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

For various plasma applications the so-called (non-relativistic) $\kappa$-distribution is widely used to reproduce and interpret the suprathermal particle populations exhibiting a power-law distribution in velocity or energy. Despite its reputation the standard $\kappa$-distribution as a concept is still disputable, mainly due to the velocity moments $M_{l}$ which make possible a macroscopic characterization, but whose existence is restricted 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 of order $l=2$ (i.e., kinetic temperature) satisfied only for $\kappa > 3/2$. In order to resolve these critical limitations we introduce the regularized $\kappa$-distribution with non-diverging moments. For the evaluation of all velocity moments a general analytical expression is provided enabling a significant step towards a macroscopic (fluid-like) description of space plasmas, and, in general, any system of $\kappa$-distributed particles.