Gravitational collapse in dusty plasmas with mass distributions and neutral gas

Jeans and two-stream instabilities are revisited for mixtures of charged an d neutral dust, and also for different species of charged dust. From the ge neral dispersion law for different dust species, limiting cases of monodisp erse or polydisperse but cold dust components are discussed, putting result s from the literature in perspective. Dispersion laws and critical Jeans le ngths 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 whe re not enough electrons are available to charge all the grains. Instabiliti es are considered for two counterstreaming dust beams of equal strength, sh owing how the Jeans and streaming instabilities are coupled in specific wav e number domains. (C) 2000 American Institute of Physics. [S1070- 664X(00)0 2907-4].