Instability due to the dust-particulate–phonon interaction

Interactions of dust particulates and phonons in a plasma are studied from a quantum mechanical viewpoint. An attraction between negatively charged dust particulates due to a stable wake potential behind a dust particulate in the supersonic ion flow is shown to be the result of exchanging phonons between the dust particulates. A collection of dust particulates becomes hydrodynamically unstable when the ion flow becomes subsonic. The growth rate of the instability is given by γ=0.87 (ωₚᵢ/2ωpd)1/3Ωₖ, where ωₚᵢ is the ion plasma frequency, ωpd is the dust plasma frequency, and Ωₖ is the dust acoustic frequency.