Efficient calculation of the moments of runaway electron distribution functions

Abstract

Plasma current instabilities can destabilize the plasma discharge and cool the plasma rapidly. In such $\textit{disruptions}$ or in the start-up phase of the reactor, inductive electric fields are generated which accelerate electrons to relativistic velocities, resulting in a beam of $\textit{runaway electrons}$. This can potentially damage the reactor vessel and must be avoided in future reactors such as ITER. Thus, the efficient simulation of the evolution of the runaway electron current is motivated for prediction, avoidance and attenuation of disruptions. In order to improve simulations based on a self-consistent calculation of the runaway electron current, the efficient computation of the moments of analytical runaway electron distribution functions is of interest. In this respect, the general procedure is carried out through the example of the distribution function of the $\textit{avalanche}$ generation of runaway electrons according to $\textit{F\"ul\"op et al.}$. At this the runaway electron number density, the current density and the mean mass-related kinetic energy density, which result from the zeroth, first and second moment are considered. Their analysis is carried out analytically and numerically. By means of a ${\rm M{\small ATLAB}}$ implementation, suitable calculation rules are derived and analyzed with regard to runtime efficiency. Finally, a physical evaluation of the components and the magnitude of the current density vector as well as the kinetic energy density for the plasma parameter space constructed from electric field, electron density and electron temperature is carried out, applying the derived efficient calculation rules. In addition, the applicability of the selected distribution function is discussed on the basis of graphical depictions of the results.