Shock waves in a dusty plasma

In the present paper, shocks in a dusty plasma are studied. A set of macroscopic shock equations are introduced in which the charge on the dust particles and the electrostatic potential in the dusty plasma have been taken into account. It is found that two shock modes may exist in a dusty plasma. One that is called the fast mode corresponds to an acoustic wave and the other, called the slow mode, corresponds to a dust-acoustic wave. The results show that the electrostatic energy of dust particles affects the shock speed and shock heating. The shock speed of the slow mode is found to be strongly dependent on the nondimensional dust density parameter p. In a tenuous dust plasma of p<<1 for the slow mode, the flow of energy as the shock heats is mainly converted into thermal energy of the dust particles; for the fast mode, the plasma heating may be reduced and partly transferred into an increase of the charge on the dust particles when they cross the shock.