On the applicability of $\kappa$-distributions

Abstract

The standard (non-relativistic) $\kappa$-distribution is widely used to fit data and to describe macroscopic thermodynamical behavior, e.g.\ the pressure (temperature) as the second moment of the distribution function. By contrast to a Maxwellian distribution, for small relevant values $\kappa <2$ there exists a significant, but unphysical contribution to the pressure from unrealistic, superluminal particles with speeds exceeding the speed of light. Similar concerns exist for the entropy. We demonstrate here that by using the recently introduced regularized $\kappa$-distribution one can avoid such unphysical behaviour.

arXiv comment8 pages, 4 Figures

References in corpus (10)

• Kappa distributions: theory and applications in space plasmas
• The effects of a kappa-distribution in the heliosheath on the global heliosphere and ENA flux at 1 AU
• On the normalised FRB luminosity function
• A Hitch-hiker's Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics
• On the interpretation and applicability of $\kappa$-distributions
• Electron Power-Law Spectra in Solar and Space Plasmas
• The space-fractional diffusion-advection equation: Analytical solutions and critical assessment of numerical solutions
• Modeling space plasma dynamics with anisotropic Kappa distributions
• On the entropy of plasmas described with regularized $\kappa$-distributions
• Ultrarelativistic generalized Lorentzian thermodynamics and the differential cosmic ray energy flux

Cited by in corpus (7)

• Linear Dispersion Theory of Parallel Electromagnetic Modes for Regularized Kappa-Distributions
• The $\kappa$-cookbook: a novel generalizing approach to unify $\kappa$-like distributions for plasma particle modeling
• Generalized anisotropic $\kappa$-cookbook: 2D fitting of Ulysses electron data
• Relativistic regularized kappa distributions
• Towards a realistic evaluation of transport coefficients in non-equilibrium space plasmas
• A dispersion function for the regularized kappa distribution function
• Heat-flux Instabilities of Regularized Kappa Distributed Strahl Electrons Resolved with ALPS