Theory of dust-acoustic shocks

It is shown that after a sufficiently long propagation time, the nonlinear dust-acoustic waves appear as a stationary shock wave structure. The latter arises as a result of a balance between the nonlinear wave breaking and the dissipation of the wave energy due to the variation of the dust particle charges. The presented analytical theory shows that a necessary condition for the shock formation demands that the dust acoustic wave frequency ω is considerably smaller than the dust charging frequency ωq0. In this frequency regime, the shock wave propagation is described by the well-known Burgers equation. Furthermore, the breakdown of the analytical theory has been studied by solving the basic set of fluid equations numerically. The numerical solutions exhibit that shock waves may also occur for ω of the order of ωq0, viz in a wave frequency regime that is not covered by our analytical theory.