Modified Jeans Instability for Dusty Plasmas: Linear Theory

Abstract

Summary form only given. In the simplest case, a dust grain immersed in a plasma is negatively charged due to particle collection, owing to the fact that electrons are typically more mobile than ions and that electron emission from the grain is not taken into account. In this scenario, known as primary charging, the shielding potential is monotonic and well approximated by the Debye-Huckel potential when the grain radius is small compared to the linearized Debye length. However, the scenario described above changes significantly when other processes are taken into account, such as for instance electron emission from the grain, due to thermionic, photoelectric or secondary emission. In this case, Delzanno et al. showed that the shielding potential is no longer monotonic but can present an attractive potential well (reminiscent of the Lennard-Jones potential for the attraction among atoms). The presence of a potential well in the shielding potential has important consequences as it can lead to attractive forces on other grains even if they have the same sign of charge. Moreover, this mechanism can be particularly important for dust aggregation in astrophysical systems. In the astrophysical context, the simplest theory of aggregation of masses in space is the Jeans instability, where a uniform distribution of masses can collapse as a result of a perturbation with wavelength greater than the Jeans wavelength. In this study, we will present the kinetic theory of the modified Jeans instability, where particles interact through the gravitational and electrostatic forces. The latter, however, is not modeled with the Coulomb or Debye-Huckel potential but with the potential well discovered by G.L. Delzanno et al. (2004 and 2005). We will show how the Lennard-Jones like shielding potential can indeed exist for carbon dust grains which emit photoelectrons in response to a UV field. Furthermore, the well acts broadening the spectrum of gravitationally unstable modes and enhance their growth rates, even with respect to the pure gravitational case. On the other hand, a pure Debye-Huckel potential always acts to stabilize the system