Dust-acoustic shock waves: Effect of plasma density gradient

Abstract

The propagation of dust-acoustic shock waves in an inhomogeneous collisional dusty plasma is studied, where the equilibrium plasma densities and dust charges are spatially nonuniform but the dust density is uniform. It is shown that, in such a plasma, the dust charge density can change continuously from tenuous to dense state. The effect of collisions of the dust with neutral gas causes the damping of the amplitude, while collisionless dissipation arising from nonadiabatic dust charge variation results in the formation of the shock structure. The amplitude is proportional to the square root of the phase velocity of the linear dust-acoustic wave but inversely proportional to the square root of the equilibrium dust charge number, both of them vary with spatial positions. Due to the inhomogeneity, the relationships among the amplitude, the Mach number, and the width (rise time) of the shock front do not follow the simple monotonic behavior as in the homogeneous cases.