Jeans instability in a degenerate electron-positron-ion and classical dusty plasma

We follow the quantum hydrodynamic model to study the newly suggested problem of Jeans instability in collisionless self-gravitating multicomponent, dense, astrophysical quantum plasmas. Here, the quantum effects appear through the quantum diffraction and Fermi pressure, whereas the quantum statistical effects are important only for degenerate electron-positron-ion and dust being the heaviest is treated as classical. We have obtained dispersion relations for three particular plasmas; every time, Fermi pressure is found to be numerically larger than the quantum diffraction term which tends to stabilize Jeans instability even more than the Madelung term. The Jeans critical wave number and the corresponding critical mass are defined for particular plasmas. We have displayed our results numerically and have shown that the gravitational instability of quantum electron-ion-dust plasmas and electron-positron-dust plasmas is achieved by increasing both the number density and mass of the dust grains. Moreover, the degeneracy quantum corrections effectively stabilizing the Jeans instability was focused. Published by AIP Publishing.