Linear and nonlinear theory of resonant drag instabilities in laboratory and astrophysical dusty plasmas

Resonant drag instabilities (RDIs) are produced by the interaction of streaming dust with waves in a background fluid when the dust velocity exceeds the phase velocity of a wave in the fluid. They have been proposed to drive pattern formation and turbulence in various astrophysical environments. We present insights connecting RDIs to other dusty plasma instabilities, and results characterizing the nonlinear saturation of RDIs. The linear RDI has been described by splitting of eigenvalues of the linearized dust/fluid system. Here, this framework is applied to other dusty plasma instabilities in experiment and astrophysics. This common mechanism motivates comparison of regimes of relevance, finding substantial overlap and suggesting laboratory study of astrophysical phenomena. RDIs saturate nonlinearly in an anisotropic turbulent state. Simulation of the acoustic RDI is used to elucidate the character of this turbulence. The saturation process is treated in terms of a balance between instability growth and turbulent turnover, resulting in a saturated state driven at an outer forcing range.