The Generalized Ion-sound Speed in Space and Astrophysical Plasmas

A generalized ion-sound speed for space and astrophysical plasmas in the regions of near- and far-from-thermal equilibrium is derived in the context of the new formulated invariant Kappa distribution. Inspired by the recent studies on the origin of polytropic behavior in space plasmas, it has been shown that the sound speed is connected to the extended polytropic index of Kappa distributed particles, which itself depends on the invariant Kappa index and the potential degrees of freedom. Generally, the ion-sound speed is a function of the polytropic index of Kappa distributed particles, which varies between two asymptotic regions of equilibrium and anti-equilibrium states. It is found that the ion-sound speed takes its maximum value in an equilibrium plasma and it reduces by approaching to the anti-equilibrium states. Furthermore, dispersion relation of the ion-acoustic waves in our formulism confirms, correspondingly, the recent study on the generalized formulation of Debye shielding in space plasmas. Finally, the classical and generalized relations between the ion-sound speed, the Debye length and the ion oscillation frequency have been discussed.