds that for a monochromatic wave.