  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.

Plasma Physics;Space Physics