The grain charging and the dust acoustic wave instability

Abstract

The stability of the steady charging state of the assembly of dust grains in a plasma is analyzed using, besides the equations of continuity and momentum balance, also the equations of thermal energy balance with the grain charging terms for both the electron and ion species. The grain charging terms account for the energy exchange between the dust grains and the electron and ion fluids. The grains are taken to be immobile for the purpose of this analysis. Two limiting cases are analyzed: (i) f(≡4πndλD2a)≪1 and (ii) f≫1 (nd is the dust number density, λD plasma Debye length, and a, the grain radius). The steady grain charge state is found to be stable in the case f≪1, so that the steady state grain charge qo is unaffected. On the other hand, in the limit f≫1, the state is found to be unstable provided γq(≡qoe/aTe)<12 (Te−Ti)/Te (Te, Ti are electron and ion temperatures). A coherent charging of the dust grains results as a consequence of this instability until γq≈12 (Te−Ti)/Ti. Next, by letting the grain charges be mobile, so that the perturbation of dust number density is nonzero, we examine the stability of the dust-acoustic wave (DAW). The DAW is found to be unstable, also in the f≫1 case, while stable in the f≪1. The instability of the DAW also implies a concomitant grain charge growth, which would again be of a coherent nature.