Excitation of dust acoustic waves by an ion beam in a plasma cylinder with negatively charged dust grains

An ion beam propagating through a plasma cylinder having negatively charged dust grains drives a low frequency electrostatic dust acoustic wave (DAW) to instability via Cerenkov interaction. The unstable wave frequencies and the growth rate increase with the relative density of negatively charged dust grains. The growth rate of the unstable mode scales to the one-third power of the beam density. The real part of the frequency of the unstable mode increases with the beam energy and scales to almost one-half power of the beam energy. The phase velocity, frequency, and wavelength results of the unstable mode are in compliance with the experimental observations.