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For various plasma applications the so-called (non-relativistic)$\kappa$-distribution is widely used to reproduce and interpret thesuprathermal particle populations exhibiting a power-law distribution invelocity or energy. Despite its reputation the standard $\kappa$-distributionas a concept is still disputable, mainly due to the velocity moments $M_{l}$which make possible a macroscopic characterization, but whose existence isrestricted only to low orders $l < 2\kappa-1$. In fact, the definition of the$\kappa$-distribution itself is conditioned by the existence of the moment oforder $l=2$ (i.e., kinetic temperature) satisfied only for $\kappa > 3/2$. Inorder to resolve these critical limitations we introduce the regularized$\kappa$-distribution with non-diverging moments. For the evaluation of allvelocity moments a general analytical expression is provided enabling asignificant step towards a macroscopic (fluid-like) description of spaceplasmas, and, in general, any system of $\kappa$-distributed particles.

Regularized $\kappa$-distributions with non-diverging moments