Nonlinear electrostatic modes in astrophysical plasmas with charged dust distributions

Context. Most theoretical investigations of wave phenomena in dusty plasmas have treated charged dust as additional heavy negative ions in standard multispecies models. Many dusty plasma experiments use monodisperse grains, but charged (and neutral) grains in space environments come in a whole range of sizes and compositions, hence in masses and charges. Dust density distributions having a power-law decay with size are often observed in planetary rings. Aims. There is a need to investigate larger solitary structures, since wave descriptions involving charged dust distributions have usually been limited to linear or weakly nonlinear modes. Methods. Sagdeev pseudopotential methods describe large-amplitude solitary waves in a co-moving reference frame and are adapted to include dust distributions, using mass and charge, or alternatively size, as additional variables. Observed power-law distributions lead to descriptions involving hypergeometric functions. Results. Lower limits for possible solitary wave velocities follow from requiring that the Sagdeev pseudopotentials have a local maximum for the undisturbed conditions, whereas upper limits come from ensuring that dust densities remain real. Nonlinear amplitudes increase with solitary wave velocities and relative electron temperature. Under similar plasma conditions, dust size distributions admit slower solitary wave solutions, with correspondingly smaller amplitudes than given by monodisperse dust models. For typical planetary ring conditions, the difference can be quite appreciable.