Validity of models for Dreicer generation of runaway electrons in dynamic scenarios

Abstract

Runaway electron modelling efforts are motivated by the risk these energetic particles pose to large fusion devices. The sophisticated kinetic models can capture most features of the runaway electron generation but have high computational costs which can be avoided by using computationally cheaper reduced kinetic codes. In this paper, we compare the reduced kinetic and kinetic models to determine when the former solvers, based on analytical calculations assuming quasi-stationarity, can be used. The Dreicer generation rate is calculated by two different solvers in parallel in a workflow developed in the European Integrated Modelling framework, and this is complemented by calculations of a third code that is not yet integrated into the framework. Runaway Fluid, a reduced kinetic code, NORSE, a kinetic code using non-linear collision operator, and DREAM, a linearized Fokker-Planck solver, are used to investigate the effect of a dynamic change in the electric field for different plasma scenarios spanning across the whole tokamak-relevant range. We find that on time scales shorter than or comparable to the electron collision time at the critical velocity for runaway electron generation kinetic effects not captured by reduced kinetic models play an important role. This characteristic time scale is easy to calculate and can reliably be used to determine whether there is a need for kinetic modelling, or cheaper reduced kinetic codes are expected to deliver sufficiently accurate results. This criterion can be automated, and thus it can be of great benefit for the comprehensive self-consistent modelling frameworks that are attempting to simulate complex events such as tokamak start-up or disruptions.