Extended temporal coarse-graining in a stratified and confined plasma under thermal fluctuations

Abstract: We present an extended investigation of a recently introduced model of gravitationally confined, collisionless plasma (Barbieri et al. 2024a), which showed that rapid temperature fluctuations at the base of the plasma, occurring on timescales much shorter than the electron crossing time, can drive the system into a non-thermal state characterized by anti-correlated temperature and density profiles, commonly referred to as temperature inversion. To describe this phenomenon, a temporal coarse-graining formalism was developed (Barbieri et al. 2024b). In this work, we generalize that approach to cover regimes where the timescales of temperature fluctuations are comparable to or exceed the electron crossing time. We derive a set of kinetic equations that incorporate an additional term arising from the coarse-graining procedure, which was not present in the earlier formulation. Through numerical simulations, we analyze the plasma dynamics under these broader conditions, showing that the electric field influences the system when fluctuation timescales approach the electron crossing time. However, for timescales much larger than the proton crossing time, the electric field becomes negligible. The observed behaviours are interpreted within the framework of the extended temporal coarse-graining theory, and we identify the regimes and conditions in which temperature inversion persists.