Ion Polytropic Coefficient in Bounded Plasmas With Cairns–Tsallis Distributed Electrons

The Cairns–Tsallis (CT) distribution function is employed to model the quasi-neutral region of a basic bounded-plasma system, such as the one described by Tonks and Langmuir (TL). Electrons are assumed to follow the CT distribution, while ions are generated through electron-impact ionization of cold neutral atoms. Under the plasma approximation, the ion velocity distribution function is derived, and fluid moments are taken to evaluate the ion density, temperature, and polytropic coefficient. The results indicate that the ion polytropic coefficient is strongly dependent on the electron nonextensivity ($q$) and nonthermality ($\alpha$) parameters inherent to the CT distribution. Specifically, an increase in electron nonextensivity leads to a significant deviation in the polytropic index, emphasizing the role of nonthermal effects in plasma behavior. These findings reduce to the Maxwellian case under specific limits, thus, validating the model. The study highlights the relevance of the CT distribution in capturing a broader range of physical phenomena in bounded plasmas, potentially applicable to space and astrophysical plasma environments.