2004/10/22 by Victor Munoz, Vı́ctor Muñoz, Munoz, Victor
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Plasma Physics (physics.plasm-ph) #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.physics/0410204
12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France)
arxiv created 2004/10/22 · openalex publication_date 2004/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dispersion relation of longitudinal electrostatic oscillations in a relativistic plasma is studied in the context of the nonextensive statistics formalism proposed by Tsallis [C. Tsallis, J. Stat. Phys. \bf 52, 479 (1988)], where nonextensivity is characterized by a parameter q in Tsallis's entropy. q=1 corresponds to the usual Boltzmann-Gibbs, extensive statistics formalism. In the nonrelativistic regime, normalizability of the equilibrium distribution function implies that -1≤ q≤∞. We show that in the relativistic regime much tighter constraints must be satisfied, namely 0≤ q ≤ 1+ kB T/mc2, where kB is the Boltzmann constant, T is the temperature of the plasma, and m is the particle mass. Then we study longitudinal oscillations in a proton-electron plasma, assuming immobile protons, and electrons whose distribution function maximizes Tsallis's entropy. The dispersion relation of these oscillations is written in integral form for the long wavelength limit. Explicit expressions in terms of generalized hypergeometric functions can be found for all possibles values of q in the ultra-relativistic regime.