Gravitational collapse in dusty plasmas with mass distributions and neutral gas

Jeans and two-stream instabilities are revisited for mixtures of charged and neutral dust, and also for different species of charged dust. From the general dispersion law for different dust species, limiting cases of monodisperse or polydisperse but cold dust components are discussed, putting results from the literature in perspective. Dispersion laws and critical Jeans lengths are then derived for a mixture of two dust species, or of charged and neutral dust, the latter being of interest in interstellar dust clouds where not enough electrons are available to charge all the grains. Instabilities are considered for two counterstreaming dust beams of equal strength, showing how the Jeans and streaming instabilities are coupled in specific wave number domains. (C) 2000 American Institute of Physics. [S1070- 664X(00)02907-4].