Effects of electron inertia and finite-Larmor radius correction on Jeans instability of quantum plasma with the impact of cosmic pressure

Abstract

We present a theoretical investigation of the Jeans instability in quantum plasma, taking into consideration cosmic ray (CR) pressure and diffusion effects using a generalized magneto-hydrodynamic (MHD) model. Our analysis incorporates finite electron inertia, finite electrical resistivity, and finite Larmor radius (FLR) correction. By applying the normal mode technique, we derive a unique form of a generalized dispersion relation that describes the behavior of the system. We further discuss this dispersion relation under different limiting cases. Interestingly, we find that all considered parameters have distinct impacts on the growth rate of the system in various scenarios. Additionally, our exploration reveals that both CR-driven acoustic speed as well as quantum parameter influence the conditions for Jeans instability while the remaining parameters do not have any impact on it. Consequently, when combined with the quantum parameter, electron inertia and FLR correction act as stabilizing agents to suppress instability. This research sheds light on the intricate processes involved in structure formation in the universe, highlighting the significance of considering quantum corrections, electron inertia, and FLR to accurately model the dynamics and stability of cosmic plasma systems.