Calculation of the runaway electron current in tokamak disruptions

Abstract

$\textit{Tokamak disruptions}$ 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.