Plasma oscillations and spectral index in non-extensive statistics

E. Saberian and G. Livadiotis

Physica A: Statistical Mechanics and its Applications, 2022, vol. 593, issue C

Abstract: In this paper, we have discussed the dependency of the plasma oscillations on the numbers of degrees of freedom (dimensionality) involved in the spectral indices (q or κ) of non-extensive statistical mechanics. Generally, the spectral indices have an inherent dimensional dependency, which may be ignored when a reduced velocity distribution function (VDF) has been derived from the higher dimensional ones, e.g., when studying the longitudinal oscillations or the related topics. In such cases, if we ignore the equipartition of energy, the higher dimensional dependency of the original VDF may be still included in the spectral index of our solutions. On the other hand, in many studies of the plasma oscillations in non-extensive statistics, the ordinary formalism of canonical probability distribution (the old version) had been used instead of the escort probability distribution (the modern version). The escort formalism has some advantages, as opposed to the ordinary version, which may provide more appropriate solutions for the plasma oscillations. In this study, we have re-examined this problem by utilizing the modern version of kappa distribution formalism labeled with an invariant kappa index as of zero dimensionality spectral index, κ0, which is independent of the dimensionality, the degrees of freedom, or the numbers of particles. The related dispersion relation and Landau damping rate of plasma oscillations (Langmuir waves) have been analytically derived and studied by using the Vlasov–Poisson equations for the weakly damped modes. The physical and thermodynamics features of the problem have been considered in terms of the variation of the invariant spectral index κ0.

Keywords: Non-extensive statistical mechanics; Spectral index; Electrostatic waves & oscillations; Plasma kinetic theory; Vlasov model (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437122000346
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:593:y:2022:i:c:s0378437122000346

DOI: 10.1016/j.physa.2022.126909

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().