Shock structure formation in dusty plasmas

The problem of the evolution of a perturbation in a dusty plasma and its tr ansformation into a nonlinear wave structure is considered. A computational method that allows one to solve the set of nonlinear evolutionary equation s describing variable-change dust grains, Boltzmann electrons, and inertial ions is developed. Exact steady-state solutions corresponding to ion-acous tic shock structures associated with anomalous dissipation originating from dust grain charging are found taking into account the effect of electron a nd ion charge separation. The role of this effect increases with the speed of the shock. The evolutions of an initial soliton (which is a steady-state wave solution in a plasma containing dust grains with a constant charge) a nd an initially immobile perturbation with a constant increased ion density are investigated. In a charge-varying dusty plasma, the soliton evolves in to a nonsteady shock wave structure that propagates at a constant speed and whose amplitude decreases with time. The initially immobile perturbation w ith a constant increased ion density evolves into a shock structure similar to a steady-state shock wave. In the latter case, the compression shock wa ve is accompanied by a rarefaction region (dilatation wave), which finally leads to the destruction of the shock structure. The solution of the proble m of the evolution of a perturbation and its transformation into a shock wa ve in a charge-varying dusty plasma opens up the possibility of describing real phenomena (such as supernova explosions) and laboratory and active spa ce experiments. (C) 2001 MAIK "Nauka/Interperiodica ".