  $\textit{Tokamak disruptions}$ can give rise to the $\textit{runaway
phenomenon}$, which is typical in plasma physics and describes the almost
unbound acceleration of electrons to relativistic velocities and can lead to
the formation of a $\textit{runaway electron beam}$. In tokamak reactors like
ITER, impacts of such a beam can damage the reactor wall, motivating the
development of computationally efficient and accurate simulation methods for
the runaway electron current. In present simulation software, the
$\textit{reduced kinetic modeling}$ approach is used, which can be extended by
using physically relevant moments of analytical runaway electron distribution
functions. Because of this, calculation schemes for moments related to the
density, the mean velocity and the mean kinetic energy of runaway electrons are
deduced in this work and analysed with the help of ${\rm M{\small}{\small
ATLAB}}$-implementations. At that, the screening effects of partially ionized
impurities and different representations of the runaway electron generation
region in momentum space are taken into account. First, numerical calculation
rules for the primary $\textit{hot-tail}$ generation mechanism for isotropic
and anisotropic two-dimensional descriptions of the runaway region are stated.
They are then evaluated using the results of an ITER disruption simulation.
After that, calculation concepts for said moments, related to the secondary
$\textit{avalanche}$ generation mechanism, are derived. Different lower
momentum boundaries for the runaway region and the influence of the partial
screening of the nucleus by bound electrons are discussed on the basis of
results calculated for different density combinations of a singly ionized
deuterium-neon plasma. It is shown, that the analysed calculation schemes are
physically valid and allow for the rapid investigation of physical quantities
and parameter studies.
