Modified Jeans Instability for Dust Grains in a Plasma

An investigation of the properties of linear stability is conducted for a system consisting of particles having mass $m$ and charge $q$, interacting through the gravitational and electrostatic force (Jeans instability). However, in light of recent works showing that dust particles in a plasma can have a Lennard-Jones-like shielding potential, a new set of equations has been derived, where the electrostatic interaction among the dust particles is Lennard-Jones-like instead of Coulomb-like. A new condition for the gravitational instability is derived, showing a broader spectrum of unstable modes with faster growth rates.