Simulation of MHD instabilities with fluid runaway electron model in M3D-C ¹

Abstract

Runaway electrons may be generated in a tokamak during the start up, during normal operation and during a plasma disruption. During a disruption, runaway electrons can be accelerated to high energies, potentially damaging the first wall. To predict the consequences of runaway generation during a disruption, it is necessary to consider resonant interactions of runaways with the bulk plasma. Here we consider the interactions of runaways on low mode number tearing modes. We have developed a fluid runaway electron model for the 3D MHD code M3D-C1 (Jardin et al 2012 J. Comput. Sci. Discovery 6 014002). To benchmark, we have reproduced the MHD linear tearing mode results (with runaway electrons) in a circular cylinder presented in previous analytic studies (Helander et al 2007 Phys. Plasmas 14 104142) and have extended them here with a numerical eigenvalue calculation. We find that the low mode number tearing mode has a rotation caused by the MHD - runaways interaction and the perturbed toroidal current scale length is much smaller with runaways than without and decreases as the runaway speed increases.

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

“…While various applications of the model are on their way, some studies have already been performed. Similar approaches are followed by other codes, see e.g., references [167,[285][286][287].…”

Self-consistent simulation of resistive kink instabilities with runaway electrons

“…( 3)) needs to be solved for the fluid RE model. In the previous implementation used for linear MHD simulation in a 2D mesh including RE current [14], this equation was solved using the same numerical method as other MHD equations. First a sparse matrix is constructed by way of the θ-implicit method and the Galerkin method.…”

“…M3D-C1 has been used to study several phenomena related to tokamak disruptions, such as vertical displacement event (VDE) [21], generation of halo current [22], and thermal quench due to impurities injection [23]. Given the importance of REs in disruption studies, we have implemented a fluid model of REs in M3D-C1, by adding a new equation describing the evolution of RE density [14]. The RE current is calculated using RE density based on a simplified model of RE momentum distribution.…”

“…In the experiments, high-Z impurities are expelled via deuterium injection, which also lowers the plasma density [10]. The interaction between MHD instabilities and RE current has been studied before theoretically with both analytical theory and numerical simulations [11,12,13,14,15]. In the simulation, a fluid description of RE is used to simplify the calculation, in which RE current is calculated from RE density, and the feedback of RE current to MHD is included in the generalized Ohm's law of MHD equations.…”

“…In this paper, we present a new model for coupling RE in MHD simulations, and discuss its implementation in M3D-C1. This model is based on the fluid description of REs [14]. The convection part of the RE continuity equation is treated using the method of characteristics, which can help avoid numerical instabilities associated with the Courant-Friedrichs-Lewy (CFL) condition.…”