The $\kappa$-cookbook: a novel generalizing approach to unify $\kappa$-like distributions for plasma particle modeling

Abstract

In the literature different so-called $\kappa$-distribution functions are discussed to fit and model the velocity (or energy) distributions of solar wind species, pickup ions or magnetospheric particles. Here we introduce a generalized (isotropic) $\kappa$-distribution as a "cookbook", which admits as special cases, or "recipes", all the other known versions of $\kappa$-models. A detailed analysis of the generalized distribution function is performed, providing general analytical expressions for the velocity moments, Debye length, and entropy, and pointing out a series of general requirements that plasma distribution functions should satisfy. From a contrasting analysis of the recipes found in the literature, we show that all of them lead to almost the same macroscopic parameters with a small standard deviation between them. However, one of these recipes called the regularized $\kappa$-distribution provides a functional alternative for macroscopic parameterization without any constraint for the power-law exponent $\kappa$.

20 pager, 9 Figures

References in corpus (3)

• Gibbsian theory of power law distributions
• Linear Dispersion Theory of Parallel Electromagnetic Modes for Regularized Kappa-Distributions
• Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example

Cited by in corpus (11)

• The electron acoustic waves in plasmas with two kappa-distributed electrons at the same temperatures and immobile ions
• Generalized anisotropic $\kappa$-cookbook: 2D fitting of Ulysses electron data
• Towards a realistic evaluation of transport coefficients in non-equilibrium space plasmas
• Temperature anisotropy instabilities of solar wind electrons with regularized Kappa-halos resolved with ALPS
• A dispersion function for the regularized kappa distribution function
• Collisional charging of dust particles by suprathermal plasmas. II -- Regularized Kappa distributions
• Olbertian partition function in scalar field theory
• Loading non-Maxwellian Velocity Distributions in Particle Simulations
• Electrostatic waves in astrophysical Druyvesteyn plasmas: I. Langmuir waves
• Revisiting the Ulysses electron data with a triple fit of velocity distributions
• Transport coefficients enhanced by suprathermal particles in nonequilibrium heliospheric plasmas