Effect of nonadiabaticity of dust charge variation on dust acoustic waves: Generation of dust acoustic shock waves

The effect of nonadiabaticity of dust charge variation arising due to small nonzero values of τ_ch/τ_d has been studied where τ_ch and τ_d are the dust charging and dust hydrodynamical time scales on the nonlinear propagation of dust acoustic waves. Analytical investigation shows that the propagation of a small amplitude wave is governed by a Korteweg-de Vries (KdV) Burger equation. Notwithstanding the soliton decay, the ``soliton mass'' is conserved, but the dissipative term leads to the development of a noise tail. Nonadiabaticity generated dissipative effect causes the generation of a dust acoustic shock wave having oscillatory behavior on the downstream side. Numerical investigations reveal that the propagation of a large amplitude dust acoustic shock wave with dust density enhancement may occur only for Mach numbers lying between a minimum and a maximum value whose dependence on the dusty plasma parameters is presented.