Unified Description of Kappa-type velocity distributions

Abstract

An extension of Maxwell's original prescription for an ideal gas is adopted to derive a broad class of Kappa-type velocity distributions, encompassing both fat and short-tailed forms. Within this general framework, a physically consistent fat-tailed Kappa distribution is identified that accurately fits recent suprathermal data. In particular, a kinetic physical temperature $T$ emerges naturally from the model, eliminating the need to invoke an effective temperature $T_{\kappa \ell }$, as is commonly done in the literature. Finally, it is argued that only a particular value of $\ell$ ensures a satisfactory fit to the data when the physical kinetic temperature is employed.

6 pages, 1 figure and 5 tables. Accepted for publication in Physical Review E

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• Precision Electron Measurements in the Solar Wind at 1 au from NASA's Wind Spacecraft
• Tsallis meets Boltzmann: q-index for a finite ideal gas and its thermodynamic limit