Ion acoustic shock waves in a collisional dusty plasma

Abstract

The effect of ion–dust collisions on small amplitude nonlinear dust ion acoustic waves has been investigated. Analytical investigation shows that propagation of the small amplitude wave is governed by Korteweg–de Vries (KdV) Burger equation. It is found that the coefficient of the Burger term is proportional to the ion viscosity, which arises through ion–dust collisions and depends on the temperatures and number densities of the electrons, ions and also on the number density of dust grains, as seen in a recent experiment (Nakamura et al.). Numerical investigations on the basis of that experimental data show that the dust–ion acoustic wave exhibits both oscillatory and monotonic shocks depending on the number density of dust particles, as observed in that experiment [Nakamura et al., Phys. Rev. Lett. 83, 1602 (1999)].