Ion-acoustic shock waves and chaotic motions in certain Thomas Fermi plasmas

This article investigates low-frequency ion-acoustic shock waves and chaotic motion in a collisionless, unmagnetized Thomas–Fermi plasma comprising electrons obeying the Thomas–Fermi approximation and classical positively charged ions. A linear dispersion relation is derived and numerically analyzed, revealing that the real part of the angular frequency increases with ion temperature and is damped significantly by ion viscosity, while variations in ion temperature do not affect damping rates. In the nonlinear regime, a Kadomtsev–Petviashvili–Burgers (KPB)-type equation is derived using the reductive perturbation technique. The KPB model captures key nonlinear dynamics, including the effects of dispersion and viscosity, and yields shock profiles whose amplitude and width are strongly influenced by ion viscosity, thermal pressure, and obliqueness. Additionally, under the influence of external periodic forcing, the system exhibits rich dynamic transitions from periodic to quasiperiodic and ultimately chaotic behavior, as confirmed by two-dimensional phase portraits, time series plots, Poincaré sections, and Lyapunov exponents. These findings are consistent with recent studies of nonlinear and chaotic structures in quantum and dusty plasmas (Jia et al., 2025; Li et al., 2024; Zhao et al., 2024). This study offers valuable insights into the influence of plasma parameters on shock structures and dynamic behavior, with implications for astrophysical environments (e.g., planetary rings, white dwarfs, neutron stars, and magnetars) and laboratory conditions (e.g., laser-produced and inertial confinement fusion plasmas).