Effect of dust charge inhomogeneity on linear and nonlinear dust-acoustic wave propagation

Propagation of linear as well as nonlinear dust-acoustic waves (DAWs) in an inhomogeneous dusty plasma consisting of electrons, ions, and dust particles is investigated by taking into account equilibrium dust charge inhomogeneity along with the density inhomogeneity of the plasma and dust particles. For the linear case with harmonic perturbations, coupled equations for self-consistently determining the wave amplitude and the wave number have been derived. On the other hand, nonlinear DAWs are shown to be governed by a Korteweg-de Vries (KdV) type of evolution equation having variable coefficients arising due to charge and density inhomogeneities. Qualitatively, the amplitudes of the linear and nonlinear DAWs are found to decrease (increase) as the waves propagate into regions of increasing (decreasing) dust charge, which is similar to the behavior found in the case with density inhomogeneity alone. Quantitatively, the amplitude of the dust number density perturbation in the linear wave is proportional to q(d0)(-3/2) n(d0)(-1/2) for a cold dusty plasma, while in the nonlinear regime it scales as q(d0)(-1) n(d0)(-1/4). Approximate analytical solutions of the KdV equation have been obtained by making use of a suitable set of coordinate transformations. (C) 1999 American Institute of Physics. [S1070-664X(99)04808-9].