Effect of the dust grain size-distribution on the nonlinear dispersion relation for parametric instabilities in dusty plasmas

Abstract

The nonlinear dispersion relation for parametric instabilities in dusty plasmas where the dust grain size distribution is taken into account, is addressed. The grains that are assumed spheres of different radii, are considered size-distributed according to power law, log-normal and normal distributions. The growth rate for the stimulated Brillouin scattering is deduced for each case.