The Effects of the Dust Size Distribution and the Dust Charging on Shock Waves in Dusty Plasma

By using the reductive perturbation method, the existence of dust acoustic shock waves is given for a dusty plasma considering the dust size distribution. The effects of both the dust size distribution and the dust charge variation on the characteristics of the shock wave are discussed. It is shown that the amplitude of a shock wave in plasmas considering a dust size distribution is larger than that in the case of a mono-sized dusty plasma, while its width considering the dust size distribution is smaller than that of the mono-sized dusty plasma. The speed of the shock waves also depends on different dust size distributions.