Relativistic runaway electrons are a major concern in tokamaks. Albeit significant theoretical development had been undertaken in the recent decades, we still miss a self-consistent simulator that could simultaneously capture all aspects of this phenomenon. The European framework for Integrated Modelling (EU-IM), facilitates the integration of different plasma simulation tools by providing a standard data structure for communication that enables relatively easy integration of different physics codes. A three-level modelling approach was adopted for runaway electron simulations within the EU-IM. Recently, a number of runaway electron modelling modules have been integrated into this framework. The first level of modelling (Runaway Indicator) is limited to the indication if runaway electron generation is possible or likely. The second level (Runaway Fluid) adopts an approach similar to e.g. the GO code, using analytical formulas to estimate changes in the runaway electron current density. The third level is based on the solution of the electron kinetics. One such code is LUKE that can handle the toroidicity-induced effects by solving the bounce-averaged Fokker-Planck equation. Another approach is used in NORSE, which features a fully nonlinear collision operator that makes it capable of simulating major changes in the electron distribution, for example slide-away. Both codes handle the effect of radiation on the runaway distribution. These runaway-electron modelling codes are in different stages of integration into the EU-IM infrastructure, and into the European Transport Simulator (ETS), which is a fully capable modular 1.5D core transport simulator. ETS with Runaway Fluid was benchmarked to the GO code implementing similar physics. Coherent integration of kinetic solvers requires more effort on the coupling, especially regarding the definition of the boundary between runaway and thermal populations, and on consistent calculation of resistivity. Some of these issues are discussed.
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. This paper compares 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–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.
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