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.

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• Kinetic theory
• Plasma thermodynamics
• Space & astrophysical plasma
• Space science
• Solar plasma
• Solar wind